DOCSLIB.ORG

Multi-Unit Bilateral Trade Matthias Gerstgrasser,1 Paul W

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
Multi-Unit Bilateral Trade Matthias Gerstgrasser,1 Paul W The Thirty-Third AAAI Conference on Artificial Intelligence (AAAI-19) Multi-Unit Bilateral Trade Matthias Gerstgrasser,1 Paul W. Goldberg,2 Bart de Keijzer,3 Philip Lazos,4 Alexander Skopalik5 1,2,4Department of Computer Science, University of Oxford 3School of Computer Science and Electronic Engineering, University of Essex 5Department of Applied Mathematics, University of Twente fmatthias.gerstgrasser, paul.goldberg, fi[email protected] [email protected] [email protected] Abstract term “satisfactory” can be tailored to the specific market un- der consideration, but nonetheless, in economic theory vari- We characterise the set of dominant strategy incentive com- ous universal properties have been identified and agreed on patible (DSIC), strongly budget balanced (SBB), and ex-post individually rational (IR) mechanisms for the multi-unit bilat- as important. The following three are the most fundamental eral trade setting. In such a setting there is a single buyer and ones: a single seller who holds a finite number k of identical items. • Incentive Compatibility ((DS)IC): It must be a dominant The mechanism has to decide how many units of the item are strategy for the agents (buyers and sellers) to behave truth- transferred from the seller to the buyer and how much money fully, hence not “lie” about their valuations for the items is transferred from the buyer to the seller. We consider two in the market. This enables the market mechanism to classes of valuation functions for the buyer and seller: Valua- tions that are increasing in the number of units in possession, make an informed decision about the trades to be made. and the more specific class of valuations that are increasing • Individual Rationality (IR): It must not harm the utility of and submodular. an agent to participate in the mechanism. Furthermore, we present some approximation results about • Strong Budget Balance (SBB): All monetary transfers that the performance of certain such mechanisms, in terms of so- cial welfare: For increasing submodular valuation functions, the mechanism executes are among participating agents we show the existence of a deterministic 2-approximation only. That is, no money is injected into the market, and no mechanism and a randomised e=(1−e) approximation mech- money is burnt or transferred to any agent outside of the anism, matching the best known bounds for the single-item market. setting. This paper studies the capabilities of mechanisms that sat- isfy these three fundamental properties above for a very sim- 1 Introduction ple special case of a two-sided market. Bilateral trade is the most basic such setting comprising a buyer and a seller, to- Auctions form one of the most studied applications of game gether with a single item that may be sold, i.e., transferred theory and mechanism design. In an auction setting, a sin- from the seller to the buyer against a certain payment from gle seller or auctioneer runs a pre-determined procedure or the buyer to the seller. The bilateral trade setting is a clas- mechanism (i.e., the auction) to sell one or more goods to sical one: It was studied in the seminal paper (Myerson and the buyers, and the buyers then have to strategise on the way Satterthwaite 1983) and has been studied in detail in var- they interact with the auction mechanism. An auction set- ious other publications in the economics literature. Recent ting is rather restrictive in that it involves a single seller that work in the Algorithmic Game Theory literature (Blum- is monopolistic and is assumed to be non-strategic. While rosen and Dobzinski 2016; Blumrosen and Mizrahi 2016; this is a sufficient assumption in some cases, there are many Colini-Baldeschi et al. 2017b) has focused on the welfare applications that are more complex: It is often realistic to as- properties of bilateral trade mechanisms. These works as- sume that a seller expresses a valuation for the items in her sume the existence of prior distributions over the valuations possession and that a seller wants to maximise her profit. of the buyer and seller, that may be thought of as modelling Such settings in which both buyers and sellers are consid- an intermediary’s beliefs about the buyer’s and seller’s val- ered as strategic agents are known as two-sided markets, ues for the item. whereas auction settings are often referred to as one-sided The present paper studies a generalisation of the classical markets. bilateral trade setting by allowing the seller to hold multi- The present paper falls within the area of mechanism de- ple units initially. These units are assumed to be of a sin- sign for two-sided markets, where the focus is on designing gle resource, so that both agents only express valuations in satisfactory market platforms or intermediation