RECURRENT AUCTIONS IN E-COMMERCE

Transcription

1 RECURRENT AUCTIONS IN E-COMMERCE By Juong-Sk Lee A Thess Submtted to the Graduate Faculty of Rensselaer Polytechnc Insttute n Partal Fulfllment of the Requrements for the Degree of DOCTOR OF PHILOSOPHY Major Subject: Computer Scence Approved by the Examnng Commttee: Dr. Boleslaw K. Szymansk, Thess Advser Dr. Chrstopher Carothers, Member Dr. Mukka Krshnamoorthy, Member Dr. Thagarajan Ravchandran, Member Rensselaer Polytechnc Insttute Troy, New York December 2007

2 Copyrght 2007 by Juong-Sk Lee All Rghts Reserved

3 CONTENTS LIST OF TABLES... v LIST OF FIGURES... v ACKNOWLEDGMENT...v ABSTRACT... x 1. INTRODUCTION An Aucton as a Dynamc Prcng Mechansm Challenges of Aucton Mechansms Scope of the Thess The Approach Thess Outlne BACKGROUND Introducton Basc Defntons Types of Basc Aucton Mechansms Sngle Aucton Mechansms Double Aucton Mechansms Extended Types of Aucton Mechansms General Procedure of an Aucton Mechansm Requrements for the Optmal Aucton Mechansm Analyss of Bddng Behavor Summary of the Chapter E-MARKETPLACES FOR AUCTION MECHANISMS Introducton Aucton Mechansms n E-Commerce Aucton Mechansms n Markets for Network Servces Aucton Mechansm n Markets for Computng Servces... 24

4 3.5 Aucton Mechansms n the Internet Search Engne Marketng Analyss and Characterzaton of New Aucton Markets Summary of the Chapter AN OBSERVATION UNDERPINNING THE RESEARCH Introducton Analyss of Newly Dscovered Problems Verfcaton of the Dscovered Problem Summary of the Chapter NOVEL AUCTIONS FOR HOMOGENEOUS MARKETPLACE Introducton Illustraton of the Man Idea Partcpaton Incentve Optmal Recurrng Aucton Novel Wnner Selecton Strategy Partcpaton Incentve Bdder Drop Control (PI-BDC) The Prcng Rule and the Optmal Auctoneer s Bd Prce The Optmal Strateges for Bdders Smulatons Experments and Results Smulaton Scenaros Analyss of Smulaton Results Dscrmnatory Prce Optmal Recurrng Aucton Wnner Selecton Strateges VLLF Bdder Drop Control Algorthm Optmal Dstrbuton of Resources Smulaton Experments and Results Smulaton Scenaros Analyss of Smulaton Results Summary of the Chapter v

5 6. NOVEL AUCTION FOR HETEROGENEOUS MARKETPLACES Introducton Partcpaton Incentve Generalzed Vckrey Aucton A Novel Wnner Selecton Strategy The prcng Rule of PI-GVA The Optmal Strategy for Bdders n PI-GVA Smulaton Experments and Results Smulaton Scenaros Analyss of Smulaton Results Summary of the Chapter SUMMARY AND FUTURE WORK Thess Summary Contrbutons Future Research LITERATURE CITED v

6 LIST OF TABLES Table 1.1: The market structure classfcaton... 4 Table 5.1: The nterrelatonshp of bdder s classes Table 5.2: Loss of farness v

7 LIST OF FIGURES Fgure 2.1: A classfcaton of basc aucton type Fgure 2.2: General procedures of an aucton Fgure 3.1: Aucton based economc model for computng servce markets Fgure 3.2: A comparson of the average cost per lead to purchase Fgure 4.1: The problems resultng from applcaton of tradtonal aucton mechansm to markets of a recurrng nature for pershable resources Fgure 4.2: A coeffcent of the Optmal Bd (OBP) Fgure 4.3: The bdder drop problem n the DPSB and UPSB auctons Fgure 4.4: The resource waste problem n the DPSB aucton Fgure 5.1: The demand and supply prncple Fgure 5.2: The classes of bdders n PI-ORA Fgure 5.3: The wn probablty dstrbuton n PI-ORA Fgure 5.4: Resources allocaton farness n PI-BDC Fgure 5.5: The Average Aucton Clearng Prce Fgure 5.6: The Mechansm Stablty n PI-ORA Fgure 5.7: The number of wn dstrbutons Fgure 5.8: Impact of the selecton of the reservaton prce Fgure 5.9: The average wnnng prce of wnners Fgure 6.1: Revenue comparson of TGVA and PI-GVA v

8 ACKNOWLEDGMENT TO MY LOVELY WIFE HAESOO, MY PRINCESS EUNICE AND MY MOTHER I would frst lke to thank my advsor, Clare and Roland Schmtt Dstngushed Professor Boleslaw K. Szymansk, who has encouraged and mentored me throughout my doctoral study. Addtonally I also thank all of my commttee members: Prof. Chrstopher Carothers, Prof. Mukka Krshnamoorthy and Prof. T. Ravchandran. Fnally, I would lke to thank my mother for her supports and her belef n me. I would also lke to thank my lovely wfe Haesoo for her dedcaton to me and my daughter Eunce who s a constant source of my happness. v

9 ABSTRACT Recent developments of nformaton technologes are causng shft from fxed prcng to dynamc prcng mechansms n electronc marketplaces. The latter can mprove revenue and resource utlzaton. However, the dynamsm makes seller s prce decson and buyer s budget plannng dffcult. Aucton based dynamc prcng and negotaton mechansm can resolve such dffcultes because prce emerges from buyer s (.e., bdder s) wllngness to pay. Thanks to these advantages and nherent negotaton nature, the applcaton doman of aucton as dynamc prcng and negotaton mechansm covers servce orented electronc short-term contract marketplaces. Auctons n such markets are recurrng snce the contracts must be offered repeatedly for specfc tme ntervals. In such recurrng aucton, uneven wealth dstrbuton of bdders causes the least wealthy bdders to persstently lose aucton rounds that motvate them to drop out of recurrng aucton. Ths bdder drop problem arses also n the tradtonal combnatoral wnner selecton strategy that only focuses on revenue maxmzaton. The bdders droppng out of an aucton decrease prce competton and may cause a collapse of market prce. At the same tme, all avalable resources for fulfllment of electronc servces must be sold n each aucton round to avod waste of resources. For these reasons, the prevously desgned tradtonal basc aucton mechansms may not be effcent n such servce orented electronc marketplaces. To overcome these problems, ths thess proposes and evaluates novel aucton mechansms for sellng short-term contracts n servce orented electronc marketplaces. For homogeneous market structure n whch bdders requrements are homogeneous, we propose a Partcpaton Incentve Optmal Recurrng Aucton (PI-ORA) mechansm that s ncentve compatble and a Dscrmnatory Prce Optmal Recurrng Aucton mechansm that s not ncentve compatble. Compared to the tradtonal basc aucton mechansms, the proposed mechansms (.e., PI-ORA and DP-ORA) stablze the market prces and ncrease the auctoneer s revenue by preventng the bdder drop problem and avodng the resource waste problem. Addtonally, the proposed mechansms acheve better long-term farness of resource allocatons. For markets n whch bdders x

10 requrements are heterogeneous, we propose and evaluate a Partcpaton Incentve Generalzed Vckery Aucton (PI-GVA) mechansm. Compared to the tradtonal Generalzed Vckery Aucton mechansm, the proposed PI-GVA mechansm prevents market prce collapse and stablzes the market by a novel combnatoral wnner selecton strategy n whch bdder s partcpaton s drectly rewarded. The three proposed mechansms also acheve other desrable propertes for aucton mechansm such as lght communcaton overhead needed to reach agreement between auctoneer and bdders, the smple bdder s optmal strategy that s desrable for mplementng an aucton n electronc envronments, and the dstrbuted resources allocaton. x

11 1. INTRODUCTION 1.1 An Aucton as a Dynamc Prcng Mechansm In recent years, wth the development of nformaton technologes and expanson of electronc marketplaces, the role and mportance of effcent prcng mechansm has been constantly ncreasng. In many exstng electronc marketplaces, fxed prcng or statc tme-dfferental prcng mechansms are wdely used because of ther smplcty. However, there s a natural varaton n buyer s demand over tme. For ths reason, those prcng mechansms are neffcent. They lead to under-utlzaton of resources when demand s low and under-prcng when demand s hgh. In a statc tme dfferental prcng mechansm two or more ters of on/off peak rates can mprove effcency by partally matchng lower (hgher) demand wth lower (hgher) prce. However, ths mechansm stll remans nflexble, snce demands of buyers do not follow a step functon, but rather gradually shft from on- to off-peaks and back [54]. A contnuously adjustable dynamc prcng mechansm that adapts to changng market condtons constantly s more effcent. It can maxmze resource utlzaton and the seller s revenue n varety of market condtons. Durng low utlzaton perod, low prce nvoked by the adaptve prcng can ncrease competton. Durng the hgh demand perod, hgh prces ncrease the seller s revenues. Moreover, wth such a mechansm, the prce tself becomes an mportant sgnal of controllng far resource allocaton. Hence, by ensurng that prces match current market condtons, fully adjustable dynamc prcng mechansms create a favorable outcome for both buyers and sellers. However, ths very dynamsm of those prcng mechansm makes seller s prcng decson and buyer s budget plannng dffcult. An aucton mechansm mtgates those dffcultes snce the prce emerges from the bdder s (buyer s) wllngness to pay. Hence, auctons elmnate the need for defnng a dynamc prcng structure from the seller s pont of vew and prces are decded by buyer s sde from the buyer s pont of vew. 1

12 Auctons that have been used from ancent tmes are one of the most popular market mechansms used to match supply wth demand today. They acheve ths goal by allowng buyers and sellers to establsh a mutual agreement on the product or servce prce, and the correspondng allocaton of resources to partcpants s governed by the well establshed rules and procedures. Addtonally, usng aucton as a basc dynamc prcng mechansm n electronc market envronments yelds the followng benefts: A smplfed prcng mechansm: An aucton based prcng mechansm s easly understood by market partcpants - both the buyers (bdders) and the sellers (auctoneer). A decentralzed prcng: Prces emerge from the buyer s valuaton of resources and are determned by the market on the bass of the demand and supply. Compatblty wth automated negotatons: Negotatons are an mportant part of commercal actvtes n physcal and electronc market envronments based on dynamc prcng mechansm [3]. Well defned rules and procedures of an aucton mechansm ease the dffculty and cost of the mplementaton of the automated negotatons n electronc envronments. 1.2 Challenges of Aucton Mechansms Accompanyng the recent expanson of electronc envronments, ncludng the Internet, s the growth n use of varous aucton mechansms as tools for dynamc prcng and automated negotatons n electronc commerce markets. The fracton of electronc commerce marketplaces that use aucton mechansm s rapdly ncreasng. Addtonally, 2

13 thanks to the aucton s nherent negotaton nature 1, applcaton doman of aucton mechansms have been extended to newly arsng markets. Of partcular nterests to ths thess are servce orented electronc marketplaces such as the ones for network servces, grd computng servces (ncludng utlty computng servces), and so on. An aucton n such markets s n fact a recurrng aucton, because allocaton of servce orented resources s made for a specfc tme only, and once the allocated resources become free, the seller (.e., auctoneer) needs to offer them to the buyers (.e., bdders) agan. Moreover, the resources are pershable, that s the unused resources cannot be stored for future use and are lost f unused. The computatonal power and the network bandwdth are examples of such resources, as are the arplane seats or concert tckets. We have observed that applyng tradtonal aucton mechansms to such newly created servce orented electronc marketplaces may result n an nevtable starvaton for resources for certan bdders based on ther valuaton of the resources because of recurrng nature of the marketplaces. Frequent starvaton may decrease bdder s nterests n partcpatng n an aucton. As a result, the affected bdders may decde to drop out of the future aucton rounds, thereby decreasng the long-term demand for the traded resources. Snce an aucton s non-cooperatve competton based dynamc prcng and negotaton mechansm, the lowered demand wll lead to the collapse of the value of bds that wn an aucton round and the resultng auctoneer revenue. The concluson s that to stablze revenues n a recurrng aucton for pershable resources, the auctoneer must prevent prce collapse that requres controllng the supply of resources and solvng the bdder drop problem. Ths thess dentfed ths problem and also attempts to resolve t by ntroducng novel aucton based dynamc prcng and negotaton mechansms. 1.3 Scope of the Thess The scope of ths thess s defned n terms of the market structure and propertes of the traded resources of the newly arsng servce orented electronc marketplaces. As 1 The varous aspects of an nherent negotaton nature of aucton mechansms are dscussed n several references. see for example [2, 8, 10, 26]. 3

