Experimental Studies on Market Design and e-trading

Transcription

1 Experimental Studies on Market Design and e-trading Candidate: MD Tarekul Hossain Khan Principal Supervisor: A/Prof Dongmo Zhang Co-Supervisor: Dr Zhuhan Jiang A thesis submitted for the degree of Master of Science at School of Computing and Mathematics University of Western Sydney May 09, 2012

2 Statement Of Authentication I hereby declare that this submission is my own work and, to the best of my knowledge, it contains no material previously published or written by any other person, nor material which has been accepted for the award of any other degree at the University of Western Sydney, or any other educational institution, except where due acknowledgement is made in the thesis. Date MD KHAN

3 Abstract In this project, we introduce an experimental approach to the design, analysis and implementation of electronic markets based on double auction. A double auction is a market mechanism allowing multiple buyers and sellers to buy and sell goods, commodities and services in a single market. We introduce a formal model of double auction, which specifies market policies such as matching policies, accepting policies, clearing policies, pricing policies and charging policies. Based on this model, we designed and implemented a set of market policies and tested them with different experimental settings. The most important market policies for a double auction market, accepting policies and matching policies, determine the market share and profit in most market situations. For matching policies, we first studied the properties of the equilibrium matching policy, which has been used in many double auction markets. Based on our analysis, we designed and implemented a new matching algorithm, named maximal matching, which can maximize market liquidity, including the number of transactions and buy/sell-volumes. We prove that, given the number of matches, our maximal matching algorithm also maximizes the auctioneer profit. For accepting policies, we formally define a number of typical accepting policies, such as always accepting, quote-beating accepting and equilibrium-beating accepting, and analyze their properties. We then introduce a new accepting policy, named dynamic accepting policy, which is able to filter out extra-marginal shouts by specifying a price range for the maximum ask bound and minimum bid bound. In addition, we briefly discuss clearing policies, pricing policies and charging policies. 3

4 4 Beside the formal discussion of market policies, we introduce a set of criteria for an experimental study on market design. By utilizing the Market Design Game platform JCAT for the Trading Agent Competition (TAC), we analyze our market model and identify how specific market policies influence overall market behaviour. Within the JCAT platform, we implemented our formally designed market model with the several market policies and performed a series of experiments, producing a range of experimental results. In particular, we found that matching policies and accepting policies significantly affect overall market performance. We also found that periodic clearing policy can increase the efficiency of the market more than continuous clearing policy. For charging policy, we explore a market share-based dynamic charging policy, and show that it can improve and stabilize market share as well as observably increasing profit share. We conclude that sudden and disproportionate fee charging activities have a long-term effect on trader migration, resulting in a quick loss of market share and market confidence. The results of our experiments provide a better understanding of the dependencies amongst market policies, and show that an experimental approach can greatly improve the efficiency and effectiveness of market design and e-trading study.

5 Acknowledgments First of all, I would like to thank my principal supervisor, A/Prof Dongmo Zhang, for all the opportunities, supports, understanding and academic advices he gave me over the years. I could not imagine how I could complete this thesis without his great supports as well as his patience. Most of the theories, approaches and results in this thesis were spawned from our discussions and joint work. I also thank my co-supervisor Dr Zhuhan Jiang for his valuable advices. A/Prof Dongmo Zhang is the leader of the jackaroo trading agent team and he is the main contributor of the jackaroo agent system for Market Design competitions, he trained me to build trading agents and develop new ideas and solutions for trading automation throughout my research study. I would like to thank the rest of my research colleagues in ISL for creating an educational, enjoyable, and challenging atmosphere. Meetings with members of the jackaroo teamledtothedevelopmentofmanynewideaspresentedinthisthesis. I would especially like to thank Dengji Zhao, who implemented a substantial portion of our software agent, and also his support and advices help me to clarify many problems. Also I would like to thank for team members Dr Masabumi Furuhata and A/Prof Laurent Perrussel for their great supports and friendship over the last few years. Many thanks for professional proofreading from Arwen at Syntactix. I am also grateful for suggestions and proofreading from my colleague Mr Gary Pitman at

6 uwsconnect ltd. I am especially grateful for the support of my wife Naima, my sister and my parents, I could not complete my thesis work without their supports, and to all my friends who inspired me in many ways.

7 Contents 1 Introduction Background and Motivation E-trading and e-marketplaces Auction mechanism and trading agents TAC Market design Trading automation Aims and significance Thesis contributions Thesis overview E-market model for Market design Introduction

8 8 CONTENTS 2.2 E-marketplace and Market Model E-markets Auction mechanisms Market Maker The Market Model Interaction in a Double Auction Market Trading Agents Traders Bidding Behaviour Zero-intelligence with constraint (ZI-C) Zero intelligence plus (ZIP) Roth and Erev s strategy (RE) Gjerstad-Dickhaut s strategy (GD) Trader s Market Selection Strategies Summary Market Policies Introduction Accepting Policies

9 CONTENTS Always Accepting Quote-beating Accepting Equilibrium-beating Accepting Dynamic Accepting Policy Matching Policies Equilibrium Matching Maximal Matching Clearing Policies Pricing Policies Charging Policies Summary Experimental Analysis of Market Policies Introduction Market Performance Indexes Basic Settings for Experiments Experimental Settings and Analysis Effects of Accepting Policies

10 10 CONTENTS Effects of Matching Policies Effects of Clearing Policies Testing Market Policies in a Dynamic Market Environment Summary Conclusion Summary of Contributions Future work Project Outcomes List of Tables 98 List of Figures 100 List of Algorithms 102 References 103

11 Chapter 1 Introduction Due to the rapid growth of the Internet and the World Wide Web (www), electronic trading (e-trading) has become an important platform for business owners and consumers to create new business opportunities. E-trading is performed in an e-marketplace, an electronic gathering place which accommodates multiple markets running under designed market rules. Within an e-marketplace, traders (buyers and sellers) can trade over the Internet via many different online trading mechanisms. These, provide opportunities to significantly improve the way business interact with traders. All trading performers now conduct business online, as this presents significant advantages in comparison to traditional methods [5, 17, 15]. A major step in e-marketplace development has been the automation of business activities. The continuing success of this development relies on the provision of cutting-edge functionalities with a variety of efficient trading mechanisms, in order to attract and retain multiple trading participants. Auctions have been used for many years as the major trading mechanism for finan- 1

12 2 CHAPTER 1. INTRODUCTION cial markets and electronic markets. The existing research concerned with auctions principally focuses on the theoretical aspects of market mechanisms, such as incentive comparability, profit optimization, price formation, and so on [2, 20, 25, 27]. From the implementation and market design point of view, it would benefit market owners, participants and policy makers to explore which institution and structure is most efficient, but theoretical or formal work has to date provided little guidance in specifying any established framework [12]. Most existing electronic markets run under relatively simple and fixed market mechanisms, while an electronic market with multiple market participants requires highly dynamic, efficient and reliable market mechanisms. In this thesis, we introduce an experimental approach to the design, analysis and implementation of market mechanisms from the e-marketplace development point of view. The design of a market mechanism involves the development of market policies and evaluation criteria. In this thesis, we specify a range of general market policies under certain trading structures, such as the double auction [11]. We formally represent a double auction market model, and investigate the properties of market mechanisms with different combinations of market policies. In this way, we demonstrate how we designed a variety of market mechanisms and tested them. In this chapter, we will briefly present some background knowledge and our motivation for this project.

13 1.1. BACKGROUND AND MOTIVATION Background and Motivation E-trading and e-marketplaces The term electronic trading generally denotes an advanced step in modern trading, in which the figures of buyers and sellers are replaced by electronic entities [22]. In general, e-trading is a method of trading goods such as securities (stocks and bonds), foreign currencies, and exchange-traded derivatives electronically. This kind of electronic trading platform has been initiated by way of the great advances of the Internet and information technology. The advancement of global communication networks has also provided a framework in which electronic trading can subsequently develop [39]. The continuing advancement of information technology and the Internet has allowed major market players to create extensive and sustainable competitive advantages. For the past few years, we have witnessed a rapid growth in electronic trading all over the world. For example, Australia s booming online market was worth $A26.86 billion in 2010, and is estimated to grow by more than 10% each year to be worth $A36.8 billion in 2013[33]. This indicates increasing demand for suitable and efficient e-trading mechanisms for e-marketplaces. An e-marketplace framework generally consists of a set of e-trading mechanisms providing the base from which market participants are able to coordinate their everyday transactions with their business partners. With the advancement of information technology, e-trading mechanisms efficiently deal with the activities of marketing and the procurement of commodities. The increase in e-trading has re-

14 4 CHAPTER 1. INTRODUCTION sulted in reduced transaction costs, improved liquidity, greater competition and increased transparency. However, an e-trading mechanism such as double auction is a complex market process in terms of the need to manage the interactions of multiple buyers, sellers and markets. To support this changing business environment, a system is required to cope with the mess of market participants, high dynamicity and increasing complexity of the e-trading process [17, 18, 45]. As e-trading transactions have grown in number and value, a number of challenges and unresolved issues have risen, such as the efficient design and implementation of dynamic market environments with robust e-trading mechanisms. This issue is one of the main concerns of this thesis Auction mechanism and trading agents The rules of an auction determine, on the basis of offers which have been made, the allocation of goods and money between traders. Well-designed auctions result in desirable economic outcomes. Auctions have been widely used for solving realworld resource allocation problems, and for structuring futures exchanges [11, 19, 26]. Auction mechanism design has drawn much attention in recent years from economists, mathematicians, and computer scientists. In traditional auction theory, auctions are viewed as games of incomplete information. Traditional theoretical and analytic methods from game theory have been successfully applied to some simple types of auctions. However, the assumption of prior common knowledge in the incomplete information approach may not hold in some auctions, and computing

15 1.1. BACKGROUND AND MOTIVATION 5 analytic solutions may be infeasible for others. For example, these problems exist in a double auction, in which both buyers and sellers are allowed to exchange offers simultaneously. Since double auctions allow dynamic pricing on both the supply and the demand side of the marketplace, studying them is of great importance, both to theoretical economists, and to those seeking to implement real-world market places [4]. As a result, researchers often use computer simulation of auctions, in which traders are software agents. These software agents exhibit at least three characteristics: autonomy, cooperation and learning from interaction environment [21]. Such agents are implemented via various learning algorithms and optimization techniques and have been shown to produce outcomes similar to those observed in auctions with human subjects [8]. Certainly, software agents outperform human traders [14]. With the development of automated trading agents, researchers have started to implement innovative and adaptive approaches to automatically creating auction mechanisms [6, 35, 37]. Although these approaches have produced promising results, they have one significant drawback: with the available platform the comparison are made by individual mechanism at a time, which is different from the real marketplace. Where in real market place market institutions are compete against each other using many mechanisms. From the experimental point of view, it is therefore desirable to have a platform allowing multiple markets to compete against each other, and allowing market mechanisms to be evaluated in a uniform way. Recently, organizations such as the Trading Agent Competition (TAC 1 ) have introduced a number 1