mechanisms terms of how many units they have in possession. The fi- that enable trade between buyers and sellers. In general, the nal utility of an agent (buyer or seller) is then determined Copyright c 2019, Association for the Advancement of Artificial by her valuation and the payment she paid or received. We Intelligence (www.aaai.org). All rights reserved. focus our study on characterising which mechanisms satisfy 1973 the the above three properties and which of these feasible present various mechanisms for it that approximate the op- mechanisms achieve a good social welfare (i.e., total utility timal social welfare. Their best mechanism achieves an ap- of buyer and seller combined). proximation factor of e=(e − 1). As in the present paper, Due to its simplicity, our setting is fundamental to any there are prior distributions on the traders’ valuations, and strategic setting where items are to be redistributed or re- the quantity being approximated is the expectation over the allocated. Our characterisation efforts show that all feasible priors, of the optimal allocation of the item. mechanisms must belong to a very restricted class, already The weaker notion of Bayesian incentive compatibility is for this very simple setting with one buyer, one seller, and considered in (Blumrosen and Mizrahi 2016), where the au- a relatively simple valuation structure. The specific mecha- thors propose a mechanism in which the seller offers a take- nisms we develop are very simple, and suitable for imple- it-or-leave-it price to the buyer. They prove that this mech- mentation with very little communication complexity. anism approximates the harder gain from trade objective within a factor of 1=e under a technical albeit often reason- able MHR condition on the buyer’s distribution. Our Contribution. Our first main contribution is a full The class of DSIC, IR, and SBB mechanisms for bilateral characterisation of the class of truthful, individually rational trade was characterised in (Colini-Baldeschi et al. 2016) to and strongly budget balanced mechanisms in this setting. We be the class of fixed price mechanisms. In the present work, do this separately for two classes of valuation functions: sub- we characterise this set of mechanisms for the more general modular valuations and general non-decreasing valuations. multi-unit bilateral trade setting, thereby extending their re- Section 3 presents a high-level argument for the submodu- sult. The gain from trade arising from such mechanisms was lar case. A full and rigorous formal proof for both settings analysed in (Colini-Baldeschi et al. 2017a). is given in the full version of this paper (Gerstgrasser et al. 2018). Essentially, for the general case, any mechanism that Various recent papers analyse more general two-sided aims to be truthful, strongly budget balanced and individu- markets, where there are multiple buyers and sellers, who ally rational can only allow the agents to trade a single quan- hold possibly complex valuations over the items in the mar- tity of items at a predetermined price. The trade then only ket. (Colini-Baldeschi et al. 2017b) analyse a more general occurs if both the seller and buyer agree to it. This leads to scenario with multiple buyers, sellers, and multiple distinct a very clean characterization and has the added benefit of items, and use the same feasibility requirements as ours giving a robust, simple to understand mechanism: the agents (DSIC, IR, and SBB). (Segal-Halevi, Hassidim, and Au- do not have to disclose their entire valuation to the mecha- mann 2018b) have considered a similar setting but focus on nism, and only have to communicate whether they agree to gains from trade (GFT) (i.e., the increase in social welfare trade one specific quantity at one specific price. For the sub- resulting from reallocation of the items) instead of welfare. modular case, suitable mechanisms can be characterised as They initially considered a multi-unit setting like ours (al- specifying a per-unit price, and repeatedly letting the buyer beit with multiple buyers and sellers), and they extend their and seller trade an item at that price until one of them de- work in (Segal-Halevi, Hassidim, and Aumann 2018a) to al- clines to continue. low multiple types of goods. They present a mechanism that approximates the optimal GFT asymptotically in large mar- Secondly, we give approximation mechanisms for the so- kets. (Balseiro et al. 2018) designs two-sided market mech- cial welfare objective in the Bayesian setting in Section 4, anisms for one seller and multiple buyers with a temporal for the case of submodular valuations. Theorem 4.1 presents component, where valuations are correlated between buyers a 2-approximate deterministic mechanism. For randomised but independent across time steps. A good approximation mechanisms, we show a e=(e − 1)-approximation in Theo- (of factor 1=2) of the social welfare using the more permis- rem 4.2.