14 shown n Table 1.1, a market structure can be classfed based on the number of partcpants, the number of traded resources and the knds of these resources [3]. Ths thess focuses on markets n whch there are one-to-many partcpants (.e., one seller and many buyers) and multple unts of homogeneous or heterogeneous resources. In markets tradng homogenous resources, buyers requests are homogeneous (for example, bdders request the same number of resource unts). On the other hand, n markets for heterogeneous resources, the buyers make heterogeneous requests (for example, each bdder requests the dfferent number of resource unts). From the traded resource perspectve, ths thess focuses on developng auctons for multple unts of pershable resources that are sold recurrently for a specfc tme nterval. Hence, multple wnners are selected for a specfc tme perod, an aucton round, but the resources that are not sold can not be stored for future sale, and persh for the correspondng round. Traded Resources Number of Sngle Unt Multple Unts Partcpants Homogeneous Heterogeneous Homogeneous Heterogeneous 1 to 1 1 to N M to N Table 1.1: The market structure classfcaton 1.4 The Approach Ths thess focuses on developng novel aucton mechansms that can resolve challenges descrbed n the prevous secton for newly created servce orented homogenous and heterogeneous electronc marketplaces. The aucton mechansms proposed n the thess 4

15 prevent potental revenue collapse by resolvng bdder drop problem n the recurrng aucton. For homogeneous market structure, we propose the Partcpaton Incentve Optmal Recurrng Aucton (PI-ORA) that s ncentve compatble and the Dscrmnatory Prce Optmal Recurrng Aucton (DP-ORA) that s not. We also propose the Partcpaton Incentve Generalzed Vckery Aucton (PI-GVA) for heterogeneous markets. The common dea underlyng these three aucton mechansms s to provdng rewards for bdder s partcpaton n an aucton round to mantan prce compettons and prevent bdder drop. In PI-ORA mechansm, when a bdder partcpates n aucton, ts wn probablty n future aucton rounds ncreases as ts wnnng score grows. At the same tme, the resources are allocated proportonally to the bdders bds made durng recurrng aucton. Hence, least wealthy bdders can be selected wnners durng recurrng aucton wth wn frequency proportonal to ther bds. In DP-ORA mechansm, the auctoneer allocates the traded resources nto bdders lkely to drop out of the aucton based on ther bds and track record of wns. In PI-GVA mechansm for markets wth heterogeneous resources, auctoneer selects a combnaton of bdders requests that maxmzes the sum of wnnng scores of the selected bdders. Bdder s partcpaton s rewarded by ncreasng ts wnnng score n the forthcomng aucton rounds and such ncreased wnnng score also ncreases the probablty that the bdder wll be ncluded n the wnnng combnaton of bdders. In addtonal to resolvng bdder drop problem, our approach to desgnng novel aucton mechansms also attempts to mnmze the overhead of communcaton needed to reach an agreement between the auctoneer and the bdders as well as to smplfy the bdder s optmal strategy, so t could be mplemented easly n agent based electronc envronments. 5

16 1.5 Thess Outlne Ths thess focuses on provdng effcent aucton-based dynamc prcng and negotaton mechansms for emergng servce orented electronc marketplaces. The remnder of the thess s organzed as follows. In chapter 2, we defne basc terms that are used n ths document and we survey the exstng basc types of aucton mechansms and ther extended forms that are currently used n practce or were proposed n the lteratures. We also defne a general procedure common to all aucton mechansms, and analyze the bdders bd behavor n terms of ther rsk management patterns. The gudelnes for desgnng optmal aucton mechansms that am at maxmzng seller s revenue are also descrbed n ths chapter. In chapter 3, we survey varous newly arsng servce-orented electronc marketplaces n whch auctons can be used as a dynamc prcng and negotaton mechansm. We also analyze and defne those propertes of such marketplaces that affect the bd behavor of bdders and the revenue of an auctoneer. In chapter 4, we dscuss an observaton underpnnng the research that problems arse when tradtonal aucton mechansms are appled to newly arsng servce orented electronc marketplaces. We defne these problems for both homogeneous and heterogeneous markets. We also verfy ther exstence by usng a theoretcal analyss and smulatons of auctons n such envronments. In chapter 5, we propose two novel aucton mechansms that focus on resolvng the dscovered problems for markets for homogeneous resources: the Partcpaton Incentve Optmal Recurrng Aucton (PI-ORA) that s ncentve compatble and the Dscrmnatory Prce Optmal Recurrng Aucton (DP-ORA) that s not. Varous smulatons and ther analyses verfy the observed desred propertes of the proposed novel aucton mechansms. 6

17 In chapter 6, we defne and analyze a potental market collapse problem that arses when the tradtonal combnatoral wnner selecton strategy s used n heterogeneous market wth recurrent aucton and pershable resources. To resolve ths problem, we propose the Partcpaton Incentve Generalzed Vckery Aucton (PI-GVA) that rewards bdder s partcpaton n the aucton and stablzes market prces by mantanng prce compettons. We also verfy the proposed aucton mechansm by varous smulatons and analyses. Fnally, n chapter 7, we summarze the thess and enumerate ts contrbutons. We also defne possble future research work. 7

18 2. BACKGROUND 2.1 Introducton An aucton s an effcent negotaton and dynamc prcng mechansm that resolves the, resource allocaton problems n one-to-many and many-to-many market structures. For ths reason, aucton mechansms are wdely used n varous electronc marketplaces. The techncal nfrastructure requred to support an aucton n an electronc envronment s currently avalable and well accepted [54]. Addtonally, the well defned rules and procedures of aucton mechansm are easy to mplement. To desgn optmal aucton mechansms for electronc marketplaces of nterest to ths thess, approprate basc aucton mechansms should be surveyed and analyzed frst, what s done n ths chapter. In the next secton, the basc defntons that are used n ths thess are provded. In secton 2.3, basc aucton mechansms, wdely used n varous markets, are descrbed. A general procedure of aucton mechansms s explaned n secton 2.4, and secton 2.5 descrbes the requrements of optmal aucton mechansms that maxmze the revenue of an auctoneer. The bd behavor of bdders s descrbed n secton 2.6. Fnally, secton 2.7 summarzes the chapter. 2.2 Basc Defntons By the defnton gven by McAfee and McMllan, an aucton s a market nsttuton wth an explct set of rules matchng supples wth demands for the traded resources 2, and determnng prces on the bass of bds from the market partcpants [4]. There are two types of players n aucton mechansm. One s a bdder and the other s an auctoneer. Bdder: Bdder makes ther bds to the auctoneer to buy or occupy traded resources n an aucton market. The bd may consst of a prce alone or a prce n combnaton 2 Traded objects are called resources, goods or products. In ths paper, we unformly use the term resources n order to denote them. 8

19 wth other attrbutes, such as quantty, delvery tme, etc. Hence, we refer to a valuaton of the entre bd that could be a combnaton of a prce and other attrbutes as a bd value n ths document. Auctoneer: An auctoneer creates an aucton, selects wnners for traded resources and closes the aucton by collectng the prces from and dstrbutng resources to the wnners. From the market types perspectve, varous buyers (or customers) and sellers become bdders and auctoneers, respectvely, n a general aucton mechansm. In contrast, a buyer becomes an auctoneer and many sellers become bdders n a reverse aucton mechansm. A person, a computerzed agent, or a company such as a servce provder can be bdders or auctoneers n an aucton mechansm. The thrd partes, such as varous types of brokers can also be auctoneer or bdders. Hence, n ths document, we use the term bdder to denote the buyer or bdders n general aucton mechansm, and use the term auctoneer to represent seller, or servce provder n such a mechansm. The bd of each bdder s dependent on the bdder s valuaton of the traded resource. Addtonally, each bdder has the lmt on her bds whch s her valuaton of the traded resources. Ths upper bound of a valuaton of each bdder s called as the bdder s true valuaton of the traded resource. 2.3 Types of Basc Aucton Mechansms The commonly used basc aucton mechansms can be classfed nto the followng two man categores based on the number of bddng sdes: a sngle aucton and a double aucton [2,3,6]. In a sngle aucton, partcpants can take part only n one sde of an aucton (.e., be ether an auctoneer or a bdder). In a double aucton, partcpants are free to take part n both sde of an aucton. Fgure 2.1 shows the classfcaton of basc types of aucton mechansm. 9

20 2.3.1 Sngle Aucton Mechansms Ths type of aucton can be dvded nto an open-outcry aucton and a sealed bd aucton based on bddng methods. In an open-outcry aucton, the bds are open to publc and bdders can adjust ther bds n the full knowledge of other bds. In a sealed bd aucton, only a bdder and the auctoneer can communcate wth each other, and bdder to bdder communcaton s forbdden. The basc sngle aucton sub-types wth open-cry bd are Englsh and Dutch auctons: 1) Englsh aucton In an Englsh aucton, an auctoneer creates an aucton market and proceeds to solct n open successvely hgher bds from the bdders untl no one rases the bd. The hghest bdder s the wnner and pays the prce he/she bd. 2) Dutch aucton An auctoneer announces the bds to all bdders. The auctoneer starts the bddng at an extremely hgh prce and then progressvely lowers t untl a buyer clams an tem by callng "mne", or by pressng a button that stops an automatc clock. The wnner pays the prce bd at the stop tme. The Englsh aucton s wdely used n offlne and onlne envronments to sell varous resources such as art, collectables, electronc devces, and so on. The Dutch aucton s used for sellng tradtonal pershable resources such as flowers and fsh. On the other hand, the basc sngle aucton types wth sealed bds nclude the Frst Prce Sealed Bd (FPSB) aucton and the Second Prce Sealed Bd (SPSB) aucton: 3) Frst Prce Sealed Bd (FPSB) aucton In an FPSB aucton, when a sngle unt of a resource s traded, each bdder submts one sealed bd n gnorance of all other bds to the auctoneer. The bdder wth the hghest bd s the wnner of the aucton and pays ts bd for the sngle resource traded. When multple unts of resources are traded, sealed bds are sorted from the hghest to the lowest, and tems are allocated to the bdders n the decreasng order of the bds untl all 10

21 avalable resource tems are allocated. The wnners pay ther bds, hence dfferent prces for each tem. Ths aucton mechansm s known as Dscrmnatory Prce Sealed Bd (DPSB) aucton [6]. 4) Second Prce Sealed Bd (SPSB) aucton An SPSB aucton s smlar to the FPSB aucton, snce each bdder submts one sealed bd and the hghest bdder becomes the wnner. However, the selected wnner pays the prce that s equal to the second-hghest bd. Ths aucton mechansm s also called the Vckrey Aucton [5]. When multple unts of resources are traded, sealed bds are sorted from the hghest to the lowest, and unts of resources are allocated to bdders n the order of ther bds untl ther supply s exhausted. The wnners pay the hghest bd among the losers. Hence, ths type of aucton mechansm s called a Unform Prce Sealed Bd (UPSB) aucton mechansm [6]. Vckrey proved theoretcally that the optmal bd that maxmzes each bdder s expected utlty n the SPSB aucton s her true valuaton [5]. Ths property s known as ncentve compatblty whch s very desrable for an aucton mechansm that ams at maxmzng the seller s revenue. The specfc explanaton of ncentve compatblty s ncluded n secton 2.4 of ths thess. Vckrey also showed that the average expected revenue of the Englsh aucton, the FPSB aucton and the SPSB aucton are same n an IPV (Independent Prvate Value) model wth rsk neutral bdders [5]. Ths s also known as the revenue equvalence theorem. The detal explanaton of rsk neutralty s gven n secton 2.4. The FPSB and SPSB aucton mechansms are wdely used n procurement envronments Double Aucton Mechansms A double aucton admts multple buyers and multple sellers concurrently nto the market. Thus, the double aucton must match bds of the both sdes n the market. The double aucton can be dvded nto two man classes based on the aucton clearng tme: Call Market and Contnuous Double Aucton (CDA). In a Call Market, bds are collected 11

22 over a specfc tme nterval from both sellers and buyers n a sealed manner. Then, bds are matched at the aucton clearng tme. In contrast, n CDA, an aucton s contnuously cleared each tme a new bd (whch s delvered n an open-outcry manner) s delvered. The Call Market and CDA are common mechansms for fnancal markets such as a stock exchange. Open-outcry Ascendng Englsh Sngle Aucton Sngle Item Descendng Dutch Frst Prce Sealed Bd Aucton Sealed Bd Multple Items Second Prce Sealed Bd Dscrmnatory Prce Sealed Bd Unform Prce Sealed Bd Sealed Bd Call Market Double Aucton Open-outcry Contnuous Double Aucton Fgure 2.1: A classfcaton of basc aucton type Extended Types of Aucton Mechansms Beyond the descrbed above classfcaton of the tradtonal basc aucton types, the followng extensons to the basc aucton have been proposed. 1) Mult-attrbute Aucton (MA) A Mult-attrbute Aucton allows bdders to bd on varous attrbutes beyond the prce. In ths type of an aucton, the auctoneer selects wnners based on the prce as well as on 12