16 6 CHAPTER 1. INTRODUCTION of game platforms to evaluate market mechanisms for multiple market participants simultaneously. We adopted this platform for our market design experiments TAC Market design TAC has been successfully running a number of market simulations (TAC Classic, TAC SCM, TAC Market Design) 2, with research teams from all over the world participating in the competition. This platform provides a test-bed for researchers to share information and to experiment towards the development of an efficient electronic business process. The TAC Market Design game, a competition known as TAC-CAT, is a platform which concentrates particularly on designing market policies for trading mechanisms. The simulation platform for the CAT game is similar to the environment of the NYSE 3 markets environment. This market simulation is an extended work of JCAT 4, that support multiple parallel markets with trading agents moving between them. The CAT 5 market simulation has been successfully used as the game server for several years. A CAT game consists of a set of agents. Each of these is either a buyer, a seller, or a market maker. Each market maker operates and sets the rules for a single exchange market. In a double auction, buyers and sellers-collectively called traders-trade in one of the available markets. Buyers and sellers make offers to trade, known

17 1.1. BACKGROUND AND MOTIVATION 7 as shouts, and market makers identify a compatible match for trading. Traders strategies are designed in reference to the literature and the market policies are designed by the researchers [30]. A CAT game framework consists of a CAT server and several CAT clients, which are the trading agents or market makers. A CAT server work as the communication hub for all its clients. A registry component also records the history and events of the game to validate requests from clients. CAT simulation generates a number of game reports, with the output values for different measurements used for post-game analysis [3]. By using the CAT platform, researchers have the opportunity to experiment with various market policies and the characteristics of autonomous e-trading processes. The key area of the current project is experimental study of market design. To conduct market mechanism experiments, we needed a simulation platform which could produce various experimental results in order to analyze and identify the properties of various market policies, and how these policies could be used for the development of efficient trading mechanisms. The CAT platform was an ideal simulation platform for such experiments, as it provides the necessary structure to implement multiple market participants with various market and trading strategies. Within the platform, we could develop and modify market policies and trading strategies for various trading environments. We ran the experiments as per the experiment designs, and produced a series of experimental results in order to study the ways in which trading mechanisms interact in different market settings. In Chapter 4, we describe and present detailed results of the experiments using the CAT game platform.

18 8 CHAPTER 1. INTRODUCTION Trading automation The implementation and exploration of the concept of market design for autonomous trading agents can be viewed in the light of current academic and industrial research interests in the area, as follows [1, 14, 24, 15]: Invent more provable market models and automated interaction frameworks which are the most appropriate for automation of e-trading processes Invent innovative and efficient market specification and protocols Investigation and analysis of theories, e-marketplace components and trading agent behaviours Develop flexible and sophisticated multi-agent market simulation system to test e-trading strategies and market rules Promote technology standards to maximize the compatibility of different e- trading platforms The challenges of market design for e-trading, which we will discuss in the following chapters, are as follows: How to design an efficient market model and trading mechanisms for e-trading processes. How to specify market policies for dynamic multiple markets.

19 1.2. AIMS AND SIGNIFICANCE 9 How the market will decide which sell offer and buy offer to accept. Which sell offer will be matched with which buy offer. The price to set for each matched offer. When a market will clear a matched/unmatched offer. How the market will charge service fees to earn profits. Performance criteria to evaluate the efficiency of trading mechanisms. 1.2 Aims and significance Most of the present electronic marketplaces are based on the human interaction framework, having limited functionalities. This kind of inefficient prototype has the significant limitation of interoperability in e-trading processes. There have been a number of studies conducted [30, 24, 38, 49] of e-markets and online businesses in relation to the development and deployment of Multi-Agent system infrastructure, Auctions Mechanisms, Automated Negotiation theory and coalition framework. But no such established framework exists which can entirely support an automated market platform where the traders (buyers and sellers) can perform business autonomously and efficiently. Online auction mechanisms for e-trading represent a promising aspect of online business, but they are still far away from real marketplace implementation. There are

20 10 CHAPTER 1. INTRODUCTION no specific standard protocols or frameworks to establish practical e-trading markets which have both the dynamic negotiation ability and knowledge management functionality required for the context of multiple market interactions processes. Recently, researchers have been trying to establish an appropriate and feasible market mechanism, and a communication platform for e-trading which also addresses the complexity of different market policies and their implementation. This research aims to explore the idea of various market policies for e-trading which can satisfy market performance and, efficiency requirements, and allow market participants to interact in a dynamic trading environment. 1.3 Thesis contributions This thesis makes the following major contributions to the research on market design and e-trading: 1. Introduction of a formal model of market design with double auction for autonomous trading agents. 2. Introduction of four types of trading agent strategy and their behaviours. 3. Presentation of a formal representation of various market policies. 4. Introduction of an experimental approach to the design, analysis and implementation of electronic markets.

21 1.4. THESIS OVERVIEW Conducting a set of experiments in various market environments to test the overall market performance and examination of the effects of market policies. 6. Provision of a set of evaluation criteria for the market mechanism experiments, and the study of experimental results to implement an efficient trading mechanism. Jackaroo CAT team and the authors contribution We have built a software agent system named jackaroo. A team (led by A/Prof. Dongmo Zhang), representing the University of Western Sydney (UWS), which has participated in the International Trading Agent Competition (TAC) for the past four years. The agent was built on the economic model of TAC markets design, and initiated the approach of equilibrium analysis to strategic trading agents. Our jackaroo agent has achieved significant results in previous TAC games:in the year th, rd, st and nd places in TAC market design competition. As a team member of jackaroo, my contribution has included the design, data analysis, testing and refinement of market policies. 1.4 Thesis overview This thesis focuses on the analysis of the characteristics of e-trading and market design, together with discussion of optimal market policies and possible improvement of e-marketplace architecture. The thesis is structured as follows:

22 12 CHAPTER 1. INTRODUCTION Chapter 1 describes the background, motivation and significance of this research. Chapter 2 introduces the detailed specifications and requirements for the overall market model and the formal representation of market settings. We decompose the market model in to several components. Towards the end of this chapter, we also discuss the several types of autonomous trading agent strategy used in this research. Chapter 3 introduces several market policies. We design and implement a set of market policies with particular focus on accepting policies and matching policies. We also briefly discuss several other policies, such as clearing policies, pricing policies and charging policies. Chapter 4 we present several market indices to evaluate market performance. We present the experimental designs and results for double auction markets with autonomous trading agents and several market policies. Chapter 5 concludes this thesis with a summary of our contributions and a discussion of future research directions.

23 Chapter 2 E-market model for Market design 2.1 Introduction Mechanism design is a research area in the field of economics, initiated by Leonid Hurwicz in order to bridge the gap between theoretical processes and actual economic processes [16]. Mechanism design focuses on creating incentives and rules for strategic interactions so that the desired outcome or some desirable properties are achieved. In a market mechanism, the markets play the key role in binding market participants together and adjusting their benefits and demands. Market behaviours are determined by the mechanisms designed for the market. The study of market mechanism design has been one of the central research tasks of economics and finance for several decades [23, 28, 44]. In general, a market mechanism specifies a set of rules and actions which market participants can perform. 13

24 14 CHAPTER 2. E-MARKET MODEL FOR MARKET DESIGN Existing research in market design is principally focused on single market mechanism design [36, 34, 20, 28, 41]. The market design for multiple markets run electronically is much more complicated. The central challenge of market design for e-markets is satisfying a mechanism to achieve desired properties within a dynamic market situation. E-markets differ from traditional markets in several aspects. For example, the bonding between the traders (buyers and sellers) and the market owners in e- markets is mostly temporal, as a trader can enter or leave the market at any time without any obligation. The market owner often has poor information regarding the traders and other market participants. The legal restrictions usually used to regulate market behaviours in traditional markets are often difficult to apply in e- markets. Therefore, it is important to implement proper market mechanisms which can provide a suitable platform for online trading. Market design also requires diversification of efficient trading mechanisms as well as business strategies in order to meet the different needs of market participants. In this chapter, we provide an overview of an e-market model with market mechanisms from the market design point of view. We consider market situations in which the market owners (also called market makers in auction theory) interactions with both sellers and buyers are dynamic. The most typical example of such a mechanism is a double auction. By utilizing the platform of TAC market design, which we mentioned in Chapter 1, we will explore an experimental method of market design. We implemented a set of different market policies, such as accepting policies, matching policies, clearing policies, pricing policies and charging policies, and evaluated the market mechanisms.

25 2.2. E-MARKETPLACE AND MARKET MODEL E-marketplace and Market Model E-markets An e-market is a virtual market environment where transactions are made electronically. It has two key components: the market makers 1 and the traders. A trader (buyer or seller) performs trading with an available market in the marketplace, which is run by a market maker. The market provides the mechanism whereby buyers and sellers are able to exchange any type of information and perform trade. In an e-marketplace, each market is run under a set of rules and strategies [46]. The buyers and sellers interact with the market through a trading mechanism. In the following sections, we will present the structure of a trading mechanism, and describe how to design such a trading mechanism Auction mechanisms Auction is a general term for a specific type of trading mechanism, whereby trading is accomplished via a bidding process. Auction is the most popular protocol for interaction for exchanging goods between market participants. In an auction market, there are two main participants: the seller, who wants to sell goods, and the bidder, who wants to buy goods. For a trading mechanism, one of the key rules is designing the trader and market interaction and the exchange mechanism. The general stages of an auction market can be defined as follows [10]: 1

26 16 CHAPTER 2. E-MARKET MODEL FOR MARKET DESIGN Registration phase: a trader will register with the market/auctioneer. Bidding phase: a trader will submit the bid according to the auction rules set by the markets. A submission of bids also indicates the trader is willing to buy or sell an item. Validation phase: the market will check whether the bid is valid according to the rules and will update to the bidding stack. Price quoting phase: defines the status of an offer-whether the offer is rejected or accepted by the auctioneer. A bid offer should be the highest price over ask offer. The bidder may be willing to offer a higher price than the current price to obtain specific goods. An ask offer should be the lowest offer over a bid offer and the seller may be willing to offer a lower price than the current ask offer to sell the goods. Transaction phase: all asks and bids are organized to determine possible matching pairs and set the transaction price to clear the market. Traditionally, there are two basic types of auction markets: single-sided and doublesided. In single-sided auctions, either the buyer or the seller submits their preferred price. In double-sided, buyers and sellers can both submit their preferred prices. This type of double-sided auction is also known as a double auction, which is one of the most widely used auction mechanisms. Double auction mechanisms have been studied from theoretical, practical, and experimental points of view [2, 11, 40]. Double auction protocols are differentiated by Continuous Double Auction (CDA)

27 2.2. E-MARKETPLACE AND MARKET MODEL 17 and Clearing House (CH), known as call market [11, 42]. A CDA based market is a continuously clearing market. Typically, market clearing take place as soon as prices are matched. A CH or call market is a periodically clearing market, where the market clears following a time interval. In this thesis, we focus on the market mechanisms for double auctions combining CDA and CH protocols Market Maker A market maker or auctioneer is the representative of the market institution under consideration. A market maker is responsible for all the phases involved in a trading process within a specified market. The market maker quotes both a buy and a sell price from the incoming ask orders (sell orders) and bid orders (buy orders) submitted by the sellers and buyers. The market maker finds feasible pairs and executes the orders according to certain market policies defined in the following section The Market Model The market model specifies the details of the mechanism and the roles of each market participant. In the experimental context, we designed a market based on double auction. We implemented the market model suited to autonomous trading agents with the automated market maker. The key component of the model is the structure of trading mechanism with the specification of market rules or policies

