Laws of scarcity for a finite game - exact bounds on estimations

Summary. A law of scarcity is that scarceness is rewarded. We demonstrate laws of scarcity for cores and approximate cores of games. Furthermore, we show that equal treatment core payoff vectors satisfy a condition of cyclic monotonicity. Our results are developed for parameterized collections of games and exact bounds on the maximum possible deviation of approximate core payoff vectors from satisfying a law of scarcity are stated in terms of the parameters describing the games. We note that the parameters can, in principle, be estimated.Received: 21 November 2002, Revised: 7 October 2003, JEL Classification Numbers: C71, C78, D41. Correspondence to: Myrna WoodersThis research was initiated in 1994 when the first author was in the IDEA Ph.D. Program of the Autonomous University of Barcelona. Support by the IBM Fund Award, the Latané Fund, the University of North Carolina Research Council, and the Warwick Centre for Public Economics is acknowledged. The second author gratefully acknowledges the support of the Direccio General dUniversitats of Catalonia, the Social Sciences and Humanities Research Council of Canada, and the Department of Economics of the Autonomous University of Barcelona. This article is dedicated to Marcel (Ket) Richter, a distinguished researcher and a wonderful teacher and mentor to his students. We are delighted to contribute our paper to this special issue of Economic Theory in his honor.     

Efficiency in Second-Price Auctions: A New Look at Old Data

Experiments on second-price sealed-bid private value auctions have established that subjects typically bid more than their value, despite the fact that value bidding is a dominant strategy in such auctions. Moreover, the laboratory evidence shows that subjects do not learn to bid their values as they gain more experience. In the present paper, we re-examine the second-price auction data from Kagel and Levin’s (Econ J 103:868–879, 1993) classic paper. We find that auction efficiency increases over time, even though the frequency of overbidding is unchanged. We argue that the rise in efficiency is due to a decline in the variability of overbidding. This is consistent with subjects’ learning to bid more like each other.     

Matching soulmates

We study iterated matching of soulmates (IMS), a recursive process of forming coalitions that are mutually preferred by members to any other coalition containing individuals as yet unmatched by this process. If all players can be matched this way, preferences are IMS-complete. A mechanism is a soulmate mechanism if it allows the formation of all soulmate coalitions. Our model follows Banerjee, Konishi, and Sönmez, except reported preferences are strategic variables. We investigate the incentive and stability properties of soulmate mechanisms. In contrast to prior literature, we do not impose conditions that ensure IMS-completeness. A fundamental result is that, (1) any group of players who could change their reported preferences and mutually benefit does not contain any players who were matched as soulmates and reported their preferences truthfully. As corollaries, (2) for any IMS-complete profile, soulmate mechanisms have a truthful strong Nash equilibrium, and (3) as long as all players matched as soulmates report their preferences truthfully, there is no incentive for any to deviate. Moreover, (4) soulmate coalitions are invariant core coalitions—that is, any soulmate coalition will be a coalition in every outcome in the core. To accompany our theoretical results, we present real-world data analysis and simulations that highlight the prevalence of situations in which many, but not all, players can be matched as soulmates. In the Appendix we relate IMS to other well-known coalition formation processes.     

Inessentiality of large groups and the approximate core property: an equivalence theorem

Summary Inessentiality of large groups or, in other words, effectiveness of small groups, means that almost all gains to group formation can be realized by partitions of the players into groups bounded in absolute size. The approximate core property is that all sufficiently large games have nonempty approximate cores. I consider these properties in a framework of games in characteristic function form satisfying a mild boundedness condition where, when the games have many players, most players have many substitutes. I show that large (finite) games satisfy inessentially of large groupsif and only if they satisfy the approximate core property.This paper focuses on a part of another paper, Inessentiality of Large Coalitions and the Approximate Core Property; Two Equivalence Theorems, previously circulated as a University of Bonn Sonderforschungsbereich Discussion Paper.The author is indebted to Roger Myerson for a very stimulating comment and the term inessentiality of large coalitions. She is also indebted to Robert Anderson, Sergiu Hart, and Aldo Rustichini for helpful conversations. She is especially indebted to Robert Aumann for many stimulating and helpful discussions on research leading to this paper. The author gratefully acknowledges the financial support of the SSHRC and the hospitality and support of the University of Bonn through Sonderforschungsbereich 303.     

The epsilon core of a large replica game

Sufficient conditions are given for large replica games without side payments to have non-empty approximate cores for all sufficiently large replications. No ‘balancedness’ assumptions are required. The conditions are superadditivity, a boundedness condition, and convexity of the payoff sets.     

On the Irrelevance of Risk Attitudes in Repeated Two-Outcome Games

We study equilibrium and maximin play in supergames consisting of the sequential play of a finite collection of stage games, where each stage game has two outcomes for each player. We show that for two-player supergames in which each stage game is strictly competitive, in any Nash equilibrium of the supergame, play at each stage is a Nash equilibrium of the stage game provided preferences over certain supergame outcomes satisfy a natural monotonicity condition. In particular, equilibrium play does not depend on risk attitudes. We establish an invariance result for games with more than two players when the solution concept is subgame perfection. Journal of Economic Literature Classification Numbers: C72, C9.     

DECENTRALIZED TRADE MITIGATES THE LEMONS PROBLEM*

In markets with adverse selection, only low‐quality units trade in the competitive equilibrium when the average quality of the good held by sellers is low. We show that under decentralized trade, however, both high‐ and low‐quality units trade, although with delay. Moreover, when frictions are small, the surplus realized is greater than the (static) competitive surplus. Thus, decentralized trade mitigates the lemons problem. Remarkably, payoffs are competitive as frictions vanish, even though both high‐ and low‐quality units continue to trade, and there is trade at several prices.     

Reputation in Auctions: Theory, and Evidence from eBay

Employing a procedure suggested by a simple theoretical model of auctions in which bidders and sellers have observable and heterogenous reputations for default, we examine the effect of reputation on price in a data set drawn from the online auction site eBay. Our main empirical result is that seller's, but not bidder's, reputation has an economically and statistically significant effect on price.