23 those varous attrbutes. Thus, the overall utlty of a deal for the buyer must consder not only the prce of the auctonng tem, but also a combnaton of the dfferent attrbutes. Ths dfference s a major change from the tradtonal basc aucton mechansms whch negotate only on prce. Bchler, et al descrbe generc procedures of a Mult-attrbute Aucton n electronc procurement envronments [3, 8]. A buyer frst has to defne her preference for certan goods n terms of varous attrbutes n a form of a utlty functon. The buyer has to reveal her utlty functon to supplers. A suppler should bd based on ths utlty functon. The mechansm selects the suppler who produces the hghest overall utlty for the buyer (.e., the bdder who best fulflls the buyer s preferences). The utlty functon of a Mult-attrbute Aucton s based on the Mult-Attrbute Utlty Theory (MAUT) [26]. The most wdely used mult-attrbute utlty functon n a Multattrbute Aucton s an addtve utlty functon that s defned as follows: U( xj) = U( x j ) n = 1, (2-1) where, x j denotes the bd for attrbute = 1.. n, made by the bdder j, U( x j ) represents the buyer s evaluaton of the bd x j, and U ( x j ) denotes the overall utlty of each bd attrbute x j assgned by the bdder j. The Mult-attrbute Aucton s also called a multdmensonal aucton. 2) Combnatoral Aucton In a Combnatoral Aucton, each bdder offers a bd for a collecton of resources (of the bdder's choosng) rather than placng a bd on each tem separately. Ths enables the bdder to express dependences and complementartes between varous resources. The auctoneer selects such set of these combnatoral bds that result n the hghest revenue wthout assgnng any tem to more than one bdder. Snadholm showed that the number m of possble allocatons n a combnatoral aucton s Ο ( m ), where m s the number of tems traded n the aucton. He also proved that selectng the aucton wnners n such a way that the revenue s maxmzed s NP-complete [10]. Several researchers have tred 13

24 to solve ths problem. Rothkof, at al. use a dynamc programmng approach whch takes m Ο(3 ) steps to fnd an approxmate soluton [22]. Sandholm proposes a search algorthm for wnner determnaton n polynomal tme under the severe restrctons such as number of bds [10]. He also descrbes the Internet based e-commerce server, called emedator, whch mplements several relevant procedures and protocols, ncludng an aucton house wth a generalzed combnatoral aucton [23]. 3) Generalzed Vckrey Aucton (GVA) Another mechansm for determnng prces for an allocaton of multple unts of resources s the Generalzed Vckrey Aucton [26]. In GVA, the prce of a bdder k n the effcent allocaton s computed by deductng the sum of payments of all other bdders n an allocaton from the sum of the payments that would be obtaned from those bdders n the optmum allocaton where the bdder k removed from the allocaton. The GVA mechansm s an ncentve compatble drect mechansm n whch the true valuaton bddng s a domnant strategy (.e., such bddng maxmzes each bdder s expected utlty). 2.4 General Procedure of an Aucton Mechansm In the current state of art, all aucton mechansms can be descrbes by the sx-step process descrbed below and shown n Fgure 2.2 [56]. 1) Bd Collecton and Valdaton The bd collecton and valdaton procedure collects the bds from the players partcpatng n the markets. Bds may be frm (.e., not revsable or cancelable) or changeable under predefned rules. Any set of predefned rules can be used for elgblty of the bd and bdder to partcpate n relevant aucton, ncludng but not lmted to, legal restrctons, credt lmts on partcular bdders, bdders budget lmts, bd expry, mnmum/maxmum bd amounts and szes, etc. Cancellaton of bds that do not meet such requrements comprses the valdaton porton of the procedure. 14

25 Bdders 1) Bd Collecton and Valdaton contnues untl close 2) Aucton Close 3) Valuaton and Bdder Rankng 5) Wnner Selecton Bdders notfed of results 4) Resource Rankng 6) Prcng Resources Resources desgnated to wnnng bdders Fgure 2.2: General procedures of an aucton 2) Aucton Close The aucton close can occur once a specfc set of crcumstances are met, as defned by the aucton organzer. These could nclude tme elapsed, recept of suffcent bds, avalablty of resources, or any other condtons relevant to the specfc applcaton. Once an aucton closes, bds would not be changeable. 3) Valuaton and Bd Rankng Ths procedure operates after the aucton round closes. The bd rankng procedure computes bd value for each bd collected and elgble for partcpaton accordng to any specfc rules. The most basc aucton mechansms equate the bd value wth the prce of the bd. A lot of nnovaton went nto provdng more sutable bd valuaton methods, reflectng addtonal features. In mult-attrbute auctons, multple attrbutes of the bds are combned nto a sngle bd utlty value [3, 8]. Other potental methods for assgnng a value to a bd by the gven bdder nclude addtonal nformaton about the bd and the 15

26 bdders, such as the tme of the bd, the hstory of the bdder s actvtes, etc. The fnal result of ths procedure s the lst of bdders ranked accordng to the values assgned to ther bds. 4) Resource Rankng In the resource rankng procedure, all resources avalable for allocaton n the gven round are ranked accordng to ther ntrnsc value, whch may be dentcal or dfferent for each tem. Any resource can be placed n any arbtrary order wth respect to other tems from whch ts ntrnsc value cannot be dfferentated. Any relevant factors can be used to assgn ntrnsc value rank order to the resources based on the specfc applcaton. Generally, the rankng reflects dfferences n ntrnsc value of each ndvdual unt of the resources. An example s the set of seats at the theater, where the dstance from the stage and the vsblty of the stage mpacts the ntrnsc value of a seat. 5) Wnner Selecton The wnner selecton procedure defnes the way of allocatng or mappng ranked resources offered n the market wth specfc bdders based on predefned rules. The unversally used wnner selecton procedure s to allocate avalable resources startng wth the bdder wth the hghest bd value and then followng n a decreasng order of bd values untl all resources are allocated. 6) Prcng After the wnners are selected n the wnner selecton procedure, prcng procedure compute the payments that are charged to the wnners for the allocated resources. The two man varants of prcng method n the current state of art are to pay the prce equal to the bd (also known as the frst prce rule) or equal to the bd of the next hghest bdder (also known as the second prce rule). 16

27 2.5 Requrements for the Optmal Aucton Mechansm One of the mportant desgn requrements for the tradtonal basc aucton s to maxmze seller s revenue. An aucton mechansm that satsfes ths requrement s called the optmal aucton mechansm. Addtonal desgn requrements for desgnng the aucton mechansm for electronc market envronments are descrbed n [3] as follows. Incentve compatblty: An aucton mechansm s ncentve compatble f an honest bddng true valuaton of each bdder s the domnant strategy (.e., the strategy that maxmzes the expected utlty for the bdder). Ths property s useful for agent-based automated negotatons snce t smplfes the bdder s strategy mplementaton. Effcency: In an effcent aucton, the resources should be allocated to the bdders who value them hghest. Indvdual ratonalty: The expected payoff of a bdder who behaves accordng to the domnant strategy 3 s always nonnegatve. Mnmzaton of the cost of negotatons and convergence to the agreement: In an electronc aucton mechansm, the communcaton overhead of conductng optmal negotatons and arrvng at the agreement should be mnmzed. Often, the drect mechansm n whch a bdder can communcate wth the auctoneer drectly (.e., va the sealed bds) mnmzes the communcaton overhead. Rley and Samuelson ntroduce the reservaton prce n order to desgn optmal aucton mechansm [11]. Such an aucton mechansm requres that the auctoneer sets the reservaton prce, and the bdders who bd hgher than the reservaton prce are qualfed to become wnners. Hence, the seller wll not allocate the resources below the reservaton prce. 3 Domnant strategy s strategy of bdder that maxmzes hs expected utlty. 17

28 Based on the gudelnes for the optmal aucton desgn, the Second Prce Sealed Bd (SPSB) aucton, known also as Vckrey aucton, wth reservaton prce (abbrevated as SPSB-R) has been regarded as optmal aucton mechansm for tradtonal markets [2]. Ths s because SPSB aucton not only provdes ncentve compatblty, effcency, and ndvdual ratonalty but also ts sealed bddng mnmzes the communcaton overhead and the reservaton prce maxmzes the expected revenue of allocatng the resources that can be stored n warehouse for the future use f the bd dose not meet the auctoneer s reservaton prce. 2.6 Analyss of Bddng Behavor Bddng behavor of each bdder can be classfed based on the aucton mechansm used and the rsk management characterstcs of the bdder. Each bdder estmates 4 ts gan from engagng n an aucton accordng to the followng utlty functon U ( b) U ( b ) = [ t c ( b )] q ( b ), (2-2) where t and b denote the true valuaton and the bd of bdder. c ( b ) and q ( b) represent the expected payment and the estmated wnnng probablty of bdder wth bd b respectvely. Based on ths utlty functon and rsk management characterstcs of the bdders, a bdder s bddng behavor can be classfed nto followng one of the three types: 1) Rsk neutral bddng behavor Rsk neutral bdders always try to maxmze the expected utlty (.e., gan or payoff). Hence, rsk neutral bdders consder the trade-off between the proft factor (.e., t c ( b) ) and the wnnng probablty factor q ( b). If the bdder ncreases ts bd, the 4 In a sealed bd aucton that we are consderng here, the bdder knows only hs own bd and therefore can only estmate hs gan. Only auctoneer knowng all bds s able to determne the wnners and compute the prces that they wll pay. 18

29 wnnng probablty rses, but the resultng proft factor decreases. Conversely, f the bdder decreases the bd, the proft factor ncreases at the expense of the wnnng probablty. Based on ths goal, f a bdder lost n the last aucton round usng a non-ncentve compatble mechansm wth perfectly sealed bd, such as FPSB aucton, she may ncrease her bd n the current round to ncrease the wnnng probablty n the future round. Reversely, f a bdder won n the last round, he may mantan the bd or decrease t n the current round to ncrease the proft factor. We refer to ths behavor as an adaptve bd behavor of rsk neutral bdder. In an ncentve compatble mechansm, such as the SPSB aucton, the bd behavor of rsk neutral bdders s smple because reportng the true valuaton by each bdder maxmzes the expected utlty. Hence, durng a recurrng aucton, rsk neutral bdders bd ther true valuatons n an aucton wth ncentve compatble mechansm. 2) Rsk averson bddng behavor Rsk averson bdders always try to maxmze the wnnng probablty. For ths reason, we can assume that they bd ther true valuatons. Ths behavor s also expected n recurrng aucton envronments. 3) Rsk preference bddng behavor Rsk preference bdders try to maxmze the gan gven a wn. For ths reason, we can assume that they ether bd the mnmum possble prce. Such a behavor s also expected n recurrng aucton envronments. Most of the prevous aucton related studes assume a rsk neutral bddng behavor [4,5,7,8,9,11], and we also make ths assumpton here. 19

30 2.7 Summary of the Chapter An aucton s a market nsttuton wth an explct set of rules matchng supples wth demands for the traded resources, and determnng prces on the bass of bds receved from the market partcpants. The bdders and auctoneers are two man market partcpants. The basc aucton mechansms can be classfed nto sngle aucton mechansms and double aucton mechansms. Englsh and Dutch auctons are openoutcry sngle auctons, and the Frst Prce Sealed Bd aucton and the Second Prce Sealed Bd aucton are sealed bd sngle auctons. A Contnuous Double Aucton and a Call Market are examples of a double aucton. In a Mult-attrbute Aucton, bdders bd on varous attrbutes beyond prce and the auctoneer selects wnners based on the prce as well as on those attrbutes. Such varous aucton mechansms can be descrbed by the sx-step process consstng of Bd Collecton and Valdaton, Aucton Close, Valuaton and Bd Rankng, Resource Rankng, Wnner Selecton and Prcng. The optmal aucton mechansm maxmzes the seller s revenue. Incentve compatblty, effcency, ndvdual ratonalty, and mnmzaton of negotaton cost are basc requrements n desgnng optmal aucton mechansms. From the rsk management perspectve, the bddng behavor can be classfed as a rsk neutral, rsk averson or rsk preference behavor. A rsk neutral bddng behavor tres to maxmze the expected utlty. On the other hand, a rsk averson behavor ams at maxmzng the wn probablty, whle a rsk preference behavor attempts to maxmze the proft factor of the utlty. 20

