Simulating New Markets by Introducing New Accepting Policies for the Conventional Continuous Double Auction

Transcription

1 Simulating New Markets by Introducing New Accepting Policies for the Conventional Continuous Double Auction Sina Honari Premier Ideas Support Center, School of Engineering, Shiraz University, Shiraz, Iran Maziar Gomrokchi Computer Science and Software Engineering Department Concordia University, Canada Mojtaba Ebadi Premier Ideas Support Center, School of Engineering, Shiraz University, Shiraz, Iran Amin Fos-hati Premier Ideas Support Center, School of Engineering, Shiraz University, Shiraz, Iran Jamal Bentahar Concordia Institute for Information Systems Engineering, Concordia University, Canada ABSTRACT In recent years a huge number of online auctions that use Multi Agent systems have been created. As a result there are numerous auctions that provide the same product. In this case each customer can buy a product with the lowest possible price. But searching between auctions in terms of finding the suitable product can be time consuming for consumers and also providing products in different markets is a difficult task for suppliers. So the need for an autonomous agent in these types of markets is deeply felt. On the other side the structure of an auction mechanism that provides the environment for traders to operate their trades is vital. Despite all the research that has been done about online auctions, most of them were about single markets. But in real world the stocks and commodities of companies are listed and traded in different markets. There is a growing tendency towards research about online auctions and Market Design. Particularly in recent years CAT (CATallactics) game has provided an important opportunity to develop and test new techniques in this field. In this paper after introducing CAT game and PersianCAT agent, we want to challenge the conventional accepting policy used in stock markets like New York Stock Exchange and provide a better solution that improves the general performance of the markets. General Terms Measurement, Performance, Design, Economics and Experimentation. Keywords Market Design, Multi Agent Systems, Trading Agents, Accepting Policy, Transaction Success Rate and CAT Competition. 1. INTRODUCTION In recent years a huge number of online auctions that use Multi Agent systems have been created. As a result there are numerous auctions that provide the same product. For example only on ebay hundreds or even thousands of simultaneous auctions offer the same products.in this case each customer can buy a product at the lowest possible price. But searching between auctions in terms of finding the suitable product can be time consuming. So the need for an autonomous agent in these types of markets is deeply felt. On the other side the structure of an auction mechanism that provides the environment for traders to operate their trades is vital. The structure of old auction types was based on one side auctions like English auction or Dutch auction that were simple in terms of use and implementation while all new stock markets operate using double sided auction [1]. Auctions in general attract both economics and mathematicians and they view auctions as games of incomplete information, the complexity of research and analysis of double sided auctions [1] make it difficult for them to go further in this field. In order to promote and encourage high quality research into the trading agent problem and automated mechanism design a competition called CAT[3] (CATallactics) since 2007 have been added to high profile Trading Agent Competition (TAC)[11]. Participants are encouraged to run their own markets and set the policies inside them. Despite all the researches that have been done about online auctions, most of them were about single markets [5, 6, 7, 8]. But in real world the stocks and commodities of companies are listed and traded in different markets. For example most of the American companies trade in both NYSE (New York Stock Exchange) and NASDAQ (National Association of Securities Dealers Automated Quotations). More recent works by Niu et. al. [12, 13] have focused more on multiple markets and test the performance of different market 2008 SpringSim

2 policies in Continuous Double Auction. While [12] shows the effect of a pricing policy in reducing price fluctuation in multiple markets, [13] shows the effectiveness of different charging policies in such markets. Further in this paper [13] Niu et. al. suggest that traders in general are attracted towards lower charging markets, showing these markets generate more profit. Niu et. al. s results suggest that when comparing multiple markets with homogeneous charging policies, fixed charging policy outperforms others. By contrast, in heterogeneous markets there are lots of uncertainties to reach a general conclusion. Unlike previous works that focused on other aspects of the markets, here we try to work on accepting policy in multiple markets by introducing new accepting policies in double sided auctions. The rest of the paper is organized as follows: In Section 2 we provide a history of the CAT game. Section 3 contains an overview of the game. Section 4 and 5 describe CDA and PersianCAT Markets. In sections 6 and 7 we challenge the conventional accepting policy used in double auction markets like New York Stock Exchange by simulating CDA and PersianCAT markets and comparing them in different test runs. We conclude the paper by providing a better solution for accepting policy to improve the general performance of the markets. 