28 18 CHAPTER 2. E-MARKET MODEL FOR MARKET DESIGN within the market mechanism. A combination of these market policies work as a market mechanism. A market institution consists of several market policies/rules, and each institution operates its own exchange market. The policies are represented as follows: Accepting policy: definition of the rules for validating incoming shouts and the conditions for accepting incoming orders. Matching policy: definition of how a market matches asks and bids made by traders at a given time. Clearing policy: definition of the clearing conditions for the market, which is the timing of market clearing state. Pricing policy: definition of the transaction pricing for a matched ask and bid to clear the market. Charging policy: definition of the way the market sets the fees for the traders. Fees can be set for registration, information, shouts, transactions and profit. Let us describe a market mechanism as demonstrated in Figure 2.1. Each seller and buyer is an autonomous trading agent. For the market institution, each seller and buyer submits an ask order and a bid order, respectively. Each order has a limit price, which is the least preferable price for the trader. This type of order is called a limit order. The market institution implements the policy for accepting the incoming orders, matching the accepted orders and determines transaction prices

29 2.2. E-MARKETPLACE AND MARKET MODEL 19 for the matched orders. These orders are then executed and the traders notified. The market institution can also charge fees to the traders according to the charging policy. Figure 2.1: The market model In Figure 2.1, we formally represent a double auction market mechanism. This model defines the roles of the market participants and also represents the control flow and order flow of the market institution. The market model represents the general trading process for a market from the arrival of an order to the execution of an order. As per the model, there are six traders (three sellers and three buyers) registered with the market. Each of the traders submit an order to the market

30 20 CHAPTER 2. E-MARKET MODEL FOR MARKET DESIGN institution. According to the accepting policy, the market only accepts five out of six orders. Once the orders are accepted, the market institution performs the matching according to the matching policy, where the market is only able to match four out of five accepted orders. Once the orders are matched, the pricing policy determines the transaction price, followed by clearing the matched orders according to the specified clearing policy. Charging policy is implemented at any point during the trading process in order to obtain profits from the exchange. In the following section, we formally present market preliminaries, and describe the market policies as well as the interaction processes between the traders and market makers. We consider a double auction market, where multiple buyers and sellers buy and sell homogeneous goods or a commodity. Let T = I J be a set of traders. I is the set of sellers and J is the set of buyers. We assume that I J = Ø. 2 A trader t T can submit a shout to the market maker having a fixed valuation denoted as v t. Definition 2.1. A shout consists of two components (t,p), where t T and the price p 0. For a shout s, we refer p(s) to the price of s. Definition 2.2. An ask is a shout (t,p), where t is a seller, i.e., t I. A bid is a shout (t,p), where t is a buyer, i.e., t J. For any set S of shouts, let S ask = {(t,p) S : t I} and S bid = {(t,p) S : t J}. Definition 2.3. An accepting policy is a function A : S {1,0}, which assigns 2 In practice, a trader can be a seller and a buyer for the same commodity. In this case, we have modelled two different roles, as decision-making for selling and buying is different

31 2.2. E-MARKETPLACE AND MARKET MODEL 21 incoming shout s S a value either 1(accept) or 0(reject). Let A = {s S : A(s) = 1} be the set of all shouts accepted under the accepting policy A. We denote accepted ask as A(S ask ) = {s S : s ask&a(s) = 1} and accepted bid as A(S bid ) = {s S : s bid&a(s) = 1}. Definition 2.4. Given a set of shouts S, a matching of S, denoted by M(S), is a collection of pairs (x 1,y 1 ),(x 2,y 2 ),..., where x i S ask, and y i S bid. For any (x 1,y 1 )&(x 2,y 2 ) M(S), x 1 = x 2 if and only if y 1 = y 2. Definition 2.5. Let T be the set of time points of a trading period. Given a set of matched shouts M(S), a clearing policy is a function C : T M(S) {1,0}, such that for any t T and (x,y) M(S), if C( t,(x,y)) = 1 then C( t 1,(x,y)) = 1 for all t 1 T such that t > t 1. This means that matched pair can only be cleared once. When the matched orders are cleared from the market, the market maker determines a clearing price, based on pricing policies defined as follows: Definition 2.6. Given a set of shouts S, a pricing policy P, is a function that assigns a positive real number (the clearing price) to a pair of matched ask orders and bid orders such that for any (x,y) M(S), p(x) P(x,y) p(y) Interaction in a Double Auction Market In a double auction market, traders (buyers and sellers) engage in an interaction process with the market. A trader-market interaction process passes through all

32 22 CHAPTER 2. E-MARKET MODEL FOR MARKET DESIGN the auction phases discussed in Section A trader-market interaction process starts with the registration of buyers and sellers to an available market. During a trading period, the sellers and buyers submit ask orders (sell orders) and bid orders (buy orders) to the market of the marketplace, respectively. The market maker finds feasible pairs from these incoming orders according to certain market policies, such as accepting policies, matching policies, clearing policies and pricing policies, as defined in Section Figure 2.2 is the UML representation of the interaction between traders and the market maker. A trader submits a shout (ask order and bid order) to his registered market. Each shout is dependent on each of the trader s limit prices or on their private values. If the market maker accepts the order, then the shout is a valid incoming shout. Traders can update the active shout price and re-submit to the market. If the new shout is a valid, then the new price will replace the previous price. Otherwise, the previous price will be retained as an active shout. If any shout is rejected by the market maker, a trader can update the price and re-submit until the shout becomes a valid order. Once the shout is accepted, all active shouts will wait for clearing by the market. This is done through selecting a suitable matching pair and then executing the order by setting a transaction price.

33 2.2. E-MARKETPLACE AND MARKET MODEL 23 Figure 2.2: Trader - Market interaction

34 24 CHAPTER 2. E-MARKET MODEL FOR MARKET DESIGN 2.3 Trading Agents A trader can be either a buyer or seller. Each trader is associated with a trading/bidding strategy and a market selection strategy. The trading strategy specifies how to make offers, and the market selection strategy specifies which market to choose to make an offer. Each trading agent is assigned private values for the goods it will trade. For buyers, the private value is the most it will pay for a good. For sellers, the private value is the least it will accept for a good. The private values and the number of goods to buy or sell make up the demand and supply of the markets [29]. Actions of each trader are as follows: Price set: the determination of a limit price (the least preferable price and the private value). Order submission: the submission and control of feasible orders to market institutions. Price update: the updating of price during negotiation between market makers Traders Bidding Behaviour In this section, we will introduce four automated bidding strategies which have been implemented in CAT platform: Gjerstad-Dickhaut(GD), zero-intelligence with constraint (ZI-C), zero intelligence plus (ZIP), and Roth and Erev (RE). These

35 2.3. TRADING AGENTS 25 strategies will be used in our experiments. These four bidding strategies use a similar structure to determine limit price according to calculated valuations and mark-ups (margins). Assuming that traders set limit prices depending on their valuation, the market maker determines the market price which satisfies the limit prices. Let v t be an valuation of a item by trader t and sets the limit price for order s t according to its valuations and mark-up denote as ζ t, v t +ζ t P(s t ) = v t ζ t if t I otherwise Zero-intelligence with constraint (ZI-C) ZI-C strategy was proposed by Gode and Sunder [14], and chooses a mark-up randomly drawn from a uniform distribution over a given range. The ZI-C traders are subject to budget constraints, and are not allowed to trade at loss. The ZI-C buyer draws a bid from a uniform distribution between the minimum allowed bid and its limit price. Similarly, the ZI-C seller forms an ask from a value drawn from a uniform distribution between its cost price and maximum allowed ask price. There will be no transaction for the ZI-C trader beyond the minimum allowed bid price and the maximum allowed ask price. If a ZI-C buyer has a reserve price $90 with a constraint for maximum bidding range $20, this buyer can bid up to $110. Similarly a ZI-C seller with a reserve price $90 can ask minimum $70.

36 26 CHAPTER 2. E-MARKET MODEL FOR MARKET DESIGN Zero intelligence plus (ZIP) The Zero-Intelligence Plus (ZIP) strategy is a learning-based bidding strategy designed by Cliff and Bruten [6, 7]. The ZIP strategy is reactive to market information in order to be competitive in the market. If p(s) denotes the price of an order s, and v is the valuation price, then seller i should quote p(s i ) v i and buyer j should quote p(s j ) v j. The difference between p(s) and v is refereed to as the trader s profit margin. The ZIP traders adjust their profit margin, on the basis of the prices of bids and offers, whether or not these quotes are accepted or rejected. The following adaptive rules are adhered in order to adapt the profit margin to future market conditions: Adaptive rules for the ZIP seller: If (last shout was accepted at price p (s)) then 1. any seller i for which p(s i ) p (s) should raise its profit margin 2. if (last shout was a bid) then 1. any active seller i for which p(s i ) p (s) should lower its margin else if (last shout was an offer) then 1. any active seller i for which p(s i ) p (s) should lower its margin

37 2.3. TRADING AGENTS 27 Adaptive rules for the ZIP buyer: If (last shout was accepted at price p (s)) then 1. any buyer j for which p(s j ) p (s) should raise its profit margin 2. if (last shout was an offer) then 1. any active buyer j for which p(s j ) p (s) should lower its margin else if (last shout was a bid) then 1. any active buyer j for which p(s j ) p (s) should lower its margin The profit margin is modified by using the adaptive mechanism based on the Widrow-Hoff algorithm [47]. This is a learning mechanism which continuously adjusts the error between the current value and desired value. The ZIP strategy has a set of 8 different parameters for the buyer and the seller which determines how to increase or decrease the profit margin [7, 3] Roth and Erev s strategy (RE) Roth-Erev (RE) strategy is a bidding strategy based on the RE learning algorithm [9]. This is a reinforcement-learning algorithm, which relies only on the immediate feedbacks from the mechanism, in particular the surplus that the trader is able to

38 28 CHAPTER 2. E-MARKET MODEL FOR MARKET DESIGN gain from the most recent round of trading. In RE strategy, trader t at time t chooses its mark-up ζ t, which is randomly chosen from a discrete variable ranging [0,K], where K is the number of choices. The mark-up is updated according to a direct experience which consist of choice k [0, K], experiment parameter η, payoff of trader t at time t with choice k, and recency parameter ω. At time t, the probability of mark-up p(ζ t, t) is updated as follows p(ζ t, t) = RE t, t,k k RE t, t,k where RE t, t,k is a propensity function [9, 3] given as follows: RE t, t,k = τ t if t = 0 K (1 ω)re t, t 1,k + (η,r(t, t 1,k)) otherwise Initially, propensities are even with the scale parameter τ i. At time t > 0, the propensities are updated by the experience function (η,r(t, t 1,k)), while the previous propensities are succeeded at the weight 1 ω. The experience function consists of two factors, reflecting the direct feedback from the mechanism and including opportunities of other choices [3] Gjerstad-Dickhaut s strategy (GD) The GD bidding strategy, developed by Steven Gjerstad and John Dickhaut, uses past marketplace histories of submissions and transactions to generate beliefs to

39 2.3. TRADING AGENTS 29 indicate whether a particular shout is likely to be accepted in the market [13]. In GD strategy, buyers form beliefs that a bid will be accepted. Similarly, sellers form beliefs that an ask will be accepted. The traders form these beliefs on the basis of observed market data, particularly on the frequencies of submitted bids and asks, and the accepted bids and asks resulting in a transaction. Given this information, the bidding strategy is to submit the shout which maximizes the trader s expected surpluses. This is the product of a belief and utility functions [13, 3]. The GD model considers risk-neutral traders, whose utility function is linear. The profit of the traders can be calculated as the difference between the seller s ask price and cost price, and the difference between the buyer s bid price and limit price. When the trader s maximum expected surplus is negative, there is no incentive to submit a bid or an ask and the trader abstains from bidding [13, 3] Trader s Market Selection Strategies The goal of every trader is to maximise a utility function based on the demand and supply in the market. Each trader has a demand and supply function, a bidding strategy and a market selection strategy. Some strategies which a trader can adopt to select a market to trade in are as follows: The trader randomly picks a market The trader selects a market by using a learning component based on the trader s prior transaction experience in the market

40 30 CHAPTER 2. E-MARKET MODEL FOR MARKET DESIGN The trader selects the market as an n-armed bandit problem, solved using an ǫ-greedy exploration policy [43]. Unlike the greedy selection which chooses the best market only upon estimation of profits, ǫ-greedy selects the market estimated to be the best market with a probability of 1 - ǫ The trader uses the softmax [43] exploration strategy. When the best market is not selected, then better markets among the remaining markets are selected with a higher probability In market design experiments, traders use combinations of these market selection strategies to make the trading environment more dynamic and rational. 2.4 Summary In this chapter, we have presented the market mechanisms of e-markets. In order to investigate how market models can influence market behaviours, we introduced a market model based on a double auction. We represented this model with detailed information about the market mechanisms and its implementation. Our model comprised several fundamental market policies which we shall describe in the following chapter. We also presented four types of bidding strategies (GD, ZIP, ZI-C and RE) used by trading agents for experimental purposes.

