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on Game Theory |
| By: | Nicola Dimitri |
| Abstract: | In recent years internet auctions have attracted much attention. This paper discusses a possible explanation for empirical evidence, notably in fixed-end auctions such as eBay, showing a low number of offers early in the auction, with most of the bids concentrated towards the end of the auction. This “last minute bidding” (sniping) phenomenon was first investigated by Roth and Ockenfels (2002). Unlike standard auctions where each offer is processed by the auctioneer, due to system traffic and connection time in eBay close-end auctions very late bids may get lost and left unprocessed by the auction site. Based on this observation, in a simple two-player game theoretic model with private values, we analyze how the possibility that a bid might not be accepted by the system could affect bidders’ strategic decision to offer late. We find that late bidding, with no offer early in the auction, could be a Nash Equilibrium if players’ values for the object on sale are not too different, with the difference depending upon the relevant probabilities for last minute bids to be successfully placed. |
| Keywords: | eBay auctions, last minute bidding, congestion. |
| JEL: | C72 D44 |
| Date: | 2007–12 |
| URL: | http://d.repec.org/n?u=RePEc:usi:depfid:001&r=gth |
| By: | Kets, W. (Tilburg University, Center for Economic Research) |
| Abstract: | In many contexts, players interact only with a subset of the whole population, i.e., players interact on a network. This paper a setting in which players are located on a network and play a fixed game with their neighbors. Players have incomplete information on the network structure. They have a common prior over the network, and in addition, they know the number of connections they have. That is, their type is their degree. We study the sensitivity of game-theoretic predictions to the specification of players? beliefs. We show that two priors are close in a strategic sense if and only if they assign similar probabilities to all local events, i.e., to all events involving the types of a player and his neighbors. This means that in order to fully explore the range of possible strategic outcomes, it suffices to vary the type distribution and the correlation among player types. On the other hand, it is not enough to vary only the type distribution, which has been the focus of much of the literature so far. |
| Keywords: | Network games;incomplete information;payoff continuity |
| JEL: | C72 D83 L14 Z13 |
| Date: | 2007 |
| URL: | http://d.repec.org/n?u=RePEc:dgr:kubcen:200798&r=gth |
| By: | Alexander Matros; Adamo Tim |
| Abstract: | We consider a Blotto Game with Imperfect Information. Empirical evidence suggests a symmetric monotonic Bayesian equilibrium as a solution concept. Such a pure-strategy equilibrium is found and its properties are discussed. |
| Date: | 2007–12 |
| URL: | http://d.repec.org/n?u=RePEc:pit:wpaper:332&r=gth |
| By: | Mezzetti, Claudio (University of Warwick, Department of Economics,); Tsetlin, Ilia (INSEAD) |
| Abstract: | Theoretical models of multi-unit, uniform-price auctions assume that the price is given by the highest losing bid. In practice, however, the price is usually given by the lowest winning bid. We derive the equilibrium bidding function of the lowest-winning-bid auction when there are k objects for sale and n bidders with unit demand, and prove that it converges to the bidding function of the highest-losing-bid auction if and only if the number of losers n - k gets large. When the number of losers grows large, the bidding functions converge at a linear rate and the prices in the two auctions converge in probability to the expected value of an object to the marginal winner. |
| Keywords: | Auctions; Lowest-Winning Bid; Highest-Losing Bid; k-th Price Auction, (k+1)-st; Price Auction |
| JEL: | D44 D82 |
| Date: | 2007 |
| URL: | http://d.repec.org/n?u=RePEc:wrk:warwec:832&r=gth |
| By: | Young Han Lee; Ulrike Malmendier |
| Abstract: | Traditional explanations for the popularity of auctions are efficiency and revenue maximization. We argue that auctions also induce 'overbidding,' i.e., bidding above the buyer's willingness to pay for an item outside the auction. Even if only few buyers overbid, they affect prices and allocations since auctions systematically pick those buyers as winners. We employ a novel approach to identify overbidding, using hand-collected data of eBay auctions with simultaneous fixed prices. We argue that fixed prices for identical items on the same webpage should provide an upper bound for bidders' willingness to pay in the auctions. In a first, detailed data set of board game auctions, we find that, in 42 percent of the auctions, the final price is higher than the simultaneous fixed price. The result is not explained by differences in item quality, shipping costs, or seller reputation. Auction experience, as measured by eBay's feedback score, does not eliminate overbidding. We also document that the large fraction of overbidding is induced by a small number of players: only 17 percent of bidders ever bid above the fixed price. The finding replicates in a broad cross-section of auctions (48 percent overbidding). Using a simple model of second-price auctions with a fixed price option, we show that transaction costs of switching between auctions and fixed prices are not sufficient to explain the results. Limited attention of bidders and utility of winning both contribute to explaining the empirical findings. |