2. CAT GAME HISTORY Trading in electronic markets is increasingly becoming both a commonplace economic activity and a topic of special interest within the Electronic Commerce, and Multi Agent Systems (MAS) research communities. The Trading Agent Competition (TAC) [11] is an international forum designed to promote and encourage high quality research into the trading agent problem. In 2007 CAT game was added to high profile Trading Agent Competition (TAC) [11]. CAT refers to CATallactics, which is the science of exchanges [10]. The potential of market mechanisms for controlling complex computing systems is a relatively recent phenomenon, and designers of distributed systems using such methods currently require the assistance of an expert game theorist or economist. The final goal of this competition is automated mechanism design, the automation of interaction mechanism design and the automation of strategyselection for participants in distributed computational systems. CAT is a collaborative effort between the universities of Liverpool, Southampton and Brooklyn College which is part of Market Based Control (MBC projects) and in summer 2007 CAT experienced its first finals [10]. 3. GAME OVERVIEW The game consists of trading agents (or simply traders), i.e., buyers and sellers and Specialists (Brokers). Each specialist operates and sets the rules for a single exchange market, and traders buy and sell goods in one of the available markets. In the CAT competition the trading agents are provided by the CAT game, whereas specialists (and the rules of the markets) are designed by the entrants. Each entrant is limited to operate a single market. A CAT game consists of a CATP server and several CATP clients, which may be trading agents or specialists (markets). As depicted in Figure 1 CATP clients do not talk to each other directly, instead they connect to the CATP server to communicate and the server responds to messages from clients and forwards information if needed [4]. Also the server passes the message to the registry which keeps a record of sent messages for robustness and security of the system. Figure 1. Different parts of CAT game 3.1 Traders Each trading agent has a trading strategy and a market selection strategy and private values for the goods being traded. The trading strategy is used to generate bids and asks (also called shouts), whereas the market selection strategy is used to select a market (specialist). Note that each trader is either a buyer or a seller and can not act as both of them. Each trader is furthermore endowed with a limited budget that they can spend within a trading day. This budget prevents a trader from paying excessively high fees Trading Strategies The trading strategies used in this paper for our experiments are the followings: Zero-Intelligence-Constrained (ZIC): One of the most prominent strategies that have been developed over the years is Gode and Sunder s Zero-Intelligence (ZI) trading strategy [7]. The ZI agent is not motivated to seek trading profits and ignores all market conditions when forming bids or asks. There are two types of ZI traders which are ZI-C and ZI-U traders. The former are subject to budget constraints and are not allowed to trade at loss. The latter, however, are allowed to enter loss-making transactions. In the CAT game, only ZI-C traders have been considered Zero-Intelligence-Plus (ZIP): The Zero-Intelligence Plus (or ZIP) strategy was first designed by Cliff & Bruten [6] to show that more than zero-intelligence is required to achieve efficiency close to that of markets with human traders. While the ZI strategy ignores the state of the market and past experience, the ZIP strategy uses a history of market information and is of the predictive class, adapting the agent s profit margin to the future market conditions. That is, the agent increases or lowers its profit margin to remain competitive in the market Gjerstad-Dickhaut (GD): The GD strategy [5] is based on a belief function that an agent builds to indicate whether a particular shout is likely to be accepted in the market. In the GD strategy, buyers form beliefs that a bid will be accepted and similarly sellers form beliefs that an ask will be accepted in the market. The traders form their beliefs on the basis of the history of observed market data and, particularly, on the frequencies of submitted bids and asks and of accepted bids and asks resulting in a transaction. Given this information, the bidding strategy is to submit the shout that SpringSim