41 Chapter 3 Market Policies 3.1 Introduction According to the structure of the double auction market model described in Chapter 2, the design of a market mechanism specifies each policy to be implemented in a market. In this chapter, we present the design and implementation of various market policies for double auction, such as matching policies, accepting policies, clearing policies, pricing policies and charging policies. We describe each of these market policies and how these policies influence market situations. We present some existing market policies and their properties. We then propose modified and extended work on these existing market policies. In particular, we focus on accepting policies and matching policies. These are the most important policies for double auction markets, as they determine the market share and profit in most market situ- 31

42 32 CHAPTER 3. MARKET POLICIES ations. We have designed an accepting policy named Dynamic accepting policy and a matching policy named Maximal matching. Afterwards, we also briefly describe clearing policies, pricing policies and charging policies and their implementations according to our market model. 3.2 Accepting Policies Accepting policies determine whether the shout made by a trader is permitted to enter the market. The goal of an accepting policy is to reduce shout price fluctuation in order to attract good traders and to prevent extra-marginal traders from placing shouts with very high ask prices or very low bid prices. A market maker can maximize the transaction rate by applying a suitable accepting policy. In this section, we will introduce a number of accepting policies and design their algorithms based on the formal definition of an accepting policy given in Definition 2.3 in Chapter Always Accepting Always Accepting (AA) is an accepting policy which accepts any submitted shouts at any price. Formally, the AA policy can be defined as: AA(s) = 1, for alls S

43 3.2. ACCEPTING POLICIES 33 Accepting policies significantly impact market efficiency. This policy also directly affects matching policy, as traders are allowed to submit shouts with no price restrictions. With the AA policy, the market maker has the potential to increase market share as well as the volume of accepted shouts for the market. Since there is no price bound for accepting shouts, the market receives many poor shouts (high ask prices, low bid prices). This will increase the unmatchable shouts; thus, the transaction rate will suffer significantly. This can in turn affect market confidence, with loss of market share. Figure 3.1, is an example of incoming shout (asks and bids) frequency in AA policy. From this figure, it can be seen that the accepted ask prices are very high, and the bids prices very low. This increases the number of unmatchable shouts and decreases the transaction rate. Therefore, in order to maximize the transaction rate, it is important to predict and filter the unmatchable extra-marginal shouts from the incoming shouts. (a) AA Asks (b) AA Bids (x-axis-days & y-axis-prices) Figure 3.1: (a)(b) Always Accepting

44 34 CHAPTER 3. MARKET POLICIES Quote-beating Accepting Quote-beating Accepting (QA) is a widely used accepting policy known as the New York Stock Exchange (NYSE) rule [32]. Under quote-beating accepting policy, a new shout is accepted by the market if the new shout exceeds the current best price among the unmatched shouts. Let s ask out and s bid out represent the current best unmatched ask order and bid order. QA policy can be defined as follows: 1, if s S ask &p(s) < p(s ask out ) or s S bid &p(s) > p(s bid out ); QA(s) = 0 otherwise. QA policy calculates the market price based on the current market situation and improves the shout price towards the equilibrium price. However, if the shout prices are highly dependent on randomness, the clearing price tends to be highly volatile. As Niu et al. indicate, quote-beating accepting policy frequently fails to reduce the fluctuation of the clearing price because current unmatched orders depend heavily on the randomness of individual orders [32, 31]. Particularly while the traders are mostly profit-seeking, shouts can be far from suitable in terms of price. Theoretically, it can take a long time for shouts to reach equilibrium. For example, if the sequence of incoming shouts, asks {100,85,75,70,...} and bids {10,20,25,30,...}, as shown in Figure 3.2, QA policy will be highly time consuming and inefficient in finding a matching pair.

45 3.2. ACCEPTING POLICIES 35 Figure 3.2: Incoming Sequence of Shouts In order to reduce price fluctuation, Niu et al. [32] have presented the Equilibriumbeating Accepting (EA) policy which successfully reduces price fluctuation for randomly priced shouting traders, particularly ZI-C traders introduced in chapter 2, Page Equilibrium-beating Accepting Equilibrium-beating Accepting (EA) calculates the market equilibrium price based on the history of transaction prices. Let n be the length of the history and p t be the average transaction price at time t. The equilibrium price Ê is Ê = t 0 +n t= t 0 p t n (3.1)

46 36 CHAPTER 3. MARKET POLICIES Ê is the average price of the average transaction prices in the past n time slots. The EA policy uses another component, delta, δ, which is the adjustment parameter defining the accepting range of market quotes. From a given adjustment parameter δ, and given Ê, we define the EA policy as follows: 1, if (s S ask &p(s) EA(s) = Ê +δ) or (s Sbid &p(s) Ê δ); 0 otherwise. Two boundary are set for asks and bids, labelled as ExpectedMaxAsk and ExpectedMinBid. The maximum ask price range is calculated by adding δ, with the equilibrium price and the minimum bid price range calculated by subtracting δ from the equilibrium price. The equations for the boundaries are as follows: ExpectedMaxAsk = Ê + δ ExpectedMinBid = Ê - δ From this, the asks and bids sets additional margins to meet the accepting criterion. Any asks below the maximum ask price range and closer to equilibrium price will be accepted into the market. Similarly, any bids above the minimum bid price range will be accepted into the market. For EA policy, the adjustment parameter (δ) is always fixed, and applies equally to both bid and ask. Figure 3.3, shows an example of an accepting price movement. In this figure, the middle line represents the market

47 3.2. ACCEPTING POLICIES 37 equilibrium price Ê, and the upper and lower lines represent the accepted maximum ask and minimum bid prices respectively. We set the δ to 8 so the price gap between the maximum ask and minimum bid is always equal. Figure 3.3: Price quote for EA accepting policy Whilethemarketneedstodealwithavarietyoftraders, thekeyissueismarketprice movement. A fixed δ value for asks and bids would be an inefficient solution for the market maker to adopt the price movement. For instance, if the market receives too many overqualified bids and under qualified asks in a round, assigning the fixed delta value approach may fail to identify the expected equilibrium market price quote. The market maker may specify an impractical range for accepting shouts which may reject too many good shouts which could be matched and allow too many bad shouts. The effect will be possible loss of market confidence and decreased transaction success rate. This will impact the overall market performance. Thus,

48 38 CHAPTER 3. MARKET POLICIES the key problem for EA policy is how to estimate the expected price movement in order to set the adjustment parameter δ appropriately Dynamic Accepting Policy Dynamic accepting (DA) policy addresses the problem inherent in EA policy described in Section We propose a DA policy which is capable of setting the boundary value dynamically according to market movement. This policy is applied in three stages: 1. Stage 1: Initially, the accepting policy of the market is open for all incoming shouts until a certain history length. 2. Stage 2: At policy enforce stage, the market obtains history data followed by setting the boundary values for accepting policy. 3. Stage 3: Finally set and adjustment stage market will adjust the parameters and boundary values with the changes of history information. In DA policy, boundaries are obtained from the history of transaction rates (r) and transaction volumes (v). These values are always changing, according to the actual market movement. We obtain transaction volumes (v) from the total number of transacted asks and bids from the history. Transaction rate (r) is obtained from the transacted and accepted history of asks and bids.

49 3.2. ACCEPTING POLICIES 39 Definition 3.1. Let T(S) represent the set of all the shouts in S that were transacted in the history. And A(S) represent the set of all the accepted shouts in S. Transaction volume and transaction rate are calculated as follows: v = T(S ask )+T(S bid ), r = T(Sask )+T(S bid ) A(S ask )+A(S bid ) (3.2) We denote the boundary value as δ. We calculate δ from the transaction history, based on transaction volumes (v) and transaction rates (r) as follows: δ = + k 1 v c 1 +k 2r c 2 (3.3) where k 1,k 2,c 1,c 2 0 are constant coefficient to adjust the value of v and r. is the dynamic coefficient for accepting price quote range, which is calculated from the market equilibrium price Ê presented in Equation 3.1, with the average ask and bid offers. We denote average ask offers as askquote and average bid offers as bidquote. We calculate as follows: = Ê askquote + Ê bidquote 2 (3.4) where askquote = s A(S ask ) p(s), bidquote = A(S ask ) s A(S bid ) p(s) A(S bid )

50 40 CHAPTER 3. MARKET POLICIES From Equation 3.3, if v c 1 is higher, boundary (δ) will be lower, and if v c 1 is lower, theboundarywill behigher. Also, ifk 2 r c 2 ishigher, theboundarywill behigherand if k 2 r c 2 is lower, the boundary will be lower. The boundary can adjust according to the transaction rate and transaction volume and tune the values dynamically from the transaction history by increasing or decreasing the price bound for accepting range. By using the boundary value (δ), we get the dynamic range for maximum ask and minimum bid from Ê ± δ Let us demonstrate how the process works by using a few examples. Example 3.1. Suppose the history gives the transaction volume as 20 and the transaction rate We then get Ê = 100, askquote = 107 and bidquote = 95. From Equation 3.4, we can get the value for price range as 6. If we set the coefficient parameters as k 1 = 1.5,k 2 = 1.5&c 1 = 0.2,c 2 = 0.2, then from Equation 3.3 we can obtain the boundary value δ = 8.2. Now we can get dynamic boundaries as: ExpectedMaxAsk = Ê + δ = ExpectedMinBid = Ê - δ = Example 3.2. If we get a higher transaction volume from the history, 60, and keep all the other values the same as in Example 3.1, then the boundary is 8.04, which is lower than the value in Example 3.1.