Load more

Recommended publications
  • A Study of Paul A. Samuelson's Economics
    Copyright is owned by the Author of the thesis. Permission is given for a copy to be downloaded by an individual for the purpose of research and private study only. The thesis may not be reproduced elsewhere without the permission of the Author. A Study of Paul A. Samuelson's Econol11ics: Making Economics Accessible to Students A thesis presented in partial fulfilment of the requirements for the degree of Doctor of Philosophy in Economics at Massey University Palmerston North, New Zealand. Leanne Marie Smith July 2000 Abstract Paul A. Samuelson is the founder of the modem introductory economics textbook. His textbook Economics has become a classic, and the yardstick of introductory economics textbooks. What is said to distinguish economics from the other social sciences is the development of a textbook tradition. The textbook presents the fundamental paradigms of the discipline, these gradually evolve over time as puzzles emerge, and solutions are found or suggested. The textbook is central to the dissemination of the principles of a discipline. Economics has, and does contribute to the education of students, and advances economic literacy and understanding in society. It provided a common economic language for students. Systematic analysis and research into introductory textbooks is relatively recent. The contribution that textbooks play in portraying a discipline and its evolution has been undervalued and under-researched. Specifically, applying bibliographical and textual analysis to textbook writing in economics, examining a single introductory economics textbook and its successive editions through time is new. When it is considered that an economics textbook is more than a disseminator of information, but a physical object with specific content, presented in a particular way, it changes the way a researcher looks at that textbook.
    [Show full text]
  • On the Relationship Between the VCG Mechanism and Market Clearing
    On the Relationship between the VCG Mechanism and Market Clearing Takashi Tanaka1 Na Li2 Kenko Uchida3 Abstract— We consider a social cost minimization problem well. First, it may not be easy to guarantee the existence with equality and inequality constraints in which a central co- of supply function equilibria in realistic electricity markets. ordinator allocates infinitely divisible goods to self-interested N As demonstrated by [13], a pure Nash equilibrium may fail firms under information asymmetry. We consider the Vickrey- Clarke-Groves (VCG) mechanism and study its connection to an to exist even in a relatively simple supply function bidding alternative mechanism based on market clearing-price. Under model. Second, even if the supply function equilibria are the considered set up, we show that the VCG payments are known to exist, it could be a difficult task for the firms to find equal to the path integrals of the vector field of the market them efficiently [14]. Finally, unlike the mechanism design clearing prices, indicating a close relationship between the approach (discussed next), the efficiency loss is inevitable. VCG mechanism and the “clearing-price” mechanism. We then discuss its implications for the electricity market design and The mechanism design is an alternative approach to- also exploit this connection to analyze the budget balance of wards the market power mitigation. For instance, the refer- the VCG mechanism. ences [15]–[18] consider applications of the Vickrey-Clarke- Groves (VCG) mechanism [2, Ch. 23] to several market I. INTRODUCTION design problems in power system operations. The VCG Market power monitoring and mitigation are essential mechanism provides an attractive market model since it aspects of today’s electricity market operations [1].
    [Show full text]
  • The Price Mechanism and Resource Allocation
    The Price Mechanism and Resource Allocation AS Economics Presentation 2005 Markets • A market is the place where buyers and sellers meet to exchange a product. Markets require: – Consumers i.e. buyers – Producers or firms i.e. sellers – Goods or services to trade (a recognizable output) • Examples of markets include: – Housing market: home owners and potential buyers – Labour market: employers and workers – Stock market: share owners and potential buyers – Foreign exchange market: trading currencies Sub Markets – Market Segmentation • The market for most goods can be segmented – broken down into sub markets • The market for houses – (i) sub markets for terraced, semi-detached and detached homes – (ii) the market for rented properties and owner occupied housing • The market for cars is made up of sub markets for family saloon cars, hatchbacks and high performance sports cars • The travel industry is heavily segmented Functions of the Price Mechanism • The price mechanism is the means by which decisions of consumers and businesses interact to determine the allocation of resources between different goods and services • (1) The signaling function – If prices are rising because of stronger demand from consumers, this is a signal to suppliers to expand output to meet the higher demand – When demand is strong, higher market prices act as an incentive to raise output (production) because the supplier stands to make a higher profit • (2) The rationing function – Prices serve to ration scarce resources when demand in a market outstrips supply – When there is a shortage of a product in the market, the price will rise and thus deter some consumers from purchasing the product Adam Smith and the ‘Invisible Hand’ • The 18th Century economist Adam Smith – one of the founding fathers of modern economics, described how the invisible or hidden hand of the market operated in a competitive market through the pursuit of self-interest to allocate resources in society’s best interest • This remains the central view of all free-market economists, i.e.