3 maximizes the trader s own expected surplus, which is the product of its belief function and its risk-neutral utility function Roth-Erev (RE): The Roth-Erev algorithm is a strategy designed to mimic human game-playing behavior in extensive form games [8]. The strategy relies on the immediate feedback from interacting with the mechanism, namely the surplus that the agent was able to obtain in the most recent rounds of trading. This strategy is generalpurpose enough to be used with any auction-mechanism, even where the trader does not have access to market-data, for example, in repeated sealed-bid auctions Market Selection Strategy The market selection strategies implemented by CAT competition group are: Tr: the trader randomly picks a market. Tε: the trader treats the choice of market as an n- armed bandit problem which it solves using an ε- greedy exploration policy [2]. Unlike greedy selection that chooses the best market only upon its estimation profit (exploitation), ε-greedy tries to choose what it estimates to be the best market with probability 1-ε (exploitation) and acts randomly (ε) choosing from other available markets (exploration) othervise. Tτ: the trader uses the softmax exploration policy [2]. 3.2 Specialists Specialists facilitate trade by matching bids and ask and determining the trading price in an exchange market. Each specialist operates its own exchange market. Each entrant in the game is required to design a single specialist or market, which is achieved by implementing the following policies: Charging Policy This policy sets the fees which are charged to traders and other specialists who wish to use the services provided by the specialist. Each specialist is free to set the level of the charges (from zero up). These are the following: Registration fees. Fees charged for registering with a specialist. Information fees. Fees for receiving market information from a specialist. Shout fees. Fees for successfully placing bids and asks. Transaction fees. A flat charge for each successful transaction. Profit fees. A share of the profit made by traders, where a trader s profit is calculated as the difference between the shout and transaction price. The first 4 types of fees are each a flat charge and the last one is a percentage charged on the profit made by a trader. A trader pays the registration and information fees at most once every trading day Accepting Policy This policy determines which shouts (i.e., bids and asks) are accepted. A specialist has the option to reject shouts which do not conform to the specialist s policy. For example, a beat the quote policy requires a shout to beat the market quote. If the received shout violates this, it can be immediately rejected and will not be considered for a transaction, allowing the trader to submit a new shout Clearing Policy This policy determines when and how bids and asks are matched. For example, in the well-known continuous double auction, the market is cleared as soon as new shouts arrive. Note that in CAT competition we assume that only one type of good exists. In other words, each ask can be matched with a bid if it s price is lower or equal to the price of the bid and each bid can be transacted with a ask if it s price is equal or higher to that of the ask Pricing Policy This policy determines the transaction price of a matched bid and ask. The most common is to set the price half way between the bid and ask. 3.3 Game Procedure Each game consists of several trading days, and each day consists of several rounds. The number of days and rounds in the competition is confirmed by CAT organizer group and is announced at the start of the game. Also the number of traders and specialists in the game is broadcasted to all agents. Before the start of each day, the specialists are required to announce their price lists which is defined by charging policy. This information will be broadcasted to all traders and specialists. Once a day has started, traders can register with one of the specialists (and only one specialist). Their choice of specialist is determined by their market selection strategy and depends on both the announced fees for that day, such as the registration fee, but also on the profits obtained in previous days. Different traders can have different market selection strategies and the actual strategy used by a particular trader and the parameter settings remain hidden. We now discuss the actual trading. A day is divided into a number of rounds, during which traders submit shouts to the specialist they are registered with. Each shout specifies the limit price for a single unit of the traded good. For example if an ask has a $50 value it should be matched with a bid that is at least $50. A specialist has the option to either accept or reject a shout according to the specialist s accepting policy. Once a shout is accepted, it becomes active and remains active until a transaction is successfully completed or when the trading day ends or when it is replaced by another shout of that trader. For each trader only a single shout (for a single quantity of the goo can be active at any time. If a shout is accepted by the specialist the trader should pay shout fee and if a placed shout is transacted the trader is supposed to pay the transaction and profit fees. It is the specialist s task to match bids and asks (clearing policy) and to determine the transaction price (pricing policy). Matching bids and asks can be done at any time during a round, provided the transaction is valid. This requires the bid price to be higher or at least equal to the ask price, and the transaction price to be set at some point in-between the bid and the ask price. For complete 2008 SpringSim

