http://repub.eur.nl/res/aut/1369/ List of Publications en http://repub.eur.nl/static-eur/img/logo.png http://repub.eur.nl http://repub.eur.nl/res/pub/32015/ 2012-01-01T00:00:00Z The Babylonian bridal auction, described by Herodotus, is regarded as one of the earliest uses of an auction in history. Yet, to our knowledge, the literature lacks a formal equilibrium analysis of this auction. We provide such an analysis for the two-player case with complete and incomplete information, and in so doing identify what we call the "Herodotus paradox". http://repub.eur.nl/res/pub/20754/ 2010-07-01T00:00:00Z The Babylonian bridal auction, described by Herodotus, is regarded as one of the earliest uses of an auction in history. Yet, to our knowledge, the literature lacks a formal equilibrium analysis of this auction. We provide such an analysis for the twoplayer case with complete and incompete information, and in so doing identify what we call the "Herodotus Paradox". http://repub.eur.nl/res/pub/17030/ 2009-08-31T00:00:00Z This paper presents a unified framework for characterizing symmetric equilibrium in simultaneous move, two-player, rank-order contests with complete information, in which each player's strategy generates direct or indirect affine "spillover" effects that depend on the rank-order of her decision variable. These effects arise in natural interpretations of a number of important economic environments, as well as in classic contests adapted to recent experimental and behavioral models where individuals exhibit inequality aversion or regret. We provide the closed-form solution for the symmetric Nash equilibria of this class of games, and show how it can be used to directly solve for equilibrium behavior in auctions, pricing games, tournaments, R&D races, models of litigation, and a host of other contests. http://repub.eur.nl/res/pub/16514/ 2009-04-01T00:00:00Z This paper presents a unified framework for characterizing symmetric equilibrium in simultaneous move, two-player, rank-order contests with complete information, in which each player's strategy generates direct or indirect affine "spillover" effects that depend on the rank-order of her decision variable. These effects arise in natural interpretations of a number of important economic environments, as well as in classic contests adapted to recent experimental and behavioral models where individuals exhibit inequality aversion or regret. We provide the closed-form solution for the symmetric Nash equilibria of this class of games, and show how it can be used to directly solve for equilibrium behavior in auctions, pricing games, tournaments, R&D races, models of ligitation, and a host of other contests. http://repub.eur.nl/res/pub/12374/ 2005-01-01T00:00:00Z A simple auction-theoretic framework is used to examine symmetric litigation environments where the legal ownership of a disputed asset is unknown to the court. The court observes only the quality of the case presented by each party, and awards the asset to the party presenting the best case. Rational litigants influence the quality of their cases by hiring skilful attorneys. This framework permits us to compare the equilibrium legal expenditures that arise under a continuum of legal systems. The British rule, Continental rule, American rule, and some recently proposed legal reforms are special cases of our model. http://repub.eur.nl/res/pub/6929/ 2000-11-21T00:00:00Z A simple auction-theoretic framework is used to examine symmetric litigation environments where the legal ownership of a disputed asset is unknown by the court. The court observes only the quality of the case presented by each party, and awards the asset to the party presenting the best case. Rational litigants influence the quality of their cases by hiring skillful attorneys. This framework permits us to compare the equilibrium legal expenditures that arise under a continuum of legal systems. The British rule, American rule, and some recently proposed legal reforms are special cases of our model. http://repub.eur.nl/res/pub/12398/ 1999-01-01T00:00:00Z Tullock's analysis of rent seeking and overdissipation is reconsidered. We show that, while equilibrium strategies do not permit overdissipation in expectation, for particular realizations of players' mixed strategies the total amount spent competing for rents can exceed the value of the prize. We also show that the cross-sectional incidence of overdissipation in the perfectly discriminating contest ranges from 0.50 to 0.44 as the number of players increases from two to infinity. Thus, even though the original analysis of overdissipation is flawed, there are instances in which rent-seekers spend more than the prize is worth. http://repub.eur.nl/res/pub/7804/ 1997-05-15T00:00:00Z This paper reconsiders Tullock's analysis of rent seeking and wasteful overdissipation. The purpose of this paper is to point out that even though his original analysis of overdissipation is technically flawed, the definition of overdissipation can be modified to explain instances in which rational rent-seekers spend more to win a prize than the prize is worth. We showed before that equilibrium mixed strategies in the Tullock game do not permit overdissipation in expectation: the expected total amount spent competing for rents cannot exceed the value of the prize. However, since the equilibrium involves mixed-strategies for particular realizations of the mixed strategies the total amount spent competing for rents can exceed the value of the prize! In fact, we show that the cross-sectional incidence of overdissipation may be quite high. For a symmetric perfectly discriminating contest (R = &inf;), the probability of overdissipation in a symmetric equilibrium ranges from exactly one-half in the two player case to approximately .44 as the number of players approaches