    [Show full text]
  • Trade Agreements and the Nature of Price Determination † 470 Determination by Pol Antràs and Robert W
    American Economic Review: Papers & Proceedings 2012, 102(3): 470–476 http://dx.doi.org/10.1257/aer.102.3.470 Contents † Trade Agreements and the Nature of Price Trade Agreements and the Nature of Price Determination † 470 Determination By Pol Antràs and Robert W. Staiger* I. Perfect Competition 471 The terms-of-trade theory of trade agree- from subsequently manipulating their domes- ments holds that governments are attracted to tic policy choices to undercut the market access trade agreements as a means of escape from a implications of their tariff commitments, can II. Imperfect Competition 472 terms-of-trade–driven prisoner’s dilemma see bring governments to the efficiency frontier.1 Bagwell and Staiger 1999 . One of the terms-( In this paper, we show that the nature of inter- of-trade theory’s most striking) predictions is national price determination can have important III. Matching 474 about the treatment of behind-the-border pol- effects on this prediction of the terms-of-trade icy measures in trade agreements. According theory. In particular, while the terms-of-trade to this prediction, in the noncooperative Nash theory adopts the view that international prices REFERENCES 476 equilibrium from which countries would begin are fully disciplined by market clearing condi- in the absence of a trade agreement, tariffs are tions, we show here that support for shallow set inefficiently high but behind-the-border poli- integration is overturned, and instead a need for cies are set at efficient levels. Hence, even in the “deep” integration is suggested—wherein direct context of a complex policy environment there negotiations occur over both border and behind- is no need for member governments of a trade the-border policies—if international prices are agreement to negotiate directly over the lev- determined through bargaining.
    [Show full text]
  • Pricing Public Goods for Private Sale
    Proceedings Article Pricing Public Goods for Private Sale MICHAL FELDMAN, Hebrew University and Harvard University DAVID KEMPE, University of Southern California BRENDAN LUCIER, Microsoft Research RENATO PAES LEME, Microsoft Research We consider the pricing problem faced by a seller who assigns a price to a good that confers its benefits not only to its buyers, but also to other individuals around them. For example, a snow-blower is potentially useful not only to the household that buys it, but also to others on the same street. Given that the seller is constrained to selling such a (locally) public good via individual private sales, how should he set his prices given the distribution of values held by the agents? We study this problem as a two-stage game. In the first stage, the seller chooses and announces a price for the product. In the second stage, the agents (each having a private value for the good) decide simultaneously whether or not they will buy the product. In the resulting game, which can exhibit a multiplicity of equilibria, agents must strategize about whether they will themselves purchase the good to receive its benefits. In the case of a fully public good (where all agents benefit whenever any agent purchases), we describe a pricing mechanism that is approximately revenue-optimal (up to a constant factor) when values are drawn from a regular distribution. We then study settings in which the good is only “locally” public: agents are arranged in a network and share benefits only with their neighbors. We describe a pricing method that approximately maximizes revenue, in the worst case over equilibria of agent behavior, for any d-regular network.
    [Show full text]
  • Economic Calculation and the Limits of Organization
    Economic Calculation and the Limits of Organization Peter G. Klein conomists have become increasingly frustrated with the text- book model of the firm. The "firm" of intermediate microeco- Enomics is a production function, a mysterious "black box" whose insides are off-limits to respectable economic theory (relegated instead to the lesser disciplines of management, organization theory, industrial psychology, and the like). Though useful in certain contexts, the textbook model has proven unable to account for a variety of real- world business practices: vertical and lateral integration, geographic and product-line diversification, franchising, long-term commercial contract- ing, transfer pricing, research joint ventures, and many others. As an al- ternative to viewing the firm as a production function, economists are turning to a new body ofliterature that views the firm as anorganization, itself worthy of economic analysis. This emerging literature is the best- developed part of what has come to be called the "new institutional eco- nomics."' The new perspective has deeply enhanced and enriched our un- derstanding of firms and other organizations, such that we can no longer agree with Ronald Coase's 1988 statement that "[wlhy firms exist, what determines the number of firms, what determines what firms do . are not questions of interest to most economists" (Coase 1988a, p. 5).The new theory is not without its critics; Richard Nelson (1991), for example, ob- jects that the new institutional economics tends to downplay discretion- ary differences among firms. Still, the new institutional economics-in particular, agency theory and transaction cost economics-has been *Peter G. Klein is assistant professor of economics at the University of Georgia.