51 3.2. ACCEPTING POLICIES 41 Example 3.3. If we get higher transaction rate from the history, 0.95, and keep all the other values the same as Example 3.1, then the boundary is 8.31, which is higher than the previous value in Example 3.1. In Examples 3.1, 3.2 and 3.3, we show how transaction volumes and transaction rates will affect boundary. Implementation of Dynamic Accepting policy We shall describe the implementation of Dynamic Accepting policy in two parts. Algorithm calculates the boundary, and Algorithm checks the conditions for accepting shouts. Algorithm 3.2.1: DAboundary Input: A set, H, of shouts in the history Output: boundary 1 begin 2 v 0; 3 r 0; 4 askquote AverageAskP rice [Equation 3.3] ; 5 bidquote AverageBidP rice [Equation 3.3] ; 6 if H ask And H bid then 7 v T(H ask )+T(H bid ) ; 8 r ( T(H ask +H bid ) / A(H ask +H bid ) ); 9 ep EquilibriumPrice(T(H ask ) T(H bid )); 10 pricerange = ( ep askquote + ep bidquote )/2; 11 boundary = pricerange+k 1 /v c1 +k 1 r c2 ; 12 end 13 end Algorithm consists of the following steps:

52 42 CHAPTER 3. MARKET POLICIES 1. Initialize transaction volume (v) and transaction rate (r) (lines 2-3) 2. Obtain the values for askquote and bidquote from the average ask price and average bid price [Equation 3.3] (lines 4-6) 3. Get the values for transaction volume from transacted asks T(S ask ) and transacted bids T(S bid ) (line 7) 4. Get the values for transaction rate from transacted asks T(S ask ), transacted bids T(S bid ), accepted asks A(S ask ), and accepted bids A(S bid ), (line 8) 5. Calculate equilibrium price EquilibriumPrice(T(H ask ) T(H bid )) based on Equation 3.1 and obtain the price range coefficient by using equilibrium price askquote and bidquote, (lines 9-10) 6. Obtain the boundary by using price range, transaction volume and transaction rate[equation3.4]. k 1,k 2,c 1,c 2 aretheconstantcoefficientstoadjustthevalue for transaction volume and transaction rate (line 11). Algorithm consists of the following steps: 1. Sets the history (asks and bids) length n (line 2) 2. Call Algorithm to calculate DAboundary(H) and Equilibrium price based on Equation 3.1. By using these values, set the maximum ask price range and minimum bid price range for shout accepting (lines 3-7)

53 3.2. ACCEPTING POLICIES 43 Algorithm 3.2.2: Dynamic Accepting Input: newshouts Output: accepted 1 begin 2 n H ask + H bid ; 3 if n > M inimalhistorylength then 4 boundary DAboundary(H); 5 ep EquilibriumPrice(T(H ask ) T(H bid )); 6 MaxAskPrice ep+boundary; 7 MinBidPrice ep boundary; 8 for (each shout in newshouts) do 9 if (shout is an ask And p(ask) MaxAskPrice) then 10 accepted T rue; 11 else if (shout is a bid And p(bid) MinBidPrice) then 12 accepted T rue; 13 else 14 accepted F alse; 15 end 16 end 17 else 18 accepted AlwayAccepting(shout); 19 end 20 end 3. Any incoming ask price below the maximum ask price range is accepted, and any incoming bid price above the minimum bid price range is accepted. Any other incoming shouts (asks and bids) out of these price range will be rejected (line 8-14) 4. If n < M inimalhistorylength, use Always accepting for any incoming shout (line 18)

54 44 CHAPTER 3. MARKET POLICIES 3.3 Matching Policies Matching policies determine how the market matches incoming shouts. According to the formal definition presented in Definition 2.4 in Chapter 2, each matched pair satisfy two conditions: (1) the ask price must be less or equal to a bid price, or the bid price must be higher or equal to an ask price, and (2) each order must not be matched with multiple orders at once. In this section, we shall describe two matching policies and their implementations Equilibrium Matching The matching policy most commonly used in double auctions is Equilibrium Matching (EM) [11]. Equilibrium Matching clears the matched shouts in a reported equilibrium price and matches intra-marginal asks with intra-marginal bids, so that the trader can make profit. The basic idea of equilibrium matching is as follows: Sort all asks (bids) in ascending (descending) order w.r.t. their price. Based on this sort order, starting at the top, add each ask-bid pair to the result matching, if ask s price is less than or equal to bid s price. A simple implementation of equilibrium matching is a well-known algorithm named the 4-heap algorithm, proposed by Wurman et al. [48]. The key idea of the 4-heap algorithm is to make matches between the best available prices. As soon as the

55 3.3. MATCHING POLICIES 45 market receives a new order, the 4-heap algorithm updates the current matched set and the current unmatched set. The 4-heap algorithm contains four different types of heaps, as follows: Ask-in: all the asks in the current matched set prioritized by maximal price. Ask-out: all the asks in the current unmatched set prioritized by minimal price. Bid-in: all the bids in the current matched set prioritized by minimal price. Bid-out: all the bids in the current unmatched set prioritized by maximal price. With these heaps, the 4-heap algorithm matches by always trying to make pairs if there are feasible pairs. The order at the lowest ask price is matched with the order at the highest bid price. In other words, the 4-heap algorithm makes matches from the largest bid-ask spreads. Also, a uniform clearing price is chosen in terms of the last matchable or the first unmatchable pair[25, 48]. The equilibrium matching evaluate the order in higher price with a profit gain for the traders and the auctioneer. However, equilibrium matching does not maximize market liquidity or transaction volumes. Algorithm implements equilibrium matching. There are number of matching algorithms. Note that in order to calculate equilibrium matching we use 4-heap algorithm. Figure 3.4 shows an example of equilibrium matching, where the numbers are the prices of asks and bids, M is the last matchable pair with equilibrium matching, and the arrow line links each matched pair.

56 46 CHAPTER 3. MARKET POLICIES Algorithm 3.3.1: EquilibriumMatching Input: Asks: sorted in ascending order, Bids: sorted in descending order Output: M atching 1 begin 2 Matching ; I 1; 3 while Asks and Bids do 4 Ask read I-th ask from Asks; 5 Bid read I-th bid from Bids; 6 if p(ask) p(bid) then 7 Matching Matching {(Ask,Bid)}; 8 I I +1; 9 else 10 jump out while loop; 11 end 12 end 13 end Figure 3.4: Equilibrium Matching

57 3.3. MATCHING POLICIES 47 In this example, from the list of asks and bids, we obtain the following four matches {(53, 125),(79,120),(85,112),(90,91)} for equilibrium matching, which is based on the largest bid-ask spreads. The sum of the price spread from the matches is 141. From the same list of asks and bids, the number of matches is increased if we obtain the matches as follows {(53, 82),(79,82),(85,91),(90,112)(94,120),(98,125)}. In this case, we get six matches but the sum of the price spread from the matches is 113, which is lower than with equilibrium matching. Matching on the largest bidask spreads does not enable the maximizing of the market liquidity or transaction volume Maximal Matching Unlike Equilibrium Matching, Maximal Matching (MM) aims to increase transaction volume. We found that a high intra-marginal bid can match with a lower extra-marginal ask, though with a profit loss for the buyer. We designed Maximal Matching in order to maximize the number of matches/transactions, though with less profit for some traders and auctioneers in the short-term [50]. Instead of the uniform price for all matches in Equilibrium Matching, Maximal Matching might use different prices for different traders where the sales of identical goods or services can transact at different prices. Algorithm 3.3.2[50] describes the implementation of maximal matching, which reuse the equilibrium matching as its base. We summarized the algorithm with the following five steps:

58 48 CHAPTER 3. MARKET POLICIES Algorithm 3.3.2: MaximalMatching Input: Asks: sorted in ascending order, Bids: sorted in descending order Output: M atching 1 begin 2 Matching ; 3 if Asks = or Bids = then Return; 4 M atching EquilibriumMatching(Asks, Bids); 5 MatchedAsks all asks from Matching in ascending order; 6 MatchedBids all bids from Matching in descending order; 7 if (Bids\MatchedBids) = or (Asks\MatchedAsks) = then Return; 8 M M 1 MaximalMatching(M atchedasks, (Bids\ M atchedbids)); 9 MM2 MaximalMatching((Asks\MatchedAsks), MatchedBids); 10 ExtraNumberOfMatches Min( MM1, MM2 ); 11 I ExtraNumberOfMatches; N Matching +1; 12 while I > 0 do 13 (Ask1,Bid1) read I-th in match from Matching; 14 Ask2 read N-th ask from Asks; 15 Bid2 read N-th bid from Bids; 16 Matching Matching {(Ask1,Bid2),(Ask2,Bid1)}; 17 Matching Matching \{(Ask1,Bid1)}; 18 N N +1; I I 1; 19 end 20 end 1. Given an input of shouts, calculate the matching (the set of matched pairs) with Algorithm 3.3.1, and mark all the matched shouts as matched and all the other shouts as unmatched (lines 4-6). 2. Recursively check how many matches MM can achieve if the input shouts were matched asks and unmatched bids (line 8). 3. Recursively check how many matches MM can achieve if the input shouts were unmatched asks and matched bids (line 9).

59 3.3. MATCHING POLICIES Choose the minimum of the numbers from the last two steps as the extra number of matches MM can achieve (line 10). 5. Cross match extra matchable shouts with the matched shouts in step 1: the ask in the first matched pair is rematched with the last extra matchable bid,while the bid in the pair is rematched with the last matchable ask, then the second matched pair with the second last extra matchable ask and bid, and so on until all extra matchable shouts are matched (lines 11-19). Figure 3.5 shows a matching example of Maximal Matching, where the numbers are the prices of asks and bids, M is the last matchable pair with equilibrium matching, and the arrow line links each matched pair. (a) Decompose of matching (b) MM Figure 3.5: (a)(b) Maximal Matching In the Figure 3.5, we show the increased number of matches which can be obtained by using the Maximal Matching Algorithm In this example, we use the

60 50 CHAPTER 3. MARKET POLICIES same example presented in Figure 3.4. Initially, we find the matching according to Algorithm 3.3.1, M is the last matchable pair for EM. We decompose the matching as in Figure 3.5 (a), with matched asks and unmatched bids, and unmatched asks and matched bids. From these two list of asks (asks1, asks2) and bids (bids1, bids2), we check how many matches MM can achieve. From asks1 and bids1 we obtained two matches as follows {(53,82),(79,82)}. And from asks2 and bids2, we can get three matches as follows {(94,112),(98,120),(113,125)}. The minimum number of matches obtained from the sub-match is two. According to the MM algorithm, we can match two extra matching over the EM algorithm described in section To achieve these extra matching require to do the rematch by cross matching showed in Figure 3.5(b). 3.4 Clearing Policies Clearing policies enforce the timing and conditions of market clearing, as we have shown in the definition of clearing policy in Definition 2.5 in Chapter 2. Clearing policy defines when to execute a transaction between a matched pair and how long the market will keep the unmatched shouts. For example, if a market sets a shortlength clearing cycle, it is possible to get more opportunities, but it will lose the opportunity to maximize the profit. On the other hand, if the market sets a long clearing cycle, it may increase profit but will lose some opportunities to maximize the number of market orders. Therefore, it is important to identify how clearing policy affects market efficiency. Typical clearing policies are classified into two types:

61 3.5. PRICING POLICIES Continuous clearing (CC): Clear the market orders as soon as a matched pair is identified 2. Periodic clearing: Also known as clearing house (CH). Clear the market orders periodically with the intention of finding a best-matching pair In continuous clearing, the timing of the shouts is more important than the pricing of the shouts. In periodic clearing, price has a significant impact on matching shouts. Our experiments show that a periodic clearing condition can perform better than a continuous clearing. However, the performance of the clearing condition depends heavily on the market environment. For example, a trading day can be divided into multiple rounds, with the market clearing in each round. Market clearing according to a round-based periodic clearing condition can improve both the order quantity and best price matching condition as well. If the market clears according to a day closing condition, it will eventually be able to get a best price for the order, but will lose transaction volume, having fewer opportunities to increase the order quantity. Hence the market efficiency is decreased. 3.5 Pricing Policies Pricing policies determine the clearing or transaction prices for each matched pair, as we have shown in the definition of pricing policy in Definition 2.6 in Chapter 2. Transaction price can be determined by a specific matched ask price and bid price. Pricing policies are partially dependent on matching and accepting policies.