4 information refer to overview of CAT [3] and communication protocol specification [9]. 3.4 Scoring Each specialist is assessed on three criteria on each Assessment Day, criteria will be normalized and then weighted equally (i.e., one-third each) to produce a score for each specialist for the assessment day. These three criteria are as follows: Profits The profit score of a specialist on a particular day is given by the total profits obtained by that specialist on that day as a proportion of the total profits obtained by all specialists on the same day. The profit score is thus a number between 0 and 1 (both inclusive) for each specialist for each day, and the profit scores for all specialists on the same day will sum to Market Share Of those traders who have registered with a specialist on a particular day, the market share score of a specialist on that day is the proportion of traders that have registered with that specialist on that day. Again, the market share score is a number between 0 and 1 (both inclusive) for each specialist for each day, and the market share scores for all specialists on the same day will sum to 1. If A1 is the number of traders registered with the first specialist in a trading day and N is the total number of traders, the market share for that specialist is (A1 N) and if A2 is the number of traders registered with the second specialist and so on and m is the total number of specialists for that trading day we have: (A1A2A3 Am) N = Transaction Success Rate The transaction success rate score for a specialist on a given day is the proportion of bids and asks placed with that specialist on that day which that specialist is able to match. Let us denote: Nb for the number of bids placed with a specialist on a given day, Na for the number of asks placed with that same specialist on the same day, Nm for the number of successful matches executed by that specialist from the bids and asks the specialist received that day. Then, the Transaction Success Rate Score for that specialist on that day is calculated as: 2 Nm Nb Na After Introduction of the CAT game, including traders and specialists (markets), we want to introduce and compare two different types of markets in the following sections. One of them named as Continuous Double Auction and the other one PersianCAT market. We will define their policies and compare their effectiveness in different test runs. 4. CDA MARKETS Continuous Double Auction (CDA) is the type of auction used in most of today s stock and commodity exchanges. In order to implement this type of market in CAT competition, following policies have been used. Note that in a real market multiple brokers (specialists) operate simultaneously in that market, however in CAT competition to reduce the complexity of the problem, each market represents only one specialist with strategies designed by that specialist. The following strategies of CDA market have been implemented by CAT competition organizers and have we no involvement in these strategies. 4.1 Charging Policy The charging policy used for CDA is fixed charging policy which keeps the fees charged by the specialist unchanged throughout the competition. 4.2 Accepting Policy What is the most indicative feature of CDA is the type of accepting policy used in this market which is Quote Beating Accepting Policy. In this policy each new coming shout must be more competitive to be accepted which means if it is a bid it must be higher than previously standing bid in terms of price and if it is an ask it should be cheaper than previously accepted ask. 4.3 Clearing Policy The type of clearing policy assigned for double sided auctions is probabilistic clearing policy which enables a market to clear with a probability when a new shout arrives. For this aim a Threshold number between 0 and 1is defined. This number shows the level of attraction of the simulated market towards clearing house or CDA, the lower end of the range being clearing houses and the higher being continuous double auctions. When a new shout arrives a random number between 0 and 1 is generated from a uniform distribution and if this number is below the threshold the action of clearing is performed. To simulate CDA market we have set the threshold value with 1 so that for every new arriving shout that a random number is created, because the value is lower than 1, it checks the possibility of transaction in that moment, making it work the same as CDA. 4.4 Pricing Policy Discriminatory Pricing Policy is the type of policy used for CDA. A pricing policy in which the transaction price is set in the interval between the matched shouts as determined by the parameter k. If this parameter is set to 0.5 the transaction price is exactly between the bid and the ask price. 