    [Show full text]
  • Market Failure in Context: Introduction Alain Marciano and Steven G
    Market Failure in Context: Introduction Alain Marciano and Steven G. Medema Market failure, conceived of as the failure of the market to bring about results that are in the best interests of society as a whole, has a long lin- eage in the history of writings on matters economic. As Steven G. Medema has shown in The Hesitant Hand, much of the history of economics can be read as a discussion of whether, and the extent to which, the self- interested actions of private agents, channeled through the market, will redound to the larger social interest. For much of this history, the answers given were negative, and it was assumed that the corrective hand of the state was needed as a constant and consistent regulating force. Thus we find Plato and Aristotle arguing for a wide range of legal restrictions to guard against macroeconomic (to use the modern term) instability; Aqui- nas making the case for rules that promote a measure of Christian justice in economic affairs; mercantilist writers lobbying for restrictions on vari- ous forms of trade (and support for others), as well as for regulations on Correspondence may be addressed to Alain Marciano, University of Montpellier, Department of Economics, Rue Raymond Dugrand, CS 79606, F-34960 Montpellier, France (e-mail: alain [email protected]); and to Steven G. Medema, Department of Economics, University of Colorado Denver, CB 181, PO Box 173364, Denver, CO 80217-3364 (e-mail: steven.medema @ucdenver.edu). The editors wish to thank Paul Dudenhefer for his diligent shepherding of this project from conference to published volume.
    [Show full text]
  • The Cost of Price: Why and How to Get Beyond Intellectual Property Internalism Amy Kapczynski
    The Cost of Price: Why and How to Get Beyond Intellectual Property Internalism Amy Kapczynski ABSTRACT The field of intellectual property (IP) law today is focused, as the name itself advertises, UCLA LAW REVIEW UCLA LAW on one particular institutional approach to scientific and cultural production: IP. When legal scholars explain this focus, they typically do so with reference to the virtues of price. Because price gives us a decentralized way to link social welfare to the production of information, IP is alleged to be more efficient than other approaches. The dominant mode of IP scholarship begins here and then addresses questions internal to IP law— for example, how broad or narrow should exceptions to IP rights be? But the internalism that characterizes the field of IP cannot, as I show, be justified by the value of efficiency. Economics offers us no a priori reason to assume that IP is more efficient than other possible approaches, most prominently government procurement and commons-based production. If we take the invitation that economists offer us to think external to IP, we also gain new insights about the implications of values other than efficiency for the choice between different institutional approaches to scientific and cultural production. We see, as I argue, that using price to guide scientific and cultural production—which is to say, using IP—may have costs not only for efficiency, but also for distributive justice and informational privacy. The IP approach is in tension with the value of distributive justice because reliance upon price may yield not only unjust distribution of existing information resources but also unjust production of future information resources.
    [Show full text]
  • The Price Mechanism and the Invisible Hand 3
    Exclusive Hyun Kim Jung Hoon Hong Daiki Kim Meejoo Song Wooseung Sohn 1 I. INTRODUCTION In our presentation, there are four main subjects that we will be explaining today. Those subjects are: 1. Private goods and the Free Market System. 2.The Price Mechanism and the Invisible Hand 3. Public goods and the market failure 4. Public hand and the government failure. Before we go into the details, let me briefly give you the overview. First we have to approach these questions by asking ourselves… What do we mean by Exclusive? Of course, the word exclusive can be heard on a regular basis. For example, an exclusive interview with Professor Kim. Then what does the word exclusive mean? According to the dictionary, the word “exclusive” is defined as “not divided or shared with others” So how is this relevant to what we are studying? How is it connected to the rights? You might ask… There were discussions as to what “exclusiveness” meant. In my perspective, there are spiritual and material interests that are protected by the laws. Since, these interests are protected, as the characteristic of the rights, the interest become exclusive when it becomes a right. In having an exclusive right would mean that a person could enjoy the right at his or her wish. Therefore, we felt that there was a close link to the free market system and the right. Well, let’s go back to the last week’s lecture. If you can remember, Sun-young gave us a splendid presentation on the bourgeoisie last week.
    [Show full text]
  • Martin L. Weitzman: Prices Vs. Quantities
    Prices vs. Quantities12 MARTIN L. WEITZMAN Massachusetts Institute of Technology I. INTRODUCTION The setting for the problem under consideration is a large economic organization or system which in some cases is best thought of as the entire economy. Within this large economic organization resources are allocated by some combination of commands and prices (the exact mixture is inessential) or even by some other unspecified mechanism. The following question arises. For one particular isolated economic variable that needs to be regulated,3 what is the best way to implement control for the benefit of the organization as a whole? Is it better to directly administer the activity under scrutiny or to fix transfer prices and rely on self-interested profit or utility maximization to achieve the same ends in decentralized fashion? This issue is taken as the prototype problem of central control which is studied in the present paper. There are a great many specific examples which fit nicely into such a framework. One of current interest is the question of whether it would be better to control certain forms of pollution by setting emission standards or by charging the appropriate pollution taxes. When quantities are employed as planning instruments, the basic operating rules from the centre take the form of quotas, targets, or commands to produce a certain level of output. With prices as instruments, the rules specify either explicitly or implicitly that profits are to be maximized at the given parametric prices. Now a basic theme of resource allocation theory emphasizes the close connection between these two modes of control.