31 3. E-MARKETPLACES FOR AUCTION MECHANISMS 3.1 Introducton Wth the expanson of electronc envronments, ncreasng domnance of a servce orented paradgm and the aucton s nherent dynamc prcng and negotaton nature, many researchers have tred to extend the applcaton areas of aucton mechansms nto newly created markets, such as the network servces and resource allocaton, the grd computng servces (ncludng utlty computng servces), the Internet search engne marketng, and so on. In ths secton, we descrbe varous electronc markets n whch an aucton can be used as a dynamc prcng and negotaton mechansm. They range from exstng e-commerce markets for physcal resources to newly created servce orented electronc markets. In ths chapter, we also analyze and characterze the common propertes of newly created servce orented electronc markets n terms of market structures and propertes of the traded resources. The remnder of ths chapter s organzed as follows. In secton 3.2, exstng and newly created markets whch can use an aucton as a basc dynamc prcng and negotaton mechansm are descrbed. Secton 3.3 characterzes common propertes of newly created markets from the pont of vew of aucton mechansms. Fnally, secton 3.4 summarzes the chapter. 3.2 Aucton Mechansms n E-Commerce Durng the past few years, there have been a tremendous number of auctons conducted over the Internet. The Forester Research forecasts that the aucton n e-commerce markets wll grow from $13 bllons n 2002 to $54 bllons n 2007 [30]. Varous types of aucton mechansms are wdely used n B2C (Busness to Customer), C2C (Customer to Customer), B2G (Busness to Government), and B2B (Busness to Busness) markets. In B2C and C2C markets, the Englsh aucton s the most popular aucton type snce t s relatvely easy to understand, allows bdder nteracton and competton, and s partcularly well suted to perods longer than a few mnutes. Addtonally, bdders enjoy placng multple bds n competton wth other bdders, and ths entertanment value of 21

32 the onlne Englsh aucton s an mportant feature n B2C and C2C markets [3]. ubd ( and ebay ( are the most promnent examples of applyng auctons to B2C and C2C markets, respectvely. ebay also uses auctons for B2C markets. In B2G and B2B markets, sealed bd aucton types (.e., FPSB or SPSB auctons) are wdely used. Those markets rely on a procurement process that requres a Reverse Aucton mechansm n whch one buyer (.e., a manufacturer) s an auctoneer that collects the bds from many sellers (.e., the supplers) who supply the resources. The tradtonal types of resources that are traded n the current e-commerce markets through varous types of aucton mechansms are: () physcal goods such as collectbles ncludng antques, stamp and cons, () electronc equpment, () real estate and (v) used equpment. Wth the recent expanson of electronc envronments, the applcaton domans of aucton mechansms are also extended to the servce orented markets such as varous electronc servces (abbrevated as e-servces here). 3.3 Aucton Mechansms n Markets for Network Servces Recently, several dynamc prcng mechansms have been studed as a method for an effcent management of the contnuously changng network resources. In Qualty of Servce (QoS) enabled networks, approprate prcng mechansms encourage bdders to choose servces adequate to ther needs and such choces result n the effcent network resource allocaton. Hence, the network can be regarded as a market n whch varous QoS enabled network servces are traded. If a fully dynamc prcng mechansm s appled to a network, prce may become a sgnal for the congeston control, admsson control, and far allocaton of network resources. However, ths very dynamsm of prcng makes both the seller s (e.g. ISP, Network Provders, etc) prcng decsons and the buyer s budget plannng dffcult. An aucton can avod these dffcultes because prce emerges from wllngness of bdders (.e. buyers) to pay. Addtonally, ts smplcty can lower complexty of the fully dynamc prcng mechansm. Therefore, several aucton based mechansms have been studed for prcng the network servces, 22

33 for congeston control and for the effcent resource allocaton n dynamcally changng networks. One of the frst attempts to use an aucton as a mechansm for the resource allocaton n a congested network was smart market proposed by Varan and Macke-Mason [12]. In a smart market approach, the network can be vewed as an aucton market n whch the router s an auctoneer and the bdder s a packet owner who wants to send ths packet through the router. Each packet has a bd value that s assgned by the packet owner based on hs/her wllngness to pay for the transfer through the router. For ths purpose, the smart market ntroduces a new packet header to express wllngness to pay of each packet owner. Each router has a threshold value that s dynamcally changed based on the network capacty and congeston. The router admts only those packets that have values hgher than the predetermned threshold that s set by each router. The aucton wnners (packets that pass through the router) pay ths threshold prce. Hence, the smart market has prcng behavor smlar to the SPSB-R aucton. However, ths mechansm has been determned to be unsutable for large networks n whch packets make many hops on a route from the source to the destnaton. The reason s that a bdder needs to bd new (hgher) values to the routers encountered after the congested ones to prevent the loss of money already spent at the congested routers. Ths s hardly scalable and may ncrease the traffc overhead n the already congested network [15]. Lazar and Sermet propose the Progressve Second Prce (PSP) aucton mechansm for the network resource (.e., bandwdth) sharng [13]. In PSP aucton, bdders submt twodmensonal bds: value n one dmenson s the prce and the value n the other s the desred quantty of network resources. The bdders can modfy ther bds teratvely n a response to the current strategy of ther opponents to reach the best response. These teratons lead to an equlbrum state n whch no bdder want to change the current state. The prcng mechansm of PSP aucton s smlar to that of the Generalzed Vckrey Aucton (GVA). For ths reason, the man advantage of the PSP aucton mechansm s that t s ncentve compatble. However, the PSP aucton mechansm can ncrease the communcaton overhead between the seller and the bdders whle both 23

34 sdes try to reach an equlbrum state, snce the bdders are allowed to bd teratvely n each aucton round. Shu, at al. proposed an aucton based network servce prcng mechansm that s called the SPAC (Smart Pay Admsson Control) [14]. The SPAC mechansm has been desgned for the DffServ network archtectures. It s nspred by the smart market aucton dea of assgnng to each packet a prce determned by the packet sender based on the sender budget and ths partcular packet value. Based on the bds of all packet senders, the SPAC mechansm decdes to whch color (QoS level) each sender s enttled. Those color marked packets are treated dfferently by recevng dfferent quanttes of bandwdth accordng to the assgned QoS level n the network nteror. In there, dfferent quanttes of bandwdth are assgned to the packets based on the marked color. When congeston arses, the router charges a congeston fee to the passng packets by rasng the prce of acqurng the hgher QoS. As a result, users wth low servce valuatons cannot wn the hgher QoS n an aucton, and wll voluntarly back down when the congeston occurs. Thus, the SPAC mechansm provdes the congeston control economcally. The prces charged to packet senders are calculated based on a varant of generalzed Vckrey aucton. Thus theoretcally, the SPAC mechansm supports ncentve compatblty and ndvdual ratonalty. 3.4 Aucton Mechansm n Markets for Computng Servces In recent years, nterest n and demands for Grd Computng Servces (GCS), ncludng Utlty Computng Servces and Dstrbuted Computng Servces, have been growng rapdly. Fully mplemented grd computng servces provde a transparent access to a wde varety of large scale geographcally dstrbuted computatonal resources (.e., CPU, memory, storage, etc.). Wth the current trend of the hgh performance computng movng nto the servce-orented computng, grd computng can be organzed nto a market n whch the GCS buyers demand computng servces needed by ter desred applcatons, and the GCS provders allocate such computng servces that enable them to return the desred computng results to the buyers [25]. Ths market provdes 24

35 followng benefts to the GCS buyers and GCS provders. From the GCS buyer pont of vew, outsourcng computng servces mnmzes the cost of desred computng compared to ownng applcaton software and hardware. On the other hand, such outsourcng mproves the grd resource utlzaton from the GCS provder s pont of vew and accordngly ncreases the provder s revenue. For effcent contractng n such a market, the GCS provders need tools for expressng ther prcng polces and mechansms that can maxmze ther profts and the resource utlzaton. For ths purpose, varous economc models, ncludng varous aucton models, for computatonal resource tradng and for establshng effcent prcng strateges have been proposed [16, 17]. Among the varous economc models, the followng two models denote basc scenaros that use the aucton mechansm: the Tender/Contract Net model and the general aucton model [16]. `computng results computng results bd bd bd bd bd e-aucton market GCS provder e-aucton market bd GCS customers (a) General Aucton Model GCS Provders (b) Tender/Contract Net Model Fgure 3.1: Aucton based economc model for computng servce markets As shown n Fgure 3.1, n a general aucton model, the GCS provder nvtes bds from many GCS buyers (.e., bdders) for each applcaton computng servce. Based on the aucton mechansm used and on the current condtons of dstrbuted computatonal resources, the GCS provder selects the wnners and clears the aucton. Aucton mechansms used n ths area often requre that the bd based proportonal resource 25

36 sharng model s followed, n whch the amount of computng resources allocated to each bdder s proportonal to the value of hs bd [17, 18]. In the Tender/Contract Net model, a reverse aucton mechansm s used. Hence, a GCS buyer (.e., an auctoneer) nvtes sealed (or open-outcry) bds from several GCS provders by advertsng hs desred applcaton computng servce and the tme constrants such as the deadlnes for recevng the results. The buyer selects the bd that offers lowest servce cost wth the acceptable tme deadlne for the delvery of the results. The selected wnner makes a contract wth the buyer, provdes the computng servce and then returns the computed result to the buyer at the prce of the provder bd. Ths s the same model as the one used n the reverse auctons n procurement envronments, where the buyer s a GCS buyer and the supplers are the several GCS provders. 3.5 Aucton Mechansms n the Internet Search Engne Marketng Next to e-bay, sponsored search advertsement auctons are one of the most common and wdespread examples of an electronc aucton system n use today wth enormous economc mpact on advertsng and computer ndustres. The revenues from the sponsored search advertsement auctons have been ncreasng contnuously and have already exceeded bllons of dollars annually. They are projected to reach $4.9 bllon n the U.S. market alone n 2009 [41]. An mportant reason for so fast and wde-spread adopton of the sponsored search advertsement s ts hgh return on nvestment (ROI) for advertsers, compared to other marketng methods. The search engne customers already pre-select themselves by ntatng a search for keywords relevant to the advertsement and then show further nterest n the advertsed products by clckng on the lnk to the specfc advertsement. Hence, as shown n Fgure 3.2, the average cost per leadng purchase s lower n the sponsored search advertsement than n other marketng channels. 26

37 Fgure 3.2: A comparson of the average cost per lead to purchase The dea behnd the sponsored search advertsement s smple. The search engne produces the search result pages wth postons for sponsored search advertsements assocated wth a partcular keyword used n the search query entered by the customer. These sponsored postons contan pad advertsements wth embedded lnks pontng to the advertser s web pages. Advertsers pay the search engne for ther advertsng whenever the search engne customer clcks on the lnk embedded n a sponsored poston. Accordngly, ths form of advertsng s called Pay-Per-Clck (PPC) advertsement. From the aucton structure pont of vew, a search engne company s an auctoneer and advertsers are aucton partcpants who bd for the sponsored postons. Hence, ths s one-to-many market structure. The resources traded n the sponsored search advertsement aucton are ranked advertsng postons n a web page produced n response to a user query. It s well known that dfferent postons yeld dfferent numbers of user clcks per tme perod, even when they dsplay the same advertsement. Generalzed Second Prce (GSP) aucton are wdely used n the most of the current sponsored search auctons. In a GSP aucton, each bdder s payment s equal to the bd of the bdder who occupes a poston wth a rank one below the payer s poston. 27

38 3.6 Analyss and Characterzaton of New Aucton Markets Dfferent market structures requre dfferent dynamc prcng and negotaton mechansms for effcent resource allocaton and revenue maxmzaton [4]. Hence, an analyss and characterzaton of newly created markets from the aucton mechansm pont of vew s one of the necessary steps n desgnng an effcent aucton based dynamc prcng and negotaton mechansm for these markets. We can characterze dscussed above newly created markets as short-term contract markets, because the resources traded n them are renewable and ther allocatons to bdders are made for a specfc tme only. Addtonally, the short-term contract markets have recurrng nature, because, once the allocated renewable resources become free, the seller (or the auctoneer) needs to offer them to the bdders agan, recurrently. From the bdder s perspectve, the short-term contract market s recurrng, snce each bdder requests the traded resources repeatedly for a specfc tme nterval. The example resources for newly created markets are varous electronc servces that are operated over the Internet. Examples are vdeo conferencng, musc on demand servce, vdeo on demand servce, and so on. In addton to ther recurrng nature, these markets trade resources that are tme senstve and pershable (.e., the fact that unused resources persh) whch s another mportant factor. The traded network or computng servces and resource for the servces cannot be stored n a warehouse for future sale and leavng them unused decreases utlzaton of the resources. Therefore, the new markets from the pont of vew of aucton mechansms can be characterzed as Recurrng Short-Term Contract Markets for Sellng Pershable Resources. Hence, from the aucton pont of vew, bdders partcpate n an aucton recurrently acqurng resources for a specfc tme nterval based on ther needs and the auctoneer opens and clears the aucton recurrently allocatng or reallocatng resources for the same tme nterval. Other recurrng short-term contract markets for sellng pershable resources n whch auctons can be used as a basc dynamc prcng and negotaton mechansm nclude car 28