5. PERSIANCAT MARKET In order to providing a better market compared to what was introduced as CDA we used a combination of policies as a new specialist. Some of these policies are new but some are exactly the same. 5.1 Charging Policy Fixed charging policy has been used for this agent the same as CDA. 5.2 Clearing Policy The clearing policy that we have used is Clear in Continuous Double Auction which in terms of operation is the same as probabilistic clearing policy with its threshold set to one. In this policy, after a shout is accepted it will be transacted if there is compatible shout, in terms of price, in the opposite column (ask or bid s column).otherwise if this shout is the outstanding shout in its column it will be transacted as soon as a compatible shout arrives in the opposite column SpringSim

5 5.3 Pricing Policy The pricing policy used here is Discriminatory pricing policy, the same as CDA, with parameter k set to Accepting Policy The new policies that we want to introduce exist in this part. Here we will define two new accepting policies which are Probabilistic Equilibrium Beating Accepting Policy and History Accepting Policy. We will implement them to measure their efficiency compared to CDA. 6. ACCEPTING POLICY PROBLEMS As we mentioned before, the markets in CAT competition are designed according to double side auctions [1]. In this type of auction there are multiple sellers and multiple buyers that participate in an auction in order to trade a commodity. Two common types of double side auctions are Continuous Double Auction (CDA) and Clearing House (CH). In continuous double auctions the buyers and sellers are matched immediately on detection of compatible bids, while in periodic double auctions also known as call markets or clearing houses, bids are collected over specified intervals of time and then the market clears at the expiration of the bidding interval. The accepting policy used in CDA markets like NYSE is Quote Beating that means each new bid must be higher than standing bid in terms of price and each new ask must be cheaper than the standing ask to be accepted. This type of accepting has some inefficiencies. Since in CAT game there are traders instead of human beings with different trading policies, the shouts generated by these traders can be far from the suitable shouts in terms of their price, so theoretically it can take a long time for the shouts to reach the equilibrium. For example if the consequence of arriving shouts is the same as in Figure 2 it is both time consuming and inefficient to reach a transaction. Ask Bid Figure 2. Arriving sequence of shouts In addition, because Transaction Success Rate (TSR) is a scoring factor, this type of accepting can lead to lost of unmatched shouts. In a test run by PersianCAT specialist with Quote Beating Accepting Policy, TSR was low with lots of fluctuations and in many days it was 0 which is the worst. You can see the result in Figures 3 and 4. These tests were conducted by GD [5] (Figure 3) and ZIC [7] (Figure 4) traders. In all figures from Figure 3 to Figure 7 horizontal axis represents number of trading days which in our experiments lasted for 200 days and vertical axis shows the scores. Figure 3. TSR of Quote Beating with GD traders Figure 4. TSR of Quote Beating with ZI-C traders 7. Solution We now introduce two new accepting policies for solving the existing problem and test them to examine their performances. 7.1 Probabilistic Equilibrium Beating Accepting Policy In this policy the first shout in the auction is accepted by a probabilistic function. This function checks the possibility of the transaction for new arriving shouts. If the possibility of the transaction is more than fifty percent shout is accepted. After accepting the first shout by this function we use Quote beating accepting policy which means only the first shout in the auction is accepted by these formulas and after that Quote beating accepting policy is used until all of the shouts in either of shout columns (ask or bi are transacted or cleared. As soon as the number of shouts in one column (ask or bi reduces to zero the equations are used to accept the first shout with higher possibility of transaction. In this case we start each auction by a shout with higher chance of transaction but still give the market the flexibility to choose the final transaction price in a point between the first accepted shouts. In this policy we introduce three different probabilistic formulas: 1) First probabilistic accepting formulas P(a)= AT( AT( B( d a B( BT( d a AN( (1) 2008 SpringSim