| JEL: | D02 D12 D44 D83 |
| Date: | 2007–12 |
| URL: | http://d.repec.org/n?u=RePEc:nbr:nberwo:13699&r=gth |
| By: | Sascha Füllbrunn (Faculty of Economics and Management, Otto-von-Guericke University Magdeburg); Abdolkarim Sadrieh (Faculty of Economics and Management, Otto-von-Guericke University Magdeburg) |
| Abstract: | The design of markets has become a major issue due to the capability of online operators to implement almost any set of market rules overnight. With this study we contribute to the literature of market design by presenting a theoretical and experimental analysis of sudden termination auctions. Our main focus is on the candle auction that has a positive termination probability at any time in the course of the auction. The second price candle auction which is technically demanding and rarely implemented offline proves to be a faster and equally efficient alternative to standard hard close auctions. |
| Keywords: | auctions, termination rules, electronic markets |
| JEL: | C73 C9 D44 |
| Date: | 2007–02 |
| URL: | http://d.repec.org/n?u=RePEc:mag:wpaper:06024&r=gth |
| By: | Luciano I. De Castro; Alvaro Riascos |
| Abstract: | This paper provides first order conditions for a very general class of single or multi-unit auctions. Under mild conditions we characterize bidding-behavior and generalize previous standard results in the literature. As an application we obtain sufficient conditions for truth-telling, monotonic best reply strategies and identification results for multi-unit auctions. |
| Date: | 2007–11–09 |
| URL: | http://d.repec.org/n?u=RePEc:col:000089:004382&r=gth |
| By: | Nir Halevy; Gary Bornstein; Lilach Sagiv |
| Date: | 2007–12–18 |
| URL: | http://d.repec.org/n?u=RePEc:cla:levrem:122247000000001806&r=gth |
| By: | Sebastian Braun; Nadja Dwenger; Dorothea Kübler |
| Abstract: | We investigate the matching algorithm used by the German central clearinghouse for university admissions (ZVS) in medicine and related subjects. This mechanism consists of three procedures based on final grades from school (“Abiturbestenverfahren”, “Auswahlverfahren der Hochschulen”) and on waiting time (“Wartezeitverfahren”). While these procedures differ in the criteria applied for admission they all make use of priority matching. In priority matching schemes, it is not a dominant strategy for students to submit their true preferences. Thus, strategic behaviour is expected. Using the full data set of applicants, we are able to detect some amount of strategic behaviour which can lead to inefficient matching. Alternative ways to organize the market are briefly discussed. |
| Keywords: | Matching, university admissions, strategic behaviour |
| JEL: | C78 D02 D78 I29 |
| Date: | 2007–12 |
| URL: | http://d.repec.org/n?u=RePEc:hum:wpaper:sfb649dp2007-070&r=gth |
| By: | Ehud Guttel; Barak Medina |
| Date: | 2007–12–18 |
| URL: | http://d.repec.org/n?u=RePEc:cla:levrem:122247000000001799&r=gth |
| By: | William Thomson (University of Rochester) |
| Abstract: | We define two families of rules to adjudicate conflicting claims. The first family contains the constrained equal awards, constrained equal losses, Talmud, and minimal overlap rules. The second family, which also contains the constrained equal awards and constrained equal losses rules, is obtained from the first one by exchanging, for each problem, how well agents with relatively larger claims are treated as compared to agents with relatively smaller claims. In each case, we identify the subfamily of consistent rules. |
| Keywords: | claims problems, constrained equal awards rule, constrained equal losses rule, Talmud rule, minimal overlap rule, ICI rules, CIC rules, consistency. |
| JEL: | C79 D63 D74 |
| Date: | 2007–12 |
| URL: | http://d.repec.org/n?u=RePEc:roc:rocher:535&r=gth |
| By: | Toru Hokari; William Thomson (University of Rochester) |
| Abstract: | We consider the problem of adjudicating conflicting claims in the context of a variable population. A property of rules is "lifted" if whenever a rule satisfies it in the two-claimant case, and the rule is bilaterally consistent, it satisfies it for any number of claimants. We identify a number of properties that are lifted, such as equal treatment of equals, resource monotonicity, composition down and composition up, and show that continuity, anonymity and self-duality are not lifted. However, each of these three properties is lifted if the rule is resource monotonic. |