39 parkng servces, varous e-servces that requre system resources to fulfll ther tasks, arlne tcket reservatons, hotel room reservatons and so on. 3.7 Summary of the Chapter Aucton mechansms have been wdely used as tradng tools that support dynamc prcng and negotatons n varous electronc markets. In addton to the current e- commerce markets, the applcaton domans of aucton mechansms are extended to the servce orented electronc markets such as the network servces, the computng servces and the Internet search engne marketng servces. In the current electronc commerce doman, an open-outcry Englsh aucton s wdely used n B2C and C2C markets whle the reverse sealed bd auctons are used n B2B and B2G markets. In network servce markets, an aucton can be used for the optmal resource allocaton n dynamcally changng QoS enabled networks. The grd computng servce markets attempt to allocate the computatonal resources, that are located n dstrbuted locatons, farly and to maxmze the resource utlzaton by an aucton based economc model. The Internet search engne marketng also uses an aucton for allocatng sponsored advertsement slots n the search result page for each search key word. In such an aucton, the generalzed second prce aucton s wdely used. The newly created servce orented aucton markets are recurrng short-term contract markets n whch pershable tme senstve resources are traded recurrently for a specfc tme perod. 29

40 4. AN OBSERVATION UNDERPINNING THE RESEARCH 4.1 Introducton The prevous desgn approaches to aucton mechansms focus on a one-tme (.e., one shot) aucton for sellng physcal resources that can be stored n the warehouse for future sales [4,5,6,7,9]. Hence, they dd not consder a recurrng nature of the auctons and the pershable property of the resources n the newly created servce orented short-term contract markets. These two features strongly affect the bddng behavor of bdders and the revenue of the auctoneer. Addtonally, we observed that applyng exstng basc aucton mechansms to newly created servce orented short-term contract markets can cause varous problems that motvated our research. For ths reason, n ths chapter, we analyze, defne and verfy the problems that should be consdered and resolved n desgnng optmal aucton mechansms for the newly created markets. The remnder of ths chapter s organzed as follows. In secton 4.2, varous problems, some of them dscovered n the course of our research, are analyzed and defned. The newly dscovered problems are verfed theoretcally and expermentally n secton 4.3. The summary of the chapter s gven n secton Analyss of Newly Dscovered Problems In most of the tradtonal basc aucton mechansms, the prces bd n an aucton are dependent only on the bdder s wllngness to pay for the traded resources. Ths means that ntentons of only bdders, but not the auctoneer, are reflected n the aucton wnnng prces. To restore the symmetrc balance of negotatng power, the Reservaton Prce Aucton (RPA) and the Cancelable Aucton (CA) mechansms were proposed [11, 31]. In RPA, only bds hgher than the auctoneer s reservaton prce are consdered durng wnner selecton. Hence, the auctoneer can select potental wnners and losers based also on the auctoneer s ntenton (.e., the reservaton prce). On the other hand, n CA, f the resultng revenue does not meet the mnmum requrement of the auctoneer, the entre aucton s cancelled. By provdng the auctoneer wth the ablty to set the 30

41 reservaton prce or to cancel an aucton, the asymmetrc negotaton power problem s resolved. However, when the pershable resources, such as short-term contracts are traded, both of these aucton mechansms waste resources. In RPA, the reservaton prce restrcts the number of wnners. Resources unused because of ths restrcton are wasted. In CA, a cancellaton of an aucton round wastes all resources allocated to ths aucton round. In addton to the resource waste problem, the recurrng nature of newly created markets results n the followng problem whose dscovery provded an underpnnng of our research. Prces bd n an aucton reflect wllngness of each bdder to pay. Ths wllngness to pay s lmted by the bdder s (prvate) true valuaton that s nfluenced by each bdder s wealth. An uneven wealth dstrbuton causes starvaton of those bdders n a recurrng aucton whose true valuatons are below the wnnng prce. Frequent starvaton for resources decreases the bdder s nterest n the future aucton rounds. Addtonally, each bdder learns f her true valuaton s suffcent to ever become a wnner. If a bdder concludes that t s mpossble or unlkely that he wll wn at the prce that he s wllng to pay, he wll drop out of the future aucton rounds. Such a drop decreases the number of bdders n future rounds. Moreover, although such a drop s the fastest n the case when all customers partcpate n each aucton round, t wll happen also when the pattern of customer s partcpaton n aucton rounds s perodc as long as the demand exceeds the supply of the traded goods n each round. Indeed, regardless of the partcpaton scheme, the lowest bddng customer loses each aucton n round n whch he partcpates.. Ths bdder wll experence starvaton for resources and wll drop out of the aucton n the long run. In a recurrng aucton, each bdder s drop out of an aucton decreases the number of actve bdders. Reducng the number of bdders gradually decreases the prce competton. Hence, the probablty of wnnng ncreases for the remanng bdders so ther attempts to decrease bds wthout losng the wnnng poston wll be successful and the wnnng bds wll declne n such a scenaro. In the long run, when the number of bdders decreases close to the number of resources, the auctoneer revenue s lkely to 31

42 drop below the acceptable level. Ths s because the remanng bdders constantly wn and as a result they may decrease ther bds to the very low level. Applyng Basc Aucton Mechansms Result n Bdder Drop Problem and Resource Waste Problem and Asymmetrc Negotatng Power Recurrng Short-Term Contract Markets Recurrng Market Structure Pershable Property of Resources Market Prce Collapse Strong need for New Aucton Mechansms Fgure 4.1: The problems resultng from applcaton of tradtonal aucton mechansm to markets of a recurrng nature for pershable resources Ths phenomenon s exacerbated n ncentve compatble auctons, such as the Second Prce Sealed Bd (SPSB) aucton or the Unform Prce Sealed Bd (UPSB) aucton, n whch all bdders bd ther true valuatons to maxmze ther expected utltes. A bdder who lost n such an aucton can easly conclude that hs true valuaton s not large enough to ever become a wnner. Hence, there s no ncentve for losers of the aucton to partcpate n the future rounds. Consequently, they may drop out of the aucton and such drops decrease the aucton clearng prce and the auctoneer s revenue. We call ths phenomenon the paradox of ncentve compatble mechansm n recurrng aucton because by achevng the goal of motvatng the bdders to bd ther true valuatons, the mechansm, when appled to a recurrng aucton, leads to the market collapse after a few rounds. The collapse may be delayed f the bdders return to the market when the 32

43 wnnng prces drop, a phenomenon that s lkely to occur when hghly desrable resources are traded. However, even n the latter case, perodc fluctuatons of the auctoneer s revenue may lead to ts demse anyway and are certanly dsadvantageous. To the best of our knowledge, the bdder drop problem n a recurrng aucton market has not been addressed n the prevous research. The Fgure 4.1 summarzes the problems arsng when tradtonal aucton mechansms are appled to markets of a recurrng nature for pershable resources. 4.3 Verfcaton of the Dscovered Problem In the Frst Prce Sealed Bd (FPSB) aucton wth sngle resource traded and under the assumpton of () a unform dstrbuton of bdders true valuatons, and () the rsk neutral bdders, the optmal bd * b that maxmzes the bdder s expected utlty (.e., proft or payoff) of bdder s * n 1 b = t n, (4-1) where t represents the true valuaton of bdder, and n denotes the number of actve bdders (.e., partcpants n the aucton) [4]. To maxmze an auctoneer s revenue from an FPSB aucton, the optmal bd of each bdder should be a fracton of hs true valuaton. Addtonally, to avod wastng of pershable resources, the sngle resource should be allocated to a sngle wnner n each aucton round. Hence, to keep the optmal bd gven by Eq. (4-1) close to the true valuaton, the number of bdders should be hgh durng each recurrng aucton round. In other words, the auctoneer should keep the suffcent number of bdders partcpatng n each round to maxmze the revenue. Fgure 4.2 shows the change of a coeffcent ( n 1)/ n of the optmal bd as a functon of the number of bdders. 33

44 Fgure 4.2: A coeffcent of the Optmal Bd (OBP) The bdder drop problem s also an mportant factor for the auctoner s revenue also n the Dscrmnatory Prce Sealed Bd aucton. Lemma 4-1: The optmal bd b m that maxmzes the expected utlty of a bdder s an ncreasng functon of the dfference between the total number of bdders and the number of wnners n the Dscrmnatory (Frst) Prce Sealed Bd aucton for the rsk neutral bdders wth the unform dstrbuton of ther prvate true valuatons. Proof: Frst, we show that the probablty of wn n such an aucton ncreases when the bd of a bdder ncreases. Second, we prove that the bd that optmzes the bdder expected utlty decreases when the dfference between the number of bdders and the wnners decreases. Ths s an extenson of the well-known case of a sngle wnner. The utlty wth bd b and the true valuaton t for n bdder aucton wth R wnners s R UbR (, ) = ( t b) s= 1 n ( 1) n s b t b s t t s 1 (4-2) 34

45 The frst factor, ( t b) monotoncally decreases wth the growth of b. It s easy to show ( ) n s s 1 R ( ) by nducton on R that the next factor, the probablty (, ) n 1 b t b pbr =, has n s s = t the followng dervatve wth regard to b p'( b, R) = n 1 ( R 1) ( n R) b ( t b) n 1 t n R 1 R 1. (4-3) Snce the dervatve s always non-negatve for feasble bds, the probablty of a wn s a non-decreasng functon of b. Hence, there s only one maxmum of the bdder s utlty. Let denote the bd at ths maxmum utlty as bm,0 U '( b, R) = 0 = p( b, R) + ( t b ) p'( bm, R), so m m m < b < t. Hence, m b m = p( bm, R) t p '( b, R). (4-4) m To prove that the optmal bd decreases when n R decreases, we need to show that the second term n Eq. (4-4) ncreases when R ncreases whle s kept constant or n other words that p(bm,r+1)p (b m,r)>p (b m,r+1)p(b m,r). Let m(b,s) denote n n 1 b s 1 t Denotng s t t b s 1 so, dm( b, s) / db = m '( b, s) R p(, br) = m (,) bs and p(b,r+1)=p(b,r)+m(b,r+1). s= 1, we need to prove the followng nequalty: n m'( b, R+ 1) p( b, R) < m( b, R+ 1) p'( b, R) m m m m whch s equvalent to We also get m'( bm, R+ 1) p'( bm, R) <. (4-5) mb (, R+ 1) pb (, R) m m m'( b, s) ( n s)( t b) b( s 1) n s s 1 = = vbs (, ) mbs (, ) bt ( b) b t b =. (4-6) 35

46 It follows from Eq. (4-6) that vbs (, )- vbs (, + 1) = 1/ b+ 1/( t- b) > 0, so that vbs (, ) > vbs (, + 1). From that, by nducton, we get that vbs (, ) > vbr (, ) for all s < R and, fnally, the followng nequalty becomes apparent, provng Ineq. (4-5) and the Lemma: p'( b, R) = p( b, R) R m'( b, s) = 1 = p( b, R) R v( b, s) m( b, s) v( b, R) > R p( b, R) s= 1 m( b, s) s= 1 > v( b, R) m( b, s) s s= 1 = R m'( b, R). m( b, R) In concluson, the droppng bdders decrease the optmal bds of the remanng bdders. On the other hand, controllng number of wnners by decreasng the number of resources can cause resource waste when pershable resources (.e., f the resources that persh when unused) are used. Hence, regardless of the auctoneer s attempt to mantan the prce, the auctoneer s revenue decreases. To strengthen our argument, we smulated recurrng UPSB and DPSB auctons under smulaton scenaros descrbed n sectons and 4.6.1, respectvely. The smulaton results, shown n Fgure 4.3, demonstrate that the bdder drop problem causes a collapse of the auctoneer s revenue. The addtonal smulatons wth results presented n Fgure 4.4 show the extent of the resource waste n RPA and CA mechansms based on smulaton scenaro of Secton As shown, 28.6 % of resources n RPA and 23.5 % of resources n CA are wasted durng recurrng aucton n whch bdders have the exponental true valuaton dstrbuton. The correspondng loss for the unform and the Gaussan dstrbutons of true valuatons were 28.0 % and 34.2 % n RPA and 32.9 % and 34.8 % n CA, respectvely. 36