62 52 CHAPTER 3. MARKET POLICIES For equilibrium matching policy, where the matching is based on the best price value, a mid-point pricing policy can perform well. Mid-point pricing takes the median price for each matched pair. Therefore, the mid-point pricing policy can be robust to the extreme orders. Definition 3.2. Let M be a match. For any (x,y) M, the mid-point pricing policy defines the clearing price of (x,y) as: P(x,y) = (p(x)+p(y))/2. For k-pricing policy the price is adjusted with a k parameter value. Definition 3.3. Given any match (x,y) M, and parameter k [0,1], the k- pricing policy defines the clearing price of (x,y) as: P(x,y) = kp(x)+(1 k)p(y). In k-pricing policy, the clearing price of a matched pair sets at some point in the interval between their prices, which is the weighted average of a bid price and ask price of the pair. The parameter k(k [0,1]) controls the price that is used for transaction. Note that pricing is independent to matching. For instance, a matched pair with a bid at $100 and ask at $80 can set the transaction price at any interval. 3.6 Charging Policies The charging policy of a market determines how fees are imposed for providing a service. Fee charging can play a significant role in overall market performance. In a competitive environment for a particular service, if one market s fee charging is higher than that of the other markets, there is a possibility of losing the traders

63 3.6. CHARGING POLICIES 53 and goodwill. Therefore, it is important to understand the properties of charging policies and their application. A market can set the fees for many conditions such as Registration fees: charged to the traders for registering with the market Information fees: for receiving other market information Shout fees: for successfully placing bids and asks Transaction fees: charged while the transaction executes Profit fees: a share of the profit made by the traders Charging policy is considered as an external strategy of a market, whereas all other policies, such as accepting, matching, clearing and pricing policies are considered as internal strategies. Charging policy is highly dependent on the markets internal policies and the overall behaviour of the marketplace. The key questions are how, when and where to charge to increase market efficiency. As there are multiple market makers, fee charging must be set dynamically to adapt to the market situations and to increase market efficiency. The most significant impact of a fee charging policy is on market share. For example, a static or fixed charging policy which, sets the fees at a specified level may not be able to maintain market stability in a dynamic market environment[30]. If the market share starts to drop and fees continuetobechargedatthesamelevel,thiscouldcauseanegativeimpactinoverall

64 54 CHAPTER 3. MARKET POLICIES market reputation. Traders who keep a long record of charging history for decisionmaking may not return to this market, even though the market may charge very low or very high but at a fixed level. From the TAC market design competition, we concluded that high fees may increase market maker s profits, but only temporarily, and usually result in the loss of traders in subsequent days. Similarly, low fees attract high volumes of traders, but may require several days to make substantial profits. Therefore, fee charging requires to change according to market movements and performance. To set fees dynamically, we introduce a dynamic charging policy based on the market demand and market share. We implemented this policy in TAC market design competitions and experimented with the ideas for dynamic charging policy. In dynamic charging policy, fees charging apply from an initial level and gradually moves to a target level. At the initial stage, the fees set at close to zero or at no fees at all. Later, the market will start to charge in consideration of two conditions, market demand and the target market share. In this case, market demand defines whether the market is the most popular market for the traders. Market share is the proportion of traders that have registered with the market. Once both conditions are fulfilled, it is safe to slowly increase the charges. From the TAC competition, we found that if the market does not satisfy these conditions and keeps charging, it has a significant impact on its ability to attract traders in the long run. We described how and when to charge, now where to charge? We introduce a simple follow-up condition that could work very well in a competitive environment. This condition is satisfied by exploring where the majority of the other markets are charging fees.

65 3.7. SUMMARY 55 From the TAC competition, we observed that if more than 60% of markets are charging only at profit fees and information fees, then it is safe to charge in profit fees and information fees only, as there will be fewer options for traders to switch markets just for a specific type of fee charging. So the market can set the charging dynamically and adjust the fees according to the market performance. 3.7 Summary In this chapter, we provided an overview of all the policies described in our market model in Section in Chapter 2, including accepting policies, matching policies, pricing policies, clearing policies and charging policies. In particular, we presented detailed designing and implementation information for a new accepting policy and a new matching policy. We formally represented some of these policies and theoretically compared the basic ideas with other existing policies. We also explained the uses and robustness of these newly proposed market policies.

66 56 CHAPTER 3. MARKET POLICIES

67 Chapter 4 Experimental Analysis of Market Policies 4.1 Introduction Based on the market model and market policies described in Chapters 2 and 3, we conducted experiments to show how market policies influence trading environments and market behaviours of autonomous trading agents in double auction markets. In this section, we analyze several market policies in various market settings and trading environments. In our experiments, we controlled both market policies and the strategies of autonomous trading agents. We focused mainly on the market policy effects and how specific market policies influence overall market behaviours. We are particularly interested in the following aspects: 57

68 58 CHAPTER 4. EXPERIMENTAL ANALYSIS OF MARKET POLICIES The ways in which accepting policies influence market performance and trading environments. The ways in which matching policies influence market performance and trading environments. They ways in which clearing policies effect market conditions. The ways in which the combinations of market policies influence market performance in competitive market environments. To investigate the above aspects, we conducted a series of experiments using the CAT platform. In this chapter, we describe the market settings for evaluation and provide details on performance indexes. Finally, we present an analysis of our experimental results. 4.2 Market Performance Indexes In our analysis, we adopted the following indexes to evaluate market policies. The aim was to show how market performance is affected by market policies. Market Share(MS): Market share means the portion of traders registered with a market per day. The sum market share for all markets on the same day will be 1. Thus, the market share for each market is a number between 0 and 1.

69 4.2. MARKET PERFORMANCE INDEXES 59 Transaction Success Rate (TSR): The Transaction Success Rate for a market on a given day is the proportion of bids and asks successfully placed from which that market is able to eventually match. If N a, N b is the number of new asks & bids successfully placed with a market on a given day, and N m is the number of successful matches executed by that market from the bids and asks received, hen TSR = 2.Nm N a+n b. If both N a, N b are zero, the transaction success rate is calculated as zero. Thus, the Transaction Success Rate for any market on any day is a number between 0 and 1. Transaction Volume (TV): The Transaction Volume is the number of successful matches M, per day: TV = M. The transaction volume is obtained at the time of clearing. The liquidity of the market is observed according to transaction volume. This index is one of the key measures for ascertaining low performance of a market. If the Transaction Volume is significantly low, then the other indexes also have negative effects. Profit: The Profit of a market on a particular day is the sum of transaction profits obtained by charging fees for each transaction. Profit Share (PR): The Profit share of a market on a particular day is given by the total profit obtained by that market on that day as a proportion of the

70 60 CHAPTER 4. EXPERIMENTAL ANALYSIS OF MARKET POLICIES total profit obtained by the total number of markets on the same day. The Profit Share is thus a number between 0 and 1 for each market for each day, and the sum profit for all market on the same day is 1. Transaction Price Standard Deviation (TPS): Transaction Price Standard Deviation represent the spreading of clearing price on a particular trading day. From the given transaction price TP, mean value of transaction price TP and the number of transactions N, TPS is calculated as follow, (TP TP) 2 TPS =. N Basic Settings for Experiments We implemented market mechanisms in the CAT platform, and evaluated the market performance based on the evaluation criteria described in Section 4.2. Each game in our experiment consisted of 500 virtual trading days and each day consisted of 10 rounds. The trade entitlement was 3, i.e., each trader could submit 3 items per day. The number of traders depended on the number of market participants. We set 40 traders for each market maker, and each trader (buyer or seller) had a single bidding strategy, either GD, ZIP, ZI-C, or RE (as described in Section 2.3 in Chapter 2). For each game, there were equal numbers of buyers and sellers for a particular bidding strategy. I.e., if there were 40 traders using GD bidding strategy, then 20 buyers and 20 sellers would be using the same bidding strategy. The valuation of the sellers and buyers prices were set within the range 50 to 150,

71 4.4. EXPERIMENTAL SETTINGS AND ANALYSIS 61 and prefixed as follows: {50, 55, 60, 65, 70, 75, 80, 85, 90, 95, 100, 105, 110, 115, 120, 125, 130, 135, 140, 145}. For this setting, the competitive equilibrium price was $97.5. To analyze the market policy effects, we conducted four types of experiment. In the following sections, we present how we set the market policies and trader strategies for the experiments. 4.4 Experimental Settings and Analysis The experiments for accepting policy effects, matching policy effects, clearing policy effects and overall market policy effects are presented in the following sections. In the first three experiments, a fixed charging policy was applied for each market to control the influences of the charging policies. In this way, we could analyze the actual effects of each individual market policy. For the last experiment, we used combinations of market policy with dynamic charging policy, so we could analyze the effects on overall market performance in a competitive trading environment. We present the experiments result in tabular and graphical format. In tabular format we present the data of Market Share (MS), Transaction Success Rate (TSR), Profit Share (PR) and Transaction Price Standard Deviation (TPS) for various market policies. And the data shows in tables for each experiments are the average experiments result of 500 virtual trading days.

72 62 CHAPTER 4. EXPERIMENTAL ANALYSIS OF MARKET POLICIES Effects of Accepting Policies We investigated how accepting policies can influence market performance. For this experiment, we used the three accepting policies described in Section 3.2 in Chapter 3: Always Accepting (AA), Quote-beating Accepting (QA) and Dynamic Accepting (DA). The always accepting policy never rejects any incoming orders. The quotebeating accepting policy rejects incoming shouts based on the best preferred price, which can filter out some of the extra-marginal traders. The dynamic accepting policy rejects incoming orders based on the market movement and competitive equilibrium price, i.e., if ask orders exceed the competitive equilibrium price or bid orders are less than the competitive equilibrium price. Hence, the dynamic accepting policy can filter to attract intra-marginal traders. We ran five sets of experiments. Four sets used four different bidding strategies, and the last combined bidding strategies from GD, ZIP, ZI-C & RE. Our intention was to test how accepting policies affect the market performance. (I) Trading with GD Traders We used 120 GD traders with the valuation range 50 to 150. Buyers and sellers were evenly split, having 60 of each. The game consisted of 500 virtual trading days with 10 rounds per day. We ran three market makers, AA, QA and DA, each representing one of the accepting policies described above. Except for the accepting policy, all other market policies for each market maker were exactly same; there were no influences on market performance due to other market policies.