    [Show full text]
  • The Rate at Which a Simple Market Converges to Efficiency As the Number of Traders Increases: an Asymptotic Result for Optimal Trading Mechanisms*
    JOURNAL OF ECONOMIC THEORY 48, 304332 (1989 ) The Rate at Which a Simple Market Converges to Efficiency as the Number of Traders Increases: An Asymptotic Result for Optimal Trading Mechanisms* THOMAS A. GRESIK John M. Olin School of Business. Washington Universiiy. SI. Louis. Missouri 63130 AND MARK A. SATTERTHWAITE Kellogg Graduate School of Management, Northwestern University, Evanston, Illinois 60208 Received January 9, 1987; revised July 19, 1988 Private information in an independent, private-values market provides incentives to traders to manipulate equilibrium prices strategically. This strategic behavior precludes ex post efficient market performance. Increasing the number of traders improves the efficiency of some trading mechanisms by enabling them to better utilize the private information traders’ bids and offers reveal. This paper shows that the expected inefficiency of optimally designed mechanisms, relative to ex post efficient allocations, decreases almost quadratically as the number of traders increases. Journal of Economic Literature Classification Numbers: 026, 022. ( 1989 Academic Press. Inc 1. INTRODUCTION Private information prevents achievement of ex post efficiency within a small, private goods market. A trading mechanism’s efficiency may improve as the number of traders increases because more traders may enable it to * The participants of the Economic Theory Workshop at the University of Chicago helped this research materially by discovering a serious error in an early version of this work. We give special thanks to Larry Jones, Ken Judd. Ehud Kalai, Isaac Melijkson. Roger Myerson, and Roger Koenker for their help. This material is based upon work supported by the National Science Foundation under Grants SOC-7907542 and SES-8520247, the Center for Advanced Study in Managerial Economics and Decision Sciences at the Kellogg School, and the Health Care Financing Administration through a grant to Northwestern’s Center for Health Services and Policy Research.
    [Show full text]
  • Auction Vs. Posted-Price: Market Mechanism, Lender Behaviors, and Transaction Outcomes in Online Crowdfunding
    Auction vs. Posted-Price: Market Mechanism, Lender Behaviors, and Transaction Outcomes in Online Crowdfunding Zaiyan Wei and Mingfeng Lin1 December 2013 Abstract We study the effect of different market mechanisms, specifically auctions and posted- prices, on participant behaviors and transaction outcomes in an online personal loan market. We develop a game theoretic model to generate empirically testable predictions, then exploit a regime change on a peer-to-peer lending site, Prosper.com, to test them. We find that under posted-prices, loans are funded with higher probability, but only at higher initial and contract interest rates, and are more likely to default. While market-based auctions may be slow in dis- covering the correct price, “expert”-based posted-price selling may yield unintended, negative welfare consequences. Keywords: Multiunit-auctions, Posted-prices, Crowdfunding, Peer-to-peer (P2P) lending, Ob- servational learning. JEL Classification: D44, L11, L86, G20 1Zaiyan Wei: Department of Economics, University of Arizona (Email: [email protected]). Mingfeng Lin: Department of Management Information Systems, University of Arizona (Email: [email protected]). The authors contribute equally in this research. We thank Keisuke Hirano, Christopher Lamoureux, Chris Parker, Stan- ley Reynolds, Siva Viswanathan, John Wooders, Mo Xiao, and numerous seminar participants for helpful comments and suggestions. All errors remain our own. 1 Introduction Auctions have long been a dominant market mechanism in electronic commerce. A prominent example is eBay.com, one of the earliest and most successful examples of e-commerce, where auctions are extensively used to match buyers and sellers through a competitive process. Auctions are also widely used in online business-to-business (B2B) procurements and many other contexts (Lucking-Reiley(2000), Bajari and Hortac¸su(2004), The Economist(2000)).
    [Show full text]