infinity. http://repub.eur.nl/res/pub/12406/ 1996-01-01T00:00:00Z In a (first price) all-pay auction, bidders simultaneously submit bids for an item. All players forfeit their bids, and the high bidder receives the item. This auction is widely used in economics to model rent seeking, R&D races, political contests, and job promotion tournaments. We fully characterize equilibrium for this class of games, and show that the set of equilibria is much larger than has been recognized in the literature. When there are more than two players, for instance, we show that even when the auction is symmetric there exists a continuum of asymmetric equilibria. Moreover, for economically important configurations of valuations, there is no revenue equivalence across the equilibria; asymmetric equilibria imply higher expected revenues than the symmetric equilibrium. http://repub.eur.nl/res/pub/12413/ 1994-12-01T00:00:00Z In Tullock's rent-seeking model, the probability a player wins the game depends on expenditures raised to the power R. We show that a symmetric mixed-strategy Nash equilibrium exists when R>2, and that overdissipation of rents does not arise in any Nash equilibrium. We derive a tight lower bound on the level of rent dissipation that arises in a symmetric equilibrium when the strategy space is discrete, and show that full rent dissipation occurs when the strategy space is continuous. Our results are shown to be consistent with recent experimental evidence on the dissipation of rents. An earlier version of this paper circulated under the title, No, Virginia, There is No Overdissipation of Rents. We are grateful to Dave Furth and Frans van Winden for stimulating conversations, and for comments provided by workshop participants from the CORE-ULB-KUL IUAP project, Purdue University, Pennsylvania State University, Rijksuniversiteit Limburg, and Washington State University. We also thank Max van de Sande Bakhuyzen and Ben Heijdra for useful discussions, and Geert Gielens for computational assistance. An earlier version of the paper was presented at the ESEM 1992 in Brussels and the Mid-West Mathematical Economics Conference in Pittsburgh. All three authors would like to thank CentER for its hospitality during the formative stages of the paper. The second author has also benefited from the financial support of the Katholieke Universitieit Leuven and the Jay N. Ross Young Faculty Scholar Award at Purdue University. The third author benefitted from visiting IGIER where part of the paper was written. The third author also benefitted from grant IUAP 26 of the Belgian Government. http://repub.eur.nl/res/pub/12415/ 1994-02-01T00:00:00Z We analyze the existence of equilibrium in an asset market under asymmetric information. Price formation is modeled as a bilateral sealed bid auction where uninformed and informed traders submit limit orders to a computerized specialist. The computerized specialist is programmed to sell to the highest bidder and buy from the seller asking the lowest price. We show that this mechanism — which is designed to model the Globex and RAES trading institutions used in Chicago, London, New York, Paris, and Germany — yields an equilibrium in which the bid-ask spread is endogenously random and the passive specialist earns nonnegative profits. http://repub.eur.nl/res/pub/12418/ 1993-12-01T00:00:00Z The paper demonstrates that in an environment of free banking where some agents have imperfect information regarding the circulation and debasement rates of alternative money suppliers, the equilibrium supply of money involves mixed strategies. It follows that the circulation and debasement rates are intrinsically stochastic, but that their averages are below the rates set by a monopoly bank. Empirical tests reveal that these predictions are consistent with the free banking era of the United States. The paper is also relevant for the discussion about the future monetary union in the EC. http://repub.eur.nl/res/pub/12419/ 1993-01-01T00:00:00Z In a world where a politician can explicitly auction off a prize to the high bidder, the standard auction literature can be used to analyse political behavior. The justice system, however, precludes politicians from explicitly selling the prize to the highest bidder. Thus politicians cannot let it become public knowledge that they are in the business of selling political favors. An institution has emerged in political markets to overcome this constraint which are termed as lobbying. Lobbyists make implicit payments to the politician through campaign contributions. If these up-front payments were rebated to those failing to receive the prize, it would be clear that the politician was selling favors. This article has examined an interesting principle arising in all-pay auctions. This principle states that a politician wishing to maximize political rents may find it in his best interest to exclude certain lobbyists from participating in the lobbying process, particularly lobbyists valuing most the political prize. http://repub.eur.nl/res/pub/12422/ 1992-01-01T00:00:00Z We show that the Varian model of sales with more than two firms has two types of equilibria: a unique symmetric equilibrium, and a continuum of asymmetric equilibria. In contrast, the 2-firm game has a unique equilibrium that is symmetric. For the n-firm case the asymmetric equilibria imply mixed strategies that can be ranked by first-order stochastic dominance. This enables one to rule out asymmetric equilibria on economic grounds by constructing a metagame in which both firms and consumers are players. The unique subgame perfect equilibrium of this metagame is symmetric. http://repub.eur.nl/res/pub/12425/ 1992-01-01T00:00:00Z Considers the hybrid situation where some customers care only about the price while others have a brand preference or care about product characteristics.