6 P(b)= d b ATd ( ) BTd ( ) BTd ( ) d b BNd ( ) 2) Second probabilistic accepting formulas B( P ˆ ( a) = (3) B( BT ( d a ˆ (4) P( b) = d b AT ( 3) Third probabilistic accepting formulas ~ P( a) = AT( AT( ( ) B( d B( d ) d a d ) d b ) AN( BT d P ~ ) ) ( b) = (6) d BT( d BN( d a B (2) (5) ( : The number of bids with prices higher or equal to a more bids with higher prices means more possibility of transaction for an ask. d a AT ( : The number of transacted asks with prices higher or equal to a, when more asks with higher prices have transactions, this ask with lower price has more chance for transaction. d a BT ( : The number of transacted bids with less or equal prices compared to 'a', when more bids with lower prices have transactions the possibility of transaction for an ask with higher price reduces. d a AN ( : The number of accepted but not transacted asks with less or equal prices compared to 'a', because more asks with lower prices that didn t have transactions means less chance for an ask with higher price to be transacted. d b A ( : The number of asks with prices less or equal to 'b', more asks with lower prices means more possibility of transaction for a bid. BT ( : The number of transacted bids with prices less or equal to 'b', when more bids with lower prices had transactions, this bid with higher price has more chance for transaction. d b BN ( : The number of accepted but not transacted bids with higher or equal prices to 'b', more bids with higher prices that didn t have transactions means less chance for a bid with lower price to be transacted. d b AT ( : The number of transacted asks with more or equal prices to 'b', because when more asks with higher prices had transactions the possibility of transaction for a bid with lower price reduces. For each pair of equations P(a) estimates the possibility of transaction for asks and P(b) checks this possibility for bids. The difference between these types is the usage of different factors. In the first pair all the possible options that could be effective have been used to check to what extend these factors are suitable, while in the second pair only the factors in opposite column (ask or bi have been used which means if this is a bid the possibility is checked by existing values in the ask column and vise versa. In this pair we want to check to what extend only considering factors in the opposite column and neglecting the factors in their own column can be useful. In the third pair the factor are the same as GD [5] trader s bidding strategy so that we can try the suitability of these equations for markets instead of traders. We have compared PersianCAT using these three types of accepting policy formulas with the conventional CDA that uses Quote beating Accepting Policy in different test runs. We do not just improve the TSR of the markets but do offer an agent which improves other criteria of the markets. In other words Market Share, Profit and TSR of the market have been improved by these specialists. This shows that accepting policy not only affects TSR but also other factors in the market. To do this we have done some experiments during 200 trading days using 100 traders. In different test runs we ve compared CDA specialist with 3 different PersianCAT specialists. We have tested these 4 specialists in different experiments in which we ve changed trader s trading strategies but in all of them trader s market selection strategy is Tε (ε=0.1, α=1).we have set α with 1 to have a constant ε (exploration) throughout our experiment. In all tables prob-1 represents PersianCAT with probabilistic equilibrium beating accepting policy that uses the first Formula, while prob-2 and prob-3 use the second and third formulas. All other policies of PersianCAT agent s are the same as what has been explained in section 5 and CDA represent CDA market using policies mentioned in section 4. All of scoring factors have been shown in these tables. For the aim of providing the same situation we ve set the fees for all 4 specialists the same that is 0 for information, registration, shout and transaction fees, and 1 for the profit fee. The results show that PersianCAT markets have a better general performance compared to CDA. In the first run illustrated by Table 1 only ZIC [7] traders have been used. In other test the same experiment have been done with the exception of changing trader s trading strategy. As you can in Tables 2, 3 and 4 GD, ZIP and RE traders have been used SpringSim