47 Fgure 4.3: The bdder drop problem n the DPSB and UPSB auctons Fgure 4.4: The resource waste problem n the DPSB aucton 4.4 Summary of the Chapter Applyng the tradtonal basc aucton mechansms to the newly created servce orented short-term contract marketplaces causes an nevtable starvaton for resources among least wealthy bdders because of recurrng nature of auctons n those marketplaces. The 37

48 starvaton may decrease the bdders nterests n the future aucton round. Fnally, the bdders may drop out of the aucton (and some of them may fnd other markets). Such dropped bdders decrease the prce competton and decrease the aucton market prce. The bdder drop problem s exacerbated n the ncentve compatble auctons because of the paradox of an ncentve compatble mechansm n recurrng auctons. The unbalanced negotaton power and the resource waste problem caused by pershable property of the short-term contracts should be consdered n desgnng optmal aucton mechansms for the newly created servce orented short-term contract marketplaces. Ths chapter also verfed theoretcally the potental market collapse by the bdder drop problem. The optmal bds are an ncreasng functon of the dfference between the number of bdders and the number of resources n the Frst Prce Sealed Bd aucton and the Dscrmnatory Prce Sealed Bd auctons. Hence, decreasng number of bdders also decreases the optmal bd of each bdder and thereby decreases the revenue of auctoneer. 38

49 5. NOVEL AUCTIONS FOR HOMOGENEOUS MARKETPLACE 5.1 Introducton To prevent the dscovered scenaro for market collapse from happenng, we ntroduce n ths chapter two aucton mechansms of a novel type of auctons that termed the Optmal Recurrng Aucton (abbrevated as ORA). ORA mechansms are applcable to marketplaces for tradng homogeneous resources. The frst one s the Partcpaton Incentve Optmal Recurrng Aucton (PI-ORA) that s ncentve compatble and the second one s the Dscrmnatory Prce Optmal Recurrng Aucton (DP-ORA) that s not. From the prcng pont of vew, PI-ORA uses a varaton of the unform prcng scheme whle DP-ORA uses the dscrmnatory prcng scheme. To descrbe the ntroduced aucton mechansms, we frst defne here the basc notons of bdders, bds, and resources. Players: There are n +1 players, numbered consecutvely startng from 0, that denotes the sngle auctoneer and n bdders numbered unquely from 1 to n. An auctoneer and each bdder enter ther bds and b, b,..., bn, respectvely n each aucton round. We also assume that all n bdders are rsk neutral and that each bdder has the prvate true valuaton t b0 1 2 for each unt of the traded resource. Resources: There are R unts of a homogeneous pershable resource that are allocated for a specfc tme perod n each aucton round. We assume that each bdder requres one unt of ths resource n each aucton round, snce each bdder s requrement s homogeneous n ths market. Hence the maxmum number of possble wnners n each aucton round s R. We also defne the farness of an aucton mechansm from two perspectves: An aucton s entrely far f a bdder wth a bd hgher than any wnner s a wnner as well. Ths condton s often referred to as prce farness. We call ths type of farness horzontal snce ths farness consders only a sngle aucton round. The other type s vertcal 39

50 farness n the recurrng aucton, where a bdder wth the hgher wllngness to pay should be the wnner more tmes than a bdder wth the lower wllngness to pay. The remnder of ths chapter s organzed as follows. In secton 5.2, the man dea of ntroduced aucton mechansms s descrbed. Secton 5.3 ntroduces the ncentve compatble Partcpaton Incentve Optmal Recurrng Aucton (PI-ORA). The verfcaton of the PI-ORA mechansm by varous smulaton experments s descrbed n Secton 5.4. Secton 5.5 ntroduces the Dscrmnatory Prce Optmal Recurrng Aucton (DP-ORA) that s not ncentve compatble. The verfcaton of the DP-ORA mechansm by varous smulatons s descrbed n secton 5.6. Fnally, the chapter s summarzed n secton Illustraton of the Man Idea The man dea of the ntroduced here Optmal Recurrng Aucton (.e., PI-ORA and DP- ORA) s based on the demand-supply prncple of mcroeconomcs [1]. In Fgure 5.1, D1 and D2 denote the demand curve for the traded pershable resources whle S1 and S2 represent the supply curve of the resources. When the overall bd decreases (.e., the entre demand curve changes from D1 to D2) durng a recurrng aucton, the mnmum market clearng prce drops from p1 to p2. In such a case, to mantan the mnmum market-clearng prce at p1, the auctoneer should decrease the supply of resources from q1 to q2 (.e., the entre supply curve needs to change from S1 to S2). Inversely, when the overall bd ncreases, the auctoneer may ncrease the supply. However, when the auctoneer decreases the supply of pershable resources for the gven tme perod, the unsold resources are wasted. Thus, n the proposed aucton mechansms, the unsold pershable resources (q1 q2 n Fgure 5.1) are assgned to the bdders who have hgh probablty of droppng out of the forthcomng aucton round. Ths assgnment prevents such a bdder from droppng out of the aucton and keeps enough bdders n the future rounds to mantan the competton for resources strong. Smultaneously, usng unsold pershable resources for the bdder drop control resolves the resource waste problem and 40

51 ncreases the number of wnners n the recurrng aucton. Addtonally, the reservaton prce prevents the asymmetrc balance of negotaton power. Prce D2 D1 S2 S1 p1 p2 q2 q1 Quantty Fgure 5.1: The demand and supply prncple 5.3 Partcpaton Incentve Optmal Recurrng Aucton In ths secton, we descrbe the novel Partcpaton Incentve Optmal Recurrng Aucton (PI-ORA) mechansm n terms of the wnner selecton strategy, the prcng rule, and the bdder s strategy Novel Wnner Selecton Strategy The frst step of the wnner selecton strategy of PI-ORA mechansm s to defne bdder s class based on each bdder s bd, where b 1,..., n = and auctoneer s bd prce (.e., reservaton prce) b 0. The auctoneer classfes the bdders nto the Defntely Wnner (DW), Possble Wnner (PW), and Defntely Loser (DL) classes usng the followng condtons: DW f b b r > n R, = 1, 2,..., n, 0 & DL f b 0, = 1, 2,..., n, (5-1) PW otherwse, 41

52 where r denotes the rank of bdder n the ncreasng order of bds of all bdders. The numbers of bdders n the DW, PW and DL classes are denoted as N dw, N pw and N dl, respectvely. Fgure 5.2 shows the bdder s classes n PI-ORA and compares them wth the classes n the tradtonal aucton mechansms. The tradtonal losers and wnner classes are defned accordng to the tradtonal aucton mechansms. WPPW represents the Wnnng Porton of the PW class, and the number of wnners n the PW class s denoted by. Hence, wppw =. N Nwppw R Ndw Lower bd Tradtonal Loser Hgher bd R Tradtonal Wnner R DL PW DW WPPW b 0 Wnner Loser Fgure 5.2: The classes of bdders n PI-ORA In each aucton round, the DW class bdders become the wnners wthout any addtonal consderatons, snce they bd hgher than the bd prce of the auctoneer and there are enough resources to assgn one to all of them. The DL class conssts of bdders who already dropped out of the aucton. Hence the DL class bdders become losers n each aucton round. The bdders who are n the PW class can be wnners or losers dependng on the bdder drop control algorthm appled. In PI-ORA mechansm, we propose the Partcpaton Incentve Bdder Drop Control for wnner selecton n PW class. The auctoneer s bd prce b n the PI-ORA mechansm plays the same role as the 0 reservaton prce does n the Reservaton Prce Aucton. By ntroducng the reservaton 42

53 prce, the proposed PI-ORA mechansm creates symmetry n the negotatng power from lack of whch the tradtonal aucton mechansms suffer Partcpaton Incentve Bdder Drop Control (PI-BDC) Enough bdders of PW class should partcpate n the future aucton rounds to mantan prce competton n the recurrng aucton. To encourage partcpaton of bdders n future aucton rounds, the Partcpaton Incentve Bdder Drop Control (PI-BDC) uses k the followng wnnng score S for each bdder PW to decde the wnners n PW class: S b B = W, (5-2) α k k where W s the number of wns by bdder, up to the current aucton round, B denotes the weghted number of partcpatons of bdder untl the current aucton round m : B m j = mn( b j b m = 1,,, ) b, (5-3) where b, j denotes the bd of bdder n aucton round j (we assume that ths prce s zero for rounds n whch bdder dd not partcpate). The term bb k / α denotes the expected number of wns based on the average cumulatve bd and the number of partcpatons. α n Eq. (5-2) s a coeffcent that controls the expected number of wns (.e., wn frequency) durng a recurrng aucton. Such defnton of B encourages bdders to bd the same prce n each aucton round, as ths s the only way n whch a bdder can receve a full credt for partcpaton n an aucton round. Thus, the wnnng score bdder P W represents the dfference between the expected and real numbers of wns durng the recurrng aucton. Hence, hgher the wnnng score of a bdder s, hgher the probablty of hm droppng out of the future rounds s because more below hs k S of 43

54 expectatons hs wnnngs are. For ths reason, the PI-BDC algorthm ranks bdders of PW class n decreasng order of ther wnnng scores and up to bdders are selected as wnners of the current aucton round. N wppw hghest ranked By Eq. (5-2), the partcpaton of a loser n the last aucton round s rewarded drectly by ncreasng her wnnng score n the current and future aucton rounds. Therefore, the PI- BDC algorthm controls the bdder drop problem by encouragng bdders partcpaton n the future aucton rounds. If the coeffcent α s ncreased, the effect of the bd on the wnnng score s dmnshed. Thus, the total number of wns acheved by the low bddng bdder s ncreases and the range of wnners broadens across the PW class. Reversely, f α s decreased, the wn dstrbuton narrows and concentrates on the hgh bddng bdders n the PW class. The optmal value of α depends on the auctoneer s strategy and the dstrbuton of true valuatons of the bdders. In our smulaton experments, descrbed later, we set α n such a way that the average value of the wnnng score of all bdders s zero. Snce n each aucton round all bdders n PW class ncrease ther wnnng scores cumulatvely by b α (assumng that they bd the same prce as j PW k j prevously) and, at the same tme, ther wnnng scores decrease cumulatvely by R N dw k wns, the balancng value s α = b ( R N ). Wth ths value, the wn frequency j PW j dw p ( b ) of each bdder P W wth bd b s defned as k b ( R N dw ) and the followng k b j PW j nequalty must be satsfed: k bj R N j PW > DW b, (5-4) max PW where b maxpw s the largest bd n PW class. In contrast, as shown n Fgure 5.3, n the tradtonal aucton mechansms, the wn probablty of a bdder outsde the Tradtonal Wnner class s zero. Hence, there s no ncentve for the bdders whose true valuatons are n the range of the Tradtonal Loser class to partcpate n the future aucton round n ncentve compatble auctons. However, n the PI-ORA mechansm, the wn 44

55 probabltes of bdders n the PW class, ncludng the Tradtonal Loser class, are hgher than zero. For ths reason, there s an ncentve to partcpate for all bdders regardless of ther true valuatons. If k of the wnnng score n Eq. (5-2) tends to nfnty, the PI-ORA mechansm converges to a tradtonal aucton mechansm. If k s small, the dstrbuton of wns n the PW class s broad. Hence, the auctoneer can choose the wn frequency dstrbuton of the PI-ORA mechansm by selectng a proper value of k. In ths selecton, the auctoneer s restrcted to those values of k and Ndw whch satsfy the Ineq. (5-4). Fgure 5.3: The wn probablty dstrbuton n PI-ORA From the farness perspectve, the partcpaton ncentve bdder drop control acheves the long-term farness of resources allocaton n the recurrng aucton. Fgure 5.4 shows the example of resources allocaton durng the recurrng aucton n the proposed partcpaton ncentve bdder drop control. In Fgure 5.4, we assume that bdders B1, B2, B3 and B4 bd $4, $3, $2, and $1, respectvely, n each aucton round, and that there are two unts of a resource allocated to the PW class (ths means that R N dw = 2). As seen n Fgure 5.4 (a), n tradtonal auctons, the wn dstrbutons are concentrated on the hghest two bd bdders (B1 and B2). However, n the proposed PI-BDC, the wn 45

56 dstrbuton s proportonally allocated to all bdders based on ther bds computed accordng to the wnnng score of Eq. (5-2). W: Wnner of the aucton round B1 B2 B3 B4 B1 B2 B3 B4 Round 1 W W Round 1 W W Round 2 W W Round 2 W W Round 3 W W Round 3 W W Round 4 W W Round 4 W W Round 5 W W Round 5 W W (a) Tradtonal Aucton (b) PI-BDC Fgure 5.4: Resources allocaton farness n PI-BDC The Prcng Rule and the Optmal Auctoneer s Bd Prce The PI-ORA mechansm uses the followng prcng rule for wnners. Wnners n the DW class pay ρ b0 whle wnners n the PW class pay ρ b, where b 0 denotes the seller s bd (.e., the mnmum prce needed to become a member of the DW class), b denotes the bd of a wnner n the PW class and ρ represents payment coeffcent. Hence the prce p( b ) that the bdder pays for a wn s ρ b ( ) { for 0 DW pb = ρ b for PW (5-5) The payment coeffcent ρ should be selected based on the followng condtons: ρ k k k t / for PW and (5-6) s 46