73 4.4. EXPERIMENTAL SETTINGS AND ANALYSIS 63 From these experiments, we observed that market performance with Dynamic Accepting (DA) is significantly better than with Always Accepting (AA) or Quotebeating Accepting (QA). From Table 4.1, it can be seen that market share (MS) for Dynamic Accepting is two times higher than Always Accepting and Quote-beating Accepting. From the trader distribution (Figure 4.1(a)) we observe that Always Accepting and Quote-beating Accepting attracted the most traders until day 150. But the traders started to migrate to the Dynamic Accepting market from day 150, and continu to do so until the end of the final trading day. Initially, Always Accepting and Quote-beating Accepting attracted the most traders because of the higher accepting rates. This allowed too many unqualified orders to enter these markets. The markets subsequently failed to execute most of these orders, which significantly decreased the transaction success rate (TSR). Always Accepting therefore scored the lowest transaction rates, followed by Quote-beating Accepting. MS TSR PR TPS AA QA DA Table 4.1: Accepting policy effects for GD traders In the early trading days, until day 150, the market share, market liquidity(tv) and profit for Dynamic Accepting was lower than Always Accepting and Quote-beating Accepting (see Figure 4.1 (a)(b)(c)(d)), but after day 150, Dynamic Accepting attracted most of the traders, which significantly increased TV, TSR, PR and overall market profits.

74 64 CHAPTER 4. EXPERIMENTAL ANALYSIS OF MARKET POLICIES (a) Trader Distribution (b) Transaction Volume (TV) (c) Profit (d) Average Profit/Match (x-axis-days & y-axis-(a)number of traders,(b)transaction volume, (c)profit margins,(d)average profit) Figure 4.1: (a)(b)(c)(d) Accepting policy effects (AA, QA, DA)

75 4.4. EXPERIMENTAL SETTINGS AND ANALYSIS 65 (II) Trading with ZIP Traders In the second set of experiments, we studied accepting policy effects with ZIP bidding strategies. For these experiments, we used the same settings as when trading with GD traders, except for the trader bidding strategy. We ran 120 ZIP traders, evenly split between buyers and sellers. We also ran the same market makers used for the GD trading environment. From this experiment, we observed that Dynamic Accepting (DA) attracts ZIP traders more efficiently than GD traders. We also noted that Dynamic Accepting market performance was significantly better than for Always Accepting (AA) and Quote-beating Accepting (QA). From Table 4.2, it can be observed that market share (MS) for Dynamic Accepting is almost two times higher than for Always Accepting and Quote-beating Accepting. MS TSR PR TPS AA QA DA Table 4.2: Accepting policies effects for ZIP traders From the trader distribution (Figure 4.2 (a)), we can observe that Always Accepting and Quote-beating Accepting attracted the most traders until day 100, where for GD traders, this was true until day 150. After day 100, traders start to migrate quickly to Dynamic Accepting. The traders migration to DA started earlier than for the GD traders. Once the traders had migrated, the trader distribution was similar

76 66 CHAPTER 4. EXPERIMENTAL ANALYSIS OF MARKET POLICIES to that of the GD traders. However, we observed that to reach the maximum 50% of market share took only 50 days, whereas for GD it increased gradually. We found ZIP traders were more sensitive on transaction success rate than GD traders. Since Always Accepting failed to transact most of the submitted offers, and Quote-beating Accepting failed to find a proper match within the time limit, traders started to migrate to the best performance market. Similar to the GD trading environment, until day 100, the MS, TV, PR and profit for Dynamic Accepting was lower than for AA and QA (see Figure 4.2 (a)(b)(c)(d)), )). However, after day 100, Dynamic Accepting attracted most of the traders, which significantly increased market liquidity (TV), profit and average profit margin.

77 4.4. EXPERIMENTAL SETTINGS AND ANALYSIS 67 (a) Trader Distribution (b) Transaction Volume (TV) (c) Profit (d) Average Profit/Match (x-axis-days & y-axis-(a)number of traders,(b)transaction volume, (c)profit margins,(d)average profit) Figure 4.2: (a)(b)(c)(d) Accepting policy effects (AA, QA, DA)

78 68 CHAPTER 4. EXPERIMENTAL ANALYSIS OF MARKET POLICIES (III) Trading with ZI-C Traders In the third set of experiments, we tested the accepting policy effects with ZI-C traders. For this experiment, we used 120 ZI-C traders, evenly split between buyers and sellers. All the other settings were similar to those of the previous experiments. In this experiment, we found that ZI-C traders learned the market environment more rapidly than ZIP and GD traders. ZI-C traders took only 20 days (Figure 4.3 (a)) to migrate to the best market. For these traders, the Dynamic Accepting (DA) market performance was significantly higher than for Always Accepting (AA) and Quote-beating Accepting(QA). From Table 4.3, it can be seen that the market share (MS) for Dynamic Accepting was two times higher than for Always Accepting and Quote-beating Accepting. This was also higher than the ZIP (table 4.2) and GD (table 4.1) market shares. MS TSR PR TPS AA QA DA Table 4.3: Accepting policy effects for ZI-C traders Market liquidity (TV), profit share (PR) and average profit margin for dynamic accepting were also significantly higher than for Always Accepting and Quote-beating Accepting (see Figure 4.3 (a)(b)(c)(d)). This started from day 20, unlike for the ZIP and GD traders, where this started from days 100 and 150, respectively.

79 4.4. EXPERIMENTAL SETTINGS AND ANALYSIS 69 (a) Trader Distribution (b) Transaction Volume (TV) (c) Profit (d) Average Profit/Match (x-axis-days & y-axis-(a)number of traders,(b)transaction volume, (c)profit margins,(d)average profit) Figure 4.3: (a)(b)(c)(d) Accepting policy effects (AA, QA, DA)

80 70 CHAPTER 4. EXPERIMENTAL ANALYSIS OF MARKET POLICIES (IV) Trading with RE Traders We then analyzed the accepting policy effects for RE bidding strategies. For this experiment, we used 120 RE traders. All the other settings were similar to those of the previous experiments. In the RE trading environment, the day-to-day trading behaviour was different to that of the GD, ZIP and ZI-C trading environments. We observed that differences between - individual market performances were barely discernible. Though to some extent the Dynamic Accepting (DA) market performed better than the Always Accepting (AA) and Quote-beating Accepting (QA), particularly in transaction success rate (TSR), the market share (MS) (see table 4.4) and trader distribution (see figure 4.4 (a)) were comparable for all markets. Even the Always Accepting market failed to attract the most traders on the initial trading days. MS TSR PR TPS AA QA DA Table 4.4: Accepting policy effects for RE traders We also found that there were no significant differences between market liquidity (TV), profit share (PR) and average profit margin (see figure 4.4 (a)(b)(c)(d)). RE traders use immediate market feedback rather than long-term performance history to make the decisions which impact the switching of markets

81 4.4. EXPERIMENTAL SETTINGS AND ANALYSIS 71 (a) Trader Distribution (b) Transaction Volume (TV) (c) Profit (d) Average Profit/Match (x-axis-days & y-axis-(a)number of traders,(b)transaction volume, (c)profit margins,(d)average profit) Figure 4.4: (a)(b)(c)(d) Accepting policy effects (AA, QA, DA)

82 72 CHAPTER 4. EXPERIMENTAL ANALYSIS OF MARKET POLICIES (V) Trading with Combined Traders In this experiment, we tested the accepting policy effects with combined bidding strategies. We used 120 traders, equally distributed between GD, ZIP, ZI-C and RE traders. The trader population of each group contained 30 traders, evenly split between buyers and sellers. From Table 4.5, it can be seen that market share (MS) for Always Accepting (AA) was marginally higher than for Dynamic Accepting (DA) and Quote-beating Accepting (QA), mainly because of random trader distribution (Figure 4.5(a)). Always accepting can also attract some greedy traders. A greedy trader particularly considers submitting only higher offer prices to maximize profit. We observed that the trader distribution significantly changed from day 350, when market share for Always Accepting and Quote-beating Accepting sharply declined, but the constant market confidence MS for Dynamic Accepting is gradually increased. TSR and PR also increased at the same time. MS TSR PR TPS AA QA DA Table 4.5: Accepting policy effects In the early trading days, until day 150, the market share and market liquidity (TV) for Dynamic Accepting was similar though slightly lower to Always Accepting and Quote-beating Accepting (see Figure 4.5 (a)(b)). But the limit order adjustment by the Dynamic Accepting market was able to maintain a higher profit margin (Figure 4.5 (c)(d)) than the other two accepting policies.

83 4.4. EXPERIMENTAL SETTINGS AND ANALYSIS 73 (a) Trader Distribution (b) Transaction Volume (TV) (c) Profit (d) Average Profit/Match (x-axis-days & y-axis-(a)number of traders,(b)transaction volume, (c)profit margins,(d)average profit) Figure 4.5: (a)(b)(c)(d) Accepting policy effects (AA, QA, DA)

84 74 CHAPTER 4. EXPERIMENTAL ANALYSIS OF MARKET POLICIES Effects of Matching Policies In these experiments, we examined how matching policies influence market performance and trading environments. We used two different types of matching policies, Maximal Matching (MM) and Equilibrium Matching (EM), presented in Section 3.3 in Chapter 3. Maximal Matching can improve market liquidity, and Equilibrium Matching can increase average profit margin. The average profit margin in MM is lower than EM, but higher market liquidity in MM may increase market share and overall profit. Similarly with Section 4.4.1, We ran five sets of experiments in order to compare these two matching policies. Four sets of experiments used four different bidding strategies, and the last used combined bidding strategies distributed equally between GD, ZIP, ZI-C & RE. As described in Chapter 3, we intended to ascertain whether Maximal Matching can maximize the market liquidity and overall profit compared to Equilibrium Matching. We also observed how these policies behaved in different trading environments. (I) Trading with GD Traders We used 80 GD traders with the valuation range 50 to 150. Buyers and sellers were evenly split, with 40 each. The game consisted of 500 virtual trading days with 10 rounds per day. We ran two markets, MM and EM, representing the matching policies described above. All other market policies were the same. In Table 4.6 and Figure 4.6, we present the experimental results for the GD trading strategy. We observed that Maximal Matching (MM) outperformed Equilibrium

85 4.4. EXPERIMENTAL SETTINGS AND ANALYSIS 75 Matching (EM) in most of the evaluation indexes. From the analysis, we found that the MS for Maximal Matching (MM) was almost two times higher than for Equilibrium Matching. Because of the higher market share, market liquidity (TV) (Figure 4.6(b)) and transaction success rate (TSR) (see Table 4.6) were also increased for Maximal Matching. Also, the profit share (PR) (see Table 4.6 & Figure 4.6(c)) was two times higher than for Equilibrium Matching. MS TSR PR TPS MM EM Table 4.6: GD Trading Strategy (MM, EM) Figure 4.6 (a), shows the trader distribution for each day. At the very beginning, the traders were equally distributed. Equilibrium Matching attracted more traders until day 150, but after 150 days, Maximal Matching started to attract the most GD traders and continued to do so until the end of 500 days. As GD bidding strategy uses a belief-and history-based learning mechanism, it takes more than 100 days to learn the market condition. Because of higher trader attraction after 150 days, the profit for the Maximal Matching market is actually higher than for the Equilibrium Matching market (see Figure 4.6 (c)), though the average profit for each transaction is much smaller (see Figure 4.6 (d)). Initially, the Equilibrium Matching profit was higher, due to higher market share.