7 respectively. The figures in each table for each one of MS, TSR and Profit shows the sum of that factor over 200 trading days and for each day it is calculated as explained in section 3.4. The total score is the sum of these three criteria divided by 3. Table 1. Test result with ZIC traders Table 2. Test result with GD traders In these experiments PersianCAT specialists show a better performance than CDA but the worse performance happened when GD traders have been used. The result shows that when the specialists use an accepting policy close to the traders trading strategy the result is not satisfactory and specialists estimation of the shouts suitable for transaction becomes inaccurate. What s more, comparing probabilistic markets, Prob-1 shows a better performance compared to other probabilistic markets, showing the factors considered in its formulas are more efficient. Prob-2 that only considers criteria in the other column (ask or bi is less efficient than Prob-1 and Prob-1 s formula operates better for markets compared to Prob-3 s formula which is the same as GD s traders trading strategy. Since the above Tables just give the sum of scores achieved by specialists and they do not give a detailed view of fluctuations in the market we show you the trend of TSR in Figure 5. This diagram which belongs to Table 10 shows that Prob-1 had the best performance and Prob-2 and CDA have followed and the worst TSR belongs to the specialist with Prob-3 accepting policy. This graph suggest that by using specialist with probabilistic equilibrium beating accepting policy more efficiency is reached in the market compared to what CDA agents have achieved. Table 3. Test result with ZIP traders Table 4. Test result with RE traders In order to compare specialists with the combination of all traders, another test with mixed traders has been done. The result is shown in Table 5 and all of ZIC, GD, RE and ZIP traders have been used with the same quantity, 26 traders of each type. Table 5. Test result with mixed traders Figure 5. TSR of agents with mixed traders To provide a better performance when working with GD traders we introduce another policy and examine its efficiency by conducting separate tests. 7.2 History-Based Accepting Policy In this accepting policy the first shout in the auction is accepted from the range of transacted shouts in the previous trading day which means the first bid is accepted if it is equal or higher than the worst (the least) transacted bid in the previous trading day. After accepting the first shout by this method we use Quote beating accepting policy which means only the first shout in the auction is accepted by history policy and after that Quote beating accepting policy is used until all of the shouts in either of shout columns (ask or bi are transacted or cleared, so as soon as the number of shouts in one column(ask or bi reduces to zero the history policy is used to accept the first shout with higher possibility of transaction, the same as what happens for probabilistic equilibrium beating accepting policy. We have used the value of only one day of trading to be more adaptive with the market and avoid late reactions, also to give the market a better chance of floating and choosing their expected price, we have 2008 SpringSim

8 added a risk period to our accepting which extends the possible accepting range to avoid restrictions. If (shout is Ask) { If (shout < yesterday_max_transaction_ask risk_perio { Accept } else { Reject } } Else if (shout is Bi { If (shout > yesterday_min_transaction_bid - risk_period ) { Accept } else { Reject }} To test this policy we have conducted the same runs but this time one more specialist have been added which is a PersianCAT specialist with history accepting policy. The other policies are the same (PersianCAT policies). These experiments use 100 traders over 200 simulation trading days. Again 5 separate runs have been conducted. Table 6 shows the result of GD traders while Table 7, 8 and 9 demonstrate ZIC, ZIP and RE traders. All agents in the table are the same and history represents PersianCAT with history accepting policy. Table 6. Test result with GD traders Table 7. Test result with ZIC traders Table 8. Test result with ZIP traders Table 9. Test result with RE traders In order to compare all specialists with the combination of traders, another test with mixed traders has been done. Again all of ZIC, GD, RE and ZIP traders have been used with the same quantity, 26 traders of each strategy. The result is clear in Table 10. Table 10. Test result with mixed traders Figure 6. MS of agents with GD traders To show you one interesting result with this test run we illustrate MS of this experiment. As you can see in Figure 6 despite better overall performance by CDA agent, history specialist has a better MS after almost 70 days of trading, showing this specialist is more adaptable to the market and has a better performance in long term periods in attracting traders. What s more the final score is very close and CDA has a better score thanks to its higher TSR in the market. As it is clear by the results in the Table 6 with GD traders, CDA still has a better performance but History specialist has reduced the gap by a close margin compared to results of Table 2 where CDA has dominated the market. It was completely unpredicted that CDA agents had a better performance with ZIP traders (Table 8) compared to results of Table 3 in which Prob-1 performed better than others. It shows even in the same market, by the same traders and only due to adding a specialist the situation will differ as CDA agent has dominated the market, but when regarding TSR score there is a small gap between CDA and prob-3 specialist showing probabilistic specialists are still doing well in this field. For ZIC traders History market shows a better performance (Table 7) compared to others while with RE traders Prob-3 and SpringSim