57 t k ρ k b / s b 0 0 for DW, (5-7) k where s = b j and, k s a constant used n Equaton (5-2). Based on the bdder s bd PW j dstrbuton, the auctoneer selects the optmal payment coeffcent ρ, the auctoneer s bd prce and the constant k that satsfy the both payment coeffcent condton (5-6) b 0 and (5-7), as well as maxmze the revenue. Thus, thanks to the payment coeffcent condtons (5-6) and (5-7), the PI-ORA mechansm guarantees that the payments of wnners are lower than ther bds. Lke other ncentve compatble mechansm, such as the Vckery aucton and the Generalzed Vckrey aucton, ths prce s uncertan untl the aucton closes. All what s guaranteed s that the prce wll not exceed the bd. In PI- ORA, the auctoneer may decde to guarantee the mnmum value of ρ, thereby assurng certan mnmum of Return on Investment (ROI) to the bdders The Optmal Strateges for Bdders The bdder s optmal strategy can be approached from two perspectves: the bd and the partcpaton level. We show below that based on the prcng rule of the PI-ORA mechansm, reportng each bdder s true valuaton maxmzes hs expected utlty (.e., t s a domnant strategy) n the PW and DW classes. Addtonally, the bdder n the DW class (.e., the bdder whose true valuaton s larger than auctoneer s bd prce) would draw no benefts from so decreasng hs bd that he would move to the PW class. Lemma 5-1: For a bdder, f t < b, then bddng hs true valuaton n each aucton 0 round maxmzes hs expected utlty. Proof: Let s assume that the bd of bdder s I t < b0, where 0 I 1. Then, ths bdder wn probablty s proportonal to wth bds I t and t s: b /( s+ b ) k k and the rato of the expected utlty 47

58 k k k k ( t ρ It) I t ( s+ t ) (1 ρ I) I ( u+ 1) s = k k k k,where u =. (5-8) k ( t ρt ) t ( s+ I t ) (1 ρ)( u+ I ) t To show that ths rato s always smaller than or equal to 1, we need to show that k (1 ρi) I 1 ρ. (5-9) k u + I 1 + u We assume that ρ < 1, hence ths nequalty holds at I = 0 and becomes equalty for I =1. The left hand sde of Ineq. (5-9) reaches the maxmum for I satsfyng the followng equaton, resultng from equatng the dervatve of the left hand sde to zero: k ( + 1) = / (5-10) I u k I uk ρ The left hand sde of the Eq. (5-10) s monotoncally growng for I 1, so Ineq. (5-9) s satsfed f and only f I or equvalently when 1 + uk + u uk / ρ, hence max 1 ρ k k k t / (5-11) s To maxmze the auctoneer revenue, we want value of ρ as close to 1 as possble. By ncreasng k, we ncrease numerator on the rght hand sde of Ineq. (5-11) but at the same tme we ncrease term t / s n the denomnator, so k and then ρ should be k selected by computng ρ for k=1,2, untl the maxmum s found. For k and ρ selected n ths way the Lemma 1 holds. Lemma 5-2: For bdder, f maxmzes the expected utlty of ths bdder. t b, then bddng hs true valuaton n each aucton round 0 48

59 Proof: The DW class members pay ρ b0, so as long as the bdder s n the DW class, hs bd mpacts nether the prce he pays for the wn nor hs utlty. Hence, any bd hgher than the reservaton prce, ncludng true valuaton, brngs the same utlty. Moreover reservaton prce s not known and bddng the true valuaton gves the bdder the hghest chance of wnnng whle n the DW class. Therefore, to prove Lemma 5-2, we just need to show that bdder gans no advantage by bddng below reservaton prce (and by dong so, movng to the PW class). Comparng bdder s utlty n the DW class wth bd t and n the PW class wth bd Jb 0, where 0 J < 1, we need to show that k k k k ( t ρb ) > ( t ρjb ) J b /( s+ J b ) 0. (5-12) Puttng ths nequalty n a form smlar to Ineq. (5-11) we get: ( p ρ J) J k u+ J k < P ρ, where u = s/ b, P= t / b > 1. (5-13) k 0 0 By analyzng the dervatve of the left hand sde of the above nequalty, we conclude that t s satsfed f and only f the maxmum s reached for nequalty ukp / ρ uk + u + 1. Hence J 1 whch s equvalent to t k ρ k b / s b 0 0 (5-14) The condton (5-14) s lkely to be more strngent than (5-11), because b for bdders n PW class analyzed n Lemma 1, but t stll must be satsfed for Lemma 2 to hold, so selectng values of k and ρ, b 0 we need to satsfy both of them. > t 0 Therefore, by selectng the optmal payment coeffcent ρ, the auctoneer s bd prce b 0 and the constant k that satsfy condtons (5-11) and (5-14), the auctoneer makes bddng true valuaton the domnant strategy n PI-ORA. Also, partcpatng n as many as possble aucton rounds maxmzes the cumulatve utlty of every bdder because the 49

60 level of partcpaton drectly ncreases the wnng score of the current aucton round and the expected number of wns. In concluson, the bdder s optmal strategy n PI-ORA mechansm s to bd hs true valuaton (makng the mechansm ncentve compatble) and to partcpate n as many as possble aucton rounds. 5.4 Smulatons Experments and Results Smulaton Scenaros In the smulatons, we compared four dfferent aucton mechansms that are based on the Unform Prce Sealed Bd (UPSB) aucton. Each aucton mechansm s executed 2000 rounds. UPSB aucton Here, we use the basc Unform Prce Sealed Bd aucton that has no bdder drop control, so bdders are allowed to drop out of the aucton at any tme. In UPSB, all wnners pay the prce equal to the hghest bd of losers. UPSB-NBD aucton Ths case uses the basc UPSB aucton but wth bdders never droppng from the aucton, regardless of ther results. PI-ORA As descrbed above, ths case nvolves selecton of the payment coeffcent ρ, the optmal auctoneer s bd prce, and the constant k n the wnnng score equaton (5- b 0 2) that satsfy the condtons Ineq. (5-11) and Ineq. (5-14). The PI-BDC algorthm s appled durng the wnner selecton process n the PW class. 50

61 PI-ORA-NBD Here, we use the PI-ORA mechansm wth no bdder droppng out of the recurrng aucton, regardless whether the starvaton arses or not. In the UPSB and PI-ORA scenaros, a bdder may drop out of the aucton at any tme as a result of starvaton for resources. The results of smulatng UPSB-NBD are used only to obtan the upper bounds on the auctoneer s revenue snce assumng no bdder drop s unrealstc. The PI-ORA-NBD scenaro s used to observe the stablty of the PI-ORA mechansm n response to the bdder drops. The wealth of each bdder lmts her wllngness to pay and s defned by the true valuaton of a unt of a resource n the aucton. For ths reason, we can equate the wealth dstrbuton wth a dstrbuton of the bdder true valuatons. In the smulatons, we consder three types of those dstrbutons, all wth the mean of 5: (1) the exponental dstrbuton, (2) the unform dstrbuton over [0, 10] range, and (3) the Gaussan dstrbuton. Once the true valuatons are allocated to bdders, such true valuatons do not change durng the recurrng aucton. There are 40 bdders n our smulatons and 20 unts of pershable resources avalable for allocaton n each aucton round. Thus, there are 20 wnners n each aucton round. Snce all of the compared aucton mechansms are ncentve compatble, each bdder bds hs true valuaton n each aucton round under the rsk neutral bddng behavor. Addtonally, bdders partcpate n an aucton contnuously untl they drop out of t. Once out of the aucton, the bdder never returns to t. The bdder s tolerance of consecutve losses, abbrevated as TCL, denotes the maxmum number of consecutve losses that a bdder can tolerate before droppng out of an aucton. TCL of each bdder s unformly dstrbuted over the range of [2, 10]. If consecutve losses of a bdder exceed hs TCL, then the bdder drops out of the aucton and never returns to t. The TCL s set to the number larger than the number of aucton rounds smulated for the UPSB-NBD and PI-ORA-NBD cases. 51

62 5.4.2 Analyss of Smulaton Results Our smulatons focus on the auctoneer s revenue, farness of resource allocaton and stablty of each aucton mechansms n response to bdder drops. In our smulatons, the average payment of wnners n each aucton round s used as a measure of auctoneer s revenue. The revenue comparson between orgnal aucton mechansm and no bdder drop assumpton case s used only to measure the mechansm stablty. We also measure the total number of wns of each bdder n the recurrng aucton n order to gauge the long-term farness. Fgure 5.5: The Average Aucton Clearng Prce As shown n Fgure 5.5, the tradtonal UPSB aucton cannot mantan the seller s desred revenue n a recurrng aucton because the losers of each aucton round have no 52

63 ncentve to partcpate n future aucton rounds and drop out of the aucton. Ths s the result of phenomena that we termed the paradox of an ncentve compatble mechansm n a recurrng aucton. Snce bdders reveal ther true valuatons n each bd, bdders learn ther ablty to wn and those who cannot wn drop out the aucton. The decreased prce competton for the remanng wnners results n a plunge of the aucton clearng prce (.e., the hghest bd of losers, whch quckly becomes zero). After 10 aucton rounds (that s also the upper bound on the TCL value n our smulatons), the aucton clearng prce collapses to 0, snce every loser dropped out of the aucton. Therefore, n the tradtonal basc UPSB aucton, the bdder drop problem s the sole cause of the seller s revenue collapse. An effcent bdder drop control based on the PI-BDC algorthm of the PI-ORA mechansm supports aucton partcpaton of bdders n the PW class and therefore mantans the prce competton between bdders n the DW and PW classes permanently. Addtonally, by optmally selectng the payment coeffcent ρ, the optmal auctoneer s bd prce b 0, and the constant k from Eq. (5-2), the auctoneer can stablze and maxmze the revenue regardless of the bdder true valuaton dstrbuton. The resource waste problem never arses, because the entre stock of avalable pershable resources s sold n each aucton round. Therefore, the proposed PI-ORA mechansm addresses all the problems that motvated our research. In a more general case, the dropped bdder can rejon the aucton, once the auctonclearng prce becomes suffcently low, so the revenue of the UPSB aucton mechansm settles somewhere between the revenues of the basc UPSB and the UPSB-NBD. The revenue of the basc UPSB aucton sets the lower bound snce there are no bdders returnng n ths case. The revenue of the UPSB-NBD aucton sets the upper bound, because all bdders return mmedately to the recurrng aucton n that case. Therefore, n a general case of dropped bdders beng able to rejon the aucton, the revenue may oscllate between the revenues of the basc UPSB and the UPSB-NBD dependng on how quckly bdders drop and rejon the aucton. However, n such an aucton, even f dropped losers of prevous aucton round rejon the aucton agan, they cannot become 53

64 wnners permanently when the exstng wnners never ext the aucton. Such property s one of the reasons why wthout decrease of bds, the dropped bdders are unlkely to rejon the recurrng aucton. Fgure 5.6: The Mechansm Stablty n PI-ORA The average aucton clearng prces of PI-ORA and PI-ORA-NBD n each aucton round are almost the same n each aucton round, as shown n Fgure 5.6 for varous true valuaton dstrbutons. Ths ndcates that the effcent bdder drop control algorthm makes the PI-ORA mechansm stable. 54

65 Our smulaton results show also that the proposed PI-ORA mechansm acheves the long-term farness. As shown n Fgure 5.7, ths mechansm dstrbutes the total number of avalable pershable resources proportonally to each bdder s true valuaton durng recurrng aucton. Thus, the bdder who has the hgher true valuaton and, thus, hgher actual payment for the pershable resource, wns more often than the one wth the lower true valuaton and lower actual payment under the same partcpaton level. The wn dstrbutons of Fgure 5.7 also show that the bdders whose bds (.e., true valuatons) are low are elmnated from the aucton automatcally by exceedng the number of consecutve losses defned by ther TCL. Hence, even though some resources are allocated to the bdders n PW class, the truly low bdders cannot hurt the revenue of PI- ORA. Fgure 5.7: The number of wn dstrbutons 55