| Keywords: | claims problems, consistency, lifting, constrained equal awards rule, constrained equal losses rule |
| JEL: | C79 D63 D74 |
| Date: | 2007–12 |
| URL: | http://d.repec.org/n?u=RePEc:roc:rocher:536&r=gth |
| By: | William Thomson (University of Rochester) |
| Abstract: | We consider the problem of dividing the cost of a facility when agents can be ordered in terms of the need they have for it, and accommodating an agent with a certain need allows accommodating all agents with lower needs at no extra cost. This problem is known as the “airport problem”, the facility being the runway. We review the literature devoted to its study, and formulate a number of open questions. |
| Keywords: | airport problem; monotonicity; consistency; core; Shapley value; nucleolus. |
| Date: | 2007–12 |
| URL: | http://d.repec.org/n?u=RePEc:roc:rocher:537&r=gth |
| By: | William Thomson (University of Rochester) |
| Abstract: | For the problem of adjudicating conflicting claims, we offer simple criteria to compare rules on the basis of the Lorenz order. These criteria pertain to three families of rules. The first family contains the constrained equal awards, constrained equal losses, Talmud, and minimal overlap rules (Thomson, 2007a). The second family, which also contains the constrained equal awards and constrained equal losses rules, is obtained from the first one by exchanging, for each problem, how well agents with relatively larger claims are treated as compared to agents with relatively smaller claims. The third family consists of consistent rules (Young, 1987). We also address the issue whether certain operators on the space of rules preserve the Lorenz order. |
| Keywords: | claims problems, constrained equal awards rule, constrained equal losses rule, Talmud rule, minimal overlap rule, Piniles’ rule, constrained egalitarian rule, ICI rules, CIC rules, consistent rules, Lorenz domination, operators. |
| JEL: | C79 D63 D74 |
| Date: | 2007–12 |
| URL: | http://d.repec.org/n?u=RePEc:roc:rocher:538&r=gth |
| By: | Fabrice Barthélémy (THEMA, Université de Cergy-Pontoise); Mathieu MARTIN (THEMA, Université de Cergy-Pontoise) |
| Abstract: | In this paper, we compare the five more famous methods of apportionment, the methods of Adams, Dean, Hill, Webster and Jefferson. The criteria used for this comparison is the minimization of a distance between a power vector and a population vector. The power is measured with the well-known Banzhaf power index. The populations are the ones of the different States of the U.S. We then compare the apportionment methods in terms of their ability to bring closer the power of the States to their relative population: this ensures that every citizen in the country gets the same power. The U.S. presidential election by Electors is studied through 22 censuses since 1790. Our analysis is largely based on the book written by Balinski and Young (2001). The empirical findings are linked with theoretical results. |
| Keywords: | Banzhaf index, methods of apportionment, distances, balance population-power. |
| JEL: | C7 D7 |
| Date: | 2007 |
| URL: | http://d.repec.org/n?u=RePEc:ema:worpap:2007-26&r=gth |
| By: | Stergios Skaperdas (Department of Economics, University of California-Irvine); Samarth Vaidya (School of Accounting, Economics, and Finance, Faculty of Business and Law, Deakin University) |
| Abstract: | From marketing and advertising to political campaigning and court proceedings, contending parties expend resources to persuade an audience of the correctness of their view. We examine how the probability of persuading the audience depends on the resources expended by the parties, so that persuasion can be modelled as a contest. We use a Bayesian approach whereby the audience makes inferences solely based on the evidence presented to them. The evidence is produced by the resources expended by the contending parties. We find conditions on evidence production and likelihood functions that yield the well-known additive contest success functions, including the logit function as well as the one used in all-pay auctions. We also find conditions that produce a "difference" functional form. In all cases, there are three main determinants of which side the audience chooses: (i) the truth and other objective parameters of the environment; (ii) the biases of the audience as distilled in their priors and the likelihood function employed; and (iii) the resources expended by the parties interested in persuading the audience. |
| Keywords: | Rent-seeking; Advertising; Litigation; Political campaigning; Property rights |
| JEL: | C70 D20 D70 |
| Date: | 2007–12 |
| URL: | http://d.repec.org/n?u=RePEc:irv:wpaper:070809&r=gth |