9 Prob-1 have performed better in both Table 4 and Table 9. What s more, Table 10 suggests that PersianCAT with the second formula that in none of the previous test runs was the leading specialist has the best performance. In both Tables 5 and 10 with mixed traders specialists with Probabilistic Equilibrium Beating policy have performed better. While in Table 5 prob-1 has performed better, in Table 10 prob-2 has better efficiency. In both of them that the specialists don t know what kind of traders they can expect, probabilistic specialists perform better compared to others, so in these types of markets they are more suitable. All the results show that the state of the market is undetermined and it can t be predicted to have a dominant agent for all of the markets but in general new markets had a better performance in most of the test runs. To give a general view of fluctuations in the market with mixed traders, we show you the following graph which is the TSR of the specialists in the experiment related to Table 10. As is it clear in Figure 7, specialists with probabilistic equilibrium beating accepting policy manage to perform better, knowing the maximum possible TSR in each day is 1, and got a better TSR compared to the CDA specialist and are more adaptable to markets with multiple traders. Figure 7. TSR of agents with mixed traders 8. Appendix Final CAT game included two finals which were held on Monday and Wednesday 23th and 25th of July 2007 in Vancouver Canada in conjunction with AAAI conference. PersianCAT agent competed with 9 other specialist from the US, England, Romania, Greece, Croatia and Australia and hold the sixth position. The result is on MBC Project website [10]. 9. Acknowledgment We appreciate Dr. Farhang Daneshmand s support by providing us with a research lab in the Premier Ideas Support Center of Shiraz University. We are also grateful to Mr. Mehdi Liaghat internal manager and Mr. Yousef Bazargan-Lari, project manager of Premier Ideas Support Center, for their cooperation. Finally we have the honor of consulting with Dr. Mehdi Dastani from Utrecht University. 10. CONCLUSION In this paper we introduced two new accepting policies to improve the performance of markets that use double side auctions and we conducted different tests using different trader s trading strategies. Despite lack of a dominant market in all of the experiments, in general PersianCAT markets have better performance and they have produced better TSR, MS and profit, making these markets more efficient in most of the experiments. Considering PersianCAT markets, Probabilistic Equilibrium Beating Accepting Policy has produced better results especially when dealing with traders using different strategies that the market is unaware of them. History Accepting Policy works more efficiently with GD traders but still fails to beat CDA markets by its performance. We plan to repeat the existing experiments over longer periods to make sure the results are trustful in a stable market. Also we plan to optimize existing accepting policies to achieve better TSR and more efficiency in the market. In this case our objective is to be more predictive about the trend of the market and have a better estimation of the behavior of traders in the market. 11. REFERENCES [1] Friedman, D., and Rust, J The double auction market: institutions, theories and evidence. Cambridge, MA: Perseus Publishing, [2] Sutton, R. S., and Barto, A. G Reinforcement learning: an introduction. Cambridge, MA: MIT Press. [3] Gerding, E., McBurny, P., Niu, J., Parson, S. and Phelps, S Overview of CAT: a market design competition. University Of Southampton, University Of Liverpool, Brooklyn College, Version 1.1 June [4] Gerding, E., McBurny, P. and Parson, S TAC market design: plannig and specification. Version 1.03, [5] Gjerstad, S. and Dickhaut, J Price formation in double auctions. Games and Economic Behaviour, 22:1-29, [6] Cliff, D Minimal-intelligence agents for bargaining behaviours in market-based environments. Technical Report HP-97-91, Hewlett-Packard Research Laboratories, Bristol, England. [7] Gode, D. K. and Sunder, S Allocative efficiency of markets with zero-intelligence traders: market as a partial substitute for individual rationality, Journal of Political Economy, 101(1): [8] Erev, I. and Roth, A. E Predicting how people play games: Reinforcement learning in experimental games with unique, mixed strategy equilibria. American Economic Review, 88(4): [9] Niu, J. and Parsons, S CAT document 001, TAC market design: communication protocol specification, version [10] [11] [12] Niu, J. Cai, K. Parsons, S. and Sklar, E Reducing price fluctuation in continuous double auctions through pricing policy and shout improvement. In Proceedings of the 5th AAMAS Conference. [13] Niu, J. Cai, K. Parsons, S. and Sklar, E Some preliminary results on competition between markets for automated traders. American Association for Artificial Intelligence SpringSim