86 76 CHAPTER 4. EXPERIMENTAL ANALYSIS OF MARKET POLICIES (a) Trader Distribution (b) Transaction Volume (TV) (c) Profit (d) Average Profit/Match (x-axis-days & y-axis-(a)number of traders,(b)transaction volume, (c)profit margins,(d)average profit) Figure 4.6: (a)(b)(c)(d) Trading Strategy GD environment (MM, EM)

87 4.4. EXPERIMENTAL SETTINGS AND ANALYSIS 77 (II) Trading with ZIP Traders For these experiments, we used the same settings as for the experiments trading with GD traders. The only exception was the trader bidding strategy. We used 80 ZIP traders and the same market makers as used for the GD trading environment matching policy experiments. From the experimental results presented in Table 4.7 and Figure 4.7, we observed that, similarly with the GD trading environment, the Maximal Matching (MM) performance was better than that of Equilibrium Matching (EM) for most of the evaluation criteria. The market share was again two times higher than for Equilibrium Matching. Similarly, because of the higher market share, market liquidity (TV) (Figure 4.7(b)), transaction success rate (TSR) (Table 4.7) and profit share (PR) for MM (See Table 4.7 & Figure 4.7(c)), were also increased. MS TSR PR TPS MM EM Table 4.7: ZIP Trading Strategy (MM, EM) Figure 4.7 (a) shows the trader distribution for each day. At the very beginning, traders were equally distributed, but after 50 days, the MM market started to attract most of the ZIP traders, taking 100 days less than the GD traders. The ZIP bidding strategy uses a learning-based profit valuation to select a market. In this experiment, this took about 50 days to learn. Similarly to with the GD trading environment because of higher trader attraction following 50 days, the profit for

88 78 CHAPTER 4. EXPERIMENTAL ANALYSIS OF MARKET POLICIES the MM market was also higher (see Figure 4.7 (c)), though the average profit per transaction was slightly lower than for the EM market (see Figure 4.7 (d)). (a) Trader Distribution (b) Transaction Volume (TV) (c) Profit (d) Average Profit/Match (x-axis-days & y-axis-(a)number of traders,(b)transaction volume, (c)profit margins,(d)average profit) Figure 4.7: (a)(b)(c)(d) Trading Strategy ZIP environment (MM, EM)

89 4.4. EXPERIMENTAL SETTINGS AND ANALYSIS 79 (III) Trading with ZI-C Traders For this experiment, we used 80 ZI-C traders, evenly split between buyers and sellers. All other settings were the same to those detailed in the previous sections. From the experimental results for ZI-C traders presented in Table 4.8 and Figure 4.8, we may observe that the behaviours for MM and EM were similar up to 250 days (Figure 4.8 (a)). MS TSR PR TPS MM EM Table 4.8: ZI-C Trading Strategy (MM, EM) After 250 days, the traders started to switch markets, and so the traders distribution appear to be the same as the starting of the trading days. It took another 100 days to regain the trader attraction for the MM market. To increase the profit margins, at some stage the ZI-C traders start to increase the price over their limit price; this causes them to switch and explore the other markets. Once the traders switched markets it took another 100 days to return to the previous preferred market. Because of the impact of trader distribution, it can also be observed from Figure 4.8(a)(b)(c)(d) that the market liquidity (TV), profit share (PR) and average profit margin effects are also similar to in the GD and ZIP trading environments.

90 80 CHAPTER 4. EXPERIMENTAL ANALYSIS OF MARKET POLICIES (a) Trader Distribution (b) Transaction Volume (TV) (c) Profit (d) Average Profit/Match (x-axis-days & y-axis-(a)number of traders,(b)transaction volume, (c)profit margins,(d)average profit) Figure 4.8: (a)(b)(c)(d) Trading Strategy ZI-C environment (MM, EM)

91 4.4. EXPERIMENTAL SETTINGS AND ANALYSIS 81 (IV) Trading with RE Traders To test matching policies in an RE trading environment, we used 80 RE traders. All other setting were the same as those described in the previous sections. From the experimental results presented in Table 4.9 and Figure 4.9, it may be observed that the market behaviours are different from those of the GD, ZIP and ZI-C trading strategies presented in the previous sections. From Table 4.9, it can be seen that the market share (MS), transaction success rate (TSR) and profit share (PR) were almost equal for the MM and EM markets, while the results for the GD, ZIP and ZI-C strategies for Maximal Matching were two times higher than for Equilibrium Matching. In the RE trading environment, day-to-day trading behaviours were also significantly different from those of all other trading environments. MS TSR PR TPS MM EM Table 4.9: RE Trading Strategy (MM, EM) From Figure 4.9(a), we can observe that the traders were distributed almost equally; MM is only marginally higher than EM. From Figure 4.9(b)(c), it may be seen that market liquidity (TV) was slightly higher for the MM market, but that the profit margin was almost equal, and that the average profit (Figure 4.9(d)) for each transaction was also closer to that of Equilibrium Matching. The RE bidding strategy uses a learning-based strategy with human-like behaviour, and uses immediate feedback to make decisions about the next day s trading. This would be the reason why

92 82 CHAPTER 4. EXPERIMENTAL ANALYSIS OF MARKET POLICIES the market behaviour of the RE environment was different from those of the other trading environments. We also observed similar types of market behaviour for RE traders for as regards accepting policies. (a) Trader Distribution (b) Transaction Volume (TV) (c) Profit (d) Average Profit/Match (x-axis-days & y-axis-(a)number of traders,(b)transaction volume, (c)profit margins,(d)average profit) Figure 4.9: (a)(b)(c)(d) Trading Strategy RE environment (MM, EM)

93 4.4. EXPERIMENTAL SETTINGS AND ANALYSIS 83 (V) Trading with Combined Traders In this experiment, we tested the matching policy effects for using combined bidding strategies. We used 80 traders, equally distributed between GD, ZIP, ZI-C and RE traders. The trader population of each group consisted of 20 traders, evenly split between buyers and seller. From the experimental results presented in Figure 4.10, it can be observed that the market liquidity (TV) for Maximal Matching (MM) was about two times higher than for Equilibrium Matching (EM). The transaction success rate (TSR) (see Table 4.10) was also higher for MM. This is similar to the results from the GD, ZIP and ZI-C trading environments. MS TSR PR TPS MM EM Table 4.10: Matching Policy Effects MM vs EM As We have noted in the previous sections, higher market liquidity will attract traders to a specific market. This can be observed in this experiment as well. Figure 4.10 (a) shows the trader distribution for each day. At the very beginning, traders were equally distributed among the markets, but after 25 days, the Maximal Matching market attracted the most traders, which continued until day 500. Because of trader attraction, the profit gained by the MM market was actually higher than that gained by the EM market (see Figure 4.10(c)), though the average profit for each transaction for MM was much smaller than that for EM.

94 84 CHAPTER 4. EXPERIMENTAL ANALYSIS OF MARKET POLICIES (a) Trader Distribution (b) Transaction Volume (TV) (c) Profit (d) Average Profit/Match (x-axis-days & y-axis-(a)number of traders,(b)transaction volume, (c)profit margins,(d)average profit) Figure 4.10: (a)(b)(c)(d) Matching Policy Effects (MM vs EM)

95 4.4. EXPERIMENTAL SETTINGS AND ANALYSIS Effects of Clearing Policies We investigated the effects of clearing timing for bidding strategies equally selected fromgd,zip,zi-c&re.werantheexperimentsbycomparingtwodifferenttypes of clearing conditions, Continuous Clearing (CC) and Periodic Clearing (CH), as described in Section 3.4, in Chapter 3. We intended to investigate how clearing policies affect market conditions. We used 80 traders equally distributed between GD, ZIP, ZI-C and RE traders. The trader population for each group contained 20 traders, evenly split between buyers and seller. The game consisted of 500 virtual trading days with 10 rounds per day. We used two markets which used the same rules, except one used Continuous Clearing (CC) and the other used Periodic Clearing (CH). From the experimental results presented in Table 4.11 and Figure 4.11, it may be observed that the CH market performance was higher than that of the CC market in most of the evaluation criteria. MS TSR PR TPS CC CH Table 4.11: Clearing Policy Effect We can see that the CH market share (MS) and trader distribution were only ten percent higher than for the CC market. Because of the slightly higher market share, market liquidity(tv)(figure 4.11(b)) and transaction rate(tsr)(table 4.11) were also slightly increased for periodic clearing. But the most significant differences were

96 86 CHAPTER 4. EXPERIMENTAL ANALYSIS OF MARKET POLICIES intheprofitshare(pr)andprofitmargin(seetable4.11andfigure4.11(c)). Profit for the CH market was about three times higher than that of the CC market. The main reason for this was the time interval for the clearing conditions. In continuous clearing, the orders are cleared as soon as the market finds a match. In periodic clearing, the market waits for a certain interval of time to find a proper match with higher profit margins, which also ensures a higher transaction rate. Under continuous clearing conditions, a market can receive more items to clear with less profit, which can attract extra-marginal traders rather than intra-marginal traders. (a) Trader Distribution (b) Transaction Volume (TV) (c) Profit (d) Average Profit/Match (x-axis-days & y-axis-(a)number of traders,(b)transaction volume, (c)profit margins,(d)average profit) Figure 4.11: (a)(b)(c)(d) clearing policy effect CC vs CH

97 4.4. EXPERIMENTAL SETTINGS AND ANALYSIS 87 This also affects the overall profit and transaction price distribution for CC. In Table 4.11, we can see the transaction price standard deviation(tps) is significantly higher for CC compared to CH Testing Market Policies in a Dynamic Market Environment We built a market agent with new market policies designed and implemented in Chapter 3. This market competed with other dynamic markets obtained from the CAT tournament. From these experiments, we investigated how the combination of market policies influences market performance in a competitive market environment. The bidding strategies for this experiment were selected evenly from GD, ZIP, ZI-C and RE. We used 280 traders, with equal numbers of GD, ZIP, ZI-C and RE traders. The trader population of each group consisted of 70 traders, evenly split between buyers and sellers. The game consisted of 500 virtual trading days with 10 rounds per day. All other settings were the same as those used in the CAT tournament. In this experiment, we used six market agents from the CAT tournament, along with the agent jackaroo developed by us. We implemented jackaroo using the market policies presented in the Chapter 3, notably Dynamic Accepting (DA) policy, Maximal Matching (MM) policy, periodic clearing policy (CH), K-pricing policy and Dynamic Charging policy. From the experimental results presented in Table 4.12 and Figure 4.12, we can see that jackaroo s market share (MS) was only the second-

98 88 CHAPTER 4. EXPERIMENTAL ANALYSIS OF MARKET POLICIES best (21%), but its overall performance was superior to those of the other six CAT market agents. Transaction success rate (TSR) and profit share (PR) were also higher than for all the other agents. MS TSR PR TPS CAT CAT CAT CAT CAT CAT jackaroo Table 4.12: Dynamic Markets Environment We observed that Dynamic Accepting was able to attract only good traders, and that Maximal Matching increased transaction volumes (TV), which eventually attracted more traders. Though the market share was not the best, we found that profit and average profit margin was significantly higher than for all other CAT agents (see figure 4.12(c)(d)). For jackaroo, higher transaction volume and periodic clearing policy facilitate finding proper matches between accepted asks and bids orders and maximizing the profit margin. Figure 4.12(e) presents only the profit fee-charging for market agents. Most of the agents were imposed charging for profit share. From the fee-charging figure, it may be observed that static fee-charging (CAT2 and CAT3) or high fee-charging (CAT5) had a negative impact on market share and profit margin. We found that our dynamic charging worked very well in stabilizing market performance and in

99 4.4. EXPERIMENTAL SETTINGS AND ANALYSIS 89 (a) Trader Distribution (b) Transaction Volume (TV) (c) Profit (d) Average Profit/Match (e) Profit Fees (x-axis-days & y-axis-(a)number of traders,(b)transaction volume, (c)profit margins,(d)average profit,(e)profit fees) Figure 4.12: (a)(b)(c)(d)(e) Dynamic CAT markets