66 5.5 Dscrmnatory Prce Optmal Recurrng Aucton In ths secton, we descrbe the proposed Dscrmnatory Prce Optmal Recurrng Aucton (DP-ORA) mechansm n whch multple wnners are selected and each wnner pays hs bd. Hence, the DP-ORA mechansm s not ncentve compatble Wnner Selecton Strateges The frst step of DP-ORA mechansm s the same as the frst step of DP-ORA mechansm. Hence, as shown n Fgure 5.2, n each aucton rounds, an auctoneer classfes the bdders nto one of the three classes: Defnte Wnner (DW), Possble Wnner (PW) and Defnte Loser (DL) based on the bds made by the bdders and the auctoneer. As we already explaned, the DW class bdders become wnners and the DL class bdders become losers wthout any addtonal consderatons. The bdders n the PW class can be wnners or losers based on the descrbed below Valuable Last Loser Frst (VLLF) bdder drop control algorthm VLLF Bdder Drop Control Algorthm By selectng wnners n the PW class, the DP-ORA mechansm encourages them to stay n the aucton, so the wnners should nclude those bdders n the PW class who are consderng droppng out of the aucton. For ths purpose, we propose the Valuable Last Loser Frst Bdder Drop Control (VLLF-BDC) algorthm. The man dea behnd ths algorthm s to allocate the desred resources to a bdder before he drops out of an aucton. The algorthm conssts of two phases. In the frst phase, the bdders who lost n the last aucton round but bd hgher n the current round than n the prevous one are marked as potental wnners. The marked bdders are ranked accordng to ther bds and up to N wppw hghest ranked marked bdders are selected as wnners of the current aucton round. If the number of the marked bdders s smaller than resources are allocated n the second phase of the algorthm. N wppw, the remanng 56

67 The wnner selecton n the frst phase s nfluenced by the bd and the wnnng record of the prevous aucton round, so there could be some loss of farness. To compensate for t, n the second phase, the hghest bddng unmarked bdders n the PW class are selected as wnners of the remanng resources. By markng only those last losers who bd hgher n the current round than n the prevous one, the algorthm prevents bdders wth low bddng patterns from becomng wnners Optmal Dstrbuton of Resources By usng the VLLF bdder drop control algorthm, the proposed DP-ORA mechansm attempts to mantan the prce competton and therefore to stablze the auctoneer revenue. To be successful, t requres that some resources be reserved for the bdder drop control (allocatng all resources to the DW class would reduce the DP-ORA mechansm to the tradtonal DPSB aucton wth all ts dsadvantages n the recurrng aucton envronments). Snce the reservaton prce of the auctoneer defnes the membershp n the DW class, there s a need to fnd an optmal value for ths prce. Throughout ths thess, we denote the mnmum cost of a unt of traded resources as. The auctoneer should set ths cost after consderng nternal and external expenses. Ths cost can also be nterpreted as the auctoneer s desred mnmum prce for the unt of pershable resources. The specfc method for decdng thess. C m C m s beyond the scope of ths The mnmum revenue of an aucton round wth the bdder drop control should be larger than the auctoneer s proftablty revenue. A suffcent condton to ensure ths constrant s b0 N + P ( R N ) > C R, (5-15) dw pwmp dw m where P pwmp represents the average bd of wnners n the PW class. By defnton, P pwmp < b 0. Based on nequalty (5-15), 57

68 b > C 0 m (5-16) because C R< b N + P ( R N ) < b N + b R b N = b R m 0 dw pwmp dw 0 dw 0 0 dw 0. Therefore, the auctoneer should bd a hgher than the mnmum cost of a unt of pershable resources to ensure proftablty of each aucton round. The upper bound of the optmal reservaton prce s constraned by the nterrelatonshp between three types of bdder s classes and the aucton farness. As shown n Table 5.1, an ncrease n the reservaton prce decreases the number of bdders n the DW class (.e., N decreases). Ths change results n an ncrease n the number of resource unts dw reserved for the bdder drop control. Thus, n ths case, the sze of the DL class decreases (.e., N dl decreases). Snce decreasng N dl means ncreasng the prce competton, the resultng total revenue of the auctoneer usually ncreases. However, ncreasng the number of resource unts reserved for the bdder drop control decreases farness of the resource allocaton. Ths s because the wnners n the frst phase of the VLLF bdder drop control algorthm are selected based not only on ther current bds but also on ther past bds and the status n the prevous aucton rounds. Our smulaton results, as shown n Fgure 5.8, also show nter-relatonshps between the members of the DW, PW and DW classes and the revenue n the DP-ORA mechansm. Accordngly, n decdng the upper bound of the reservaton prce, the auctoneer should balance an ncrease n the total revenues wth the loss of farness nduced by the selected reservaton prce. : Increase : Decrease ~: Close to Reservaton Prce N N dw wppw N dl Revenue Farness for N ~R dw for N ~R dw Table 5.1: The nterrelatonshp of bdder s classes 58

69 Fgure 5.8: Impact of the selecton of the reservaton prce 5.6 Smulaton Experments and Results As prevously, smulatons execute 2000 aucton rounds n each run. The followng scenaros are smulated Smulaton Scenaros We compare the followng fve aucton mechansms that are based on the Dscrmnatory Prce Sealed Bd (DPSB) aucton for short-term contract markets n whch sngle tem homogeneous pershable resources are sold recurrently for a specfc tme nterval. 59

70 Tradtonal Aucton (TA): In ths case we smulate an aucton mechansm that has no bdder drop control. Hence, bdders drop out of the recurrng aucton as a result of starvaton for resources. Tradtonal Aucton wth No Bdder Drop (TA-NBD): Ths case represents an dealzed tradtonal aucton mechansm n whch bdders never drop durng the recurrng aucton even f they suffer constant consecutve losses. Reservaton Prce Aucton (RPA): Ths s the case of the TA mechansm wth a reservaton prce. Hence only the bdders who bd hgher than the reservaton prce can be selected wnners. Cancelable Aucton (CA): Ths s another varant of the TA mechansm n whch the auctoneer cancels an aucton round when the projected revenue does not meet her expectatons. Dscrmnatory Prce Optmal Recurrng Aucton (DP-ORA): Ths case represents our newly desgned DP-ORA aucton mechansm wth the VLLF bdder drop control algorthm. The smulaton results of TA-NBD are mpossble to acheve n the real recurrng aucton because no bdder drop assumpton s unrealstc. In the real world, starvaton, trggered by the uneven wealth dstrbuton, wll cause bdders to drop out of the aucton. Thus, the TA-NBD scenaro s only used for a theoretcal comparson. The wealth of each bdder lmts her wllngness to pay and dctates her true valuaton of a unt of resource n the aucton. For ths reason, we equate the wealth dstrbuton wth the dstrbuton of the bdder true valuatons. We set the auctoneer s mnmum cost of a unt of the resource at 5. Accordngly, we set the reservaton prce of RPA as 5, too. We consder three types of the standard dstrbutons of the bdder true valuatons, all wth 60

71 the mean of 5: (1) the exponental dstrbuton, (2) the unform dstrbuton over [0, 10] range, and (3) the Gaussan dstrbuton. There are 100 bdders n our smulatons. Intally, all are actve. We assume that the ntal bds are randomly selected from the range [ t / 2, t ], where t represents the true valuaton of bdder. The sealed bddng assumpton makes each bdder s bddng behavor ndependent of others. Hence, n a recurrng aucton, the bddng behavor s nfluenced only by the results of the prevous aucton rounds,.e., the wn/loss decsons nformed to each bdder by the auctoneer. Based on the assumpton of the rsk neutral bdders, each bdder wll attempt to maxmze ts expected proft. All the above consderatons motvated us to assume the followng bddng behavor. If a bdder lost n the last aucton round, she ncreases her bd by a factor of α > 1 to mprove her wn probablty n the current round. Ths ncrease of a bd stops at the true valuaton. If a bdder won n the last aucton round, she, wth equal probablty of 0.5, ether decreases the bd by a factor of β or mantans t unchanged. The decrease attempts to maxmze the expected proft factor n each bdder s utlty. α and β are set n the smulatons to 1.2 and 0.8, respectvely. The mnmum bd of each bdder s 0.1. If a bdder drops out of an aucton, hs bd s set to 0. There are 50 unts of pershable resources avalable for allocaton n each aucton round. Hence, f the resultng expected revenue of each aucton round s not hgher than or equal to 250, ths aucton round s cancelled n CA. The bdder s tolerance of consecutve losses, abbrevated as TCL, denotes the maxmum number of consecutve losses that a bdder can tolerate before droppng out of an aucton. TCL of each bdder s unformly dstrbuted over the range of [2, 10]. If the consecutve losses of a bdder exceed hs TCL, then the bdder drops out of the aucton and never returns to t. 61

72 5.6.2 Analyss of Smulaton Results Our smulatons focus on the auctoneer revenue and the resource allocaton farness. The auctoneer s revenue s proportonal to the average bd of wnners n each aucton round, so we use the latter as a measure of the former. We also measure the number of wns for each bdder n 2000 rounds of the recurrng aucton. The resultng dstrbuton s a metrc of farness, because hgher bddng bdders should be more frequent wnners than the lower bddng ones. Farness of TA-NBD s optmal, because a bdder wth the bd hgher than a wnner s also a wnner. Addtonally, by the no bdder drop assumpton, TA-NBD never loses a bdder wth the hgh wllngness to pay and the low TCL. Ths means that TA-NBD prevents the loss of farness that may result from the low TCL. Thus, we can measure the loss of farness of TA, RPA, CA and DP-ORA by ther degree of devaton from the farness of TA-NBD. We measure the loss of farness LF k of the aucton mechansm k by the dstrbuton of wns between the bdders: LF k n = 1 NWTANBDA() NWk () = 100, (5-17) R N Total _ Aucton where n denotes the total number of bdders n the recurrng aucton, NWk () represent the total number of wns by bdder durng N Total _ Aucton NW () TANBDA and of aucton rounds n TA-NBD and aucton mechansm k, respectvely. As shown n Fgure 5.9, under, varous wealth dstrbutons, TA cannot mantan the auctoneer s desred revenue. The nevtable bdders drops decrease the prce competton between bdders who reman n the aucton. Accordngly, the remanng bdders try to decrease ther bds n the forthcomng aucton rounds to maxmze ther expected proft. In the long run, the revenue of each aucton round plunges to a very low level (.e., below 1.0), compared to the auctoneer s desred mnmum cost (here 5.0). 62

73 Therefore, n TA, an nevtable bdder drop problem s the domnatng factor that decreases the auctoneer s revenue, because there are no wasted pershable resources. In RPA, the revenue of auctoneer s manly decreased by the resource waste problem. The bdder drop effect s small n ths case, because the reservaton prce prevents the wnners from decreasng ther bds to the very low level. However, RPA does not avod the resource waste problem. As a result, the auctoneer cannot acheve her desred revenue n a recurrng aucton of ths type. CA suffers from the same problem as RPA. By cancelng aucton, CA prevents the remanng bdders from decreasng ther bds to the very low levels. However, n a cancelled aucton round, the entre 50 unts of pershable resources that are assgned to the aucton round are wasted. For ths reason, the resources wasted n the cancelled aucton wll prevent the auctoneer from achevng the desred revenue. DP-ORA s able to mantan the prce competton permanently n a recurrng aucton thanks to the effcent VLLF bdder drop control algorthm. Moreover, n DP-ORA, the resource waste problem never arses, because the entre stock of pershable resources s sold n each aucton round. Therefore, the auctoneer can preserve nearly optmal level of the revenue. Addtonally, the bdders whose bds are very low are elmnated from the aucton automatcally based on ther TCL. Hence, even f the VLLF bdder drop control algorthm allocates resources to the PW class whose members bd lower than members of the Defnte Wnner class, the low true valuaton bdders cannot hurt the auctoneer s revenues under the DP-ORA mechansm. As shown n Fgure 5.9, the bdder drop and resource waste problems arse under all smulated wealth dstrbutons n our smulaton scenaros for the tradtonal aucton mechansms. 63

74 Fgure 5.9: The average wnnng prce of wnners The loss of farness of DP-ORA s remarkably lower than the one observed n TA, RPA and CA under all smulated bdders wealth dstrbutons. Ths phenomenon arses because TA, RPA and CA cannot prevent the loss of farness caused by the hgh true valuaton bdders droppng out of an aucton as a result of exceedng ther TCLs. In other words, TA, RPA and CA cannot prevent a bdder who s wllng to pay hgh prces but has low TCL from droppng out of an aucton after exceedng hs TCL at some aucton round. In each aucton round, TA, RPA and CA have the hghest possble farness, because ther wnners are selected by the current bd only. Yet, remarkably, compared wth them, DP-ORA has lower loss of farness over the lfe-tme of recurrng aucton because loss of farness that results from TCL s the domnant factor n the long run. The 64