Philip J. Reny

Correlated Information and Mechanism Design

In models of asymmetric information, possession of private information leads to rents for the possessors. This induces mechanism designers to distort away from efficiency. The authors show that this is an artifact of the presumption that information is independently distributed. Rent extraction in a large class of mechanism design games is analyzed, and a necessary and sufficient condition for arbitrarily small rents to private information is provided. Additionally, the two-person bargaining game is shown to have an efficient solution under first-order stochastic dominance and a hazard rate condition. Similar conditions allow full rent extraction in Milgrom-Weber auctions. Copyright 1992 by The Econometric Society.

A Noncooperative View of Coalition Formation and the Core

A noncooperative implementation of the core is provided for games with transferable utility. The implementation obtained here is meant to reflect the standard motivation for the core as closely as possible. In the model proposed, time is continuous. This idealized treatment of time is most amenable for capturing an essential feature of the core--there is always time to reject a noncore proposal before it is consumated. Copyright 1994 by The Econometric Society.

On the Existence of Monotone Pure Strategy Equilibria in Bayesian Games

We generalize Atheys (2001) and McAdams (2003) results on the existence of monotone pure strategy equilibria in Bayesian games. We allow action spaces to be compact locally-complete metrizable semilattices and type spaces to be partially ordered probability spaces. Our proof is based upon contractibility rather than convexity of best reply sets. Several examples illustrate the scope of the result, including new applications to multi-unit auctions with risk-averse bidders.

Backward Induction, Normal Form Perfection and Explicable Equilibria

A weakening of D. Kreps and R. Wilsons (1982) notion of sequential rationality is presented. The motivation stems from the difficulty in justifying sequentially rational behavior in subgames reachable only through a violation of sequential rationality. Although the present notion of weak sequential rationality is based upon extensive form considerations, it bears a close relation to R. Seltens (1975) normal form perfect equilibria. Backward induction outcomes can be achieved in generic games of perfect information with additional restrictions on beliefs. An example with imperfect information shows that sequential rationality is not the consequence of equilibrium play and the absence of incredible threats. Copyright 1992 by The Econometric Society.

The Existence of Subgame-Perfect Equilibrium in Continuous Games with Almost Perfect Information: A Case for Public Randomization

The starting point of this paper is a simple, regular, dynamic game in which a subgame-perfect equilibrium fails to exist. Examination of this example shows that existence would be restored if players were allowed to observe the output of a public-randomization device. The main result of the paper shows that the introduction of public randomization yields existence not only in the example but also in a large class of dynamic games. It is also argued that the introduction of public randomization is the minimal robust extension of subgame-perfect equilibrium in this class of games. Copyright 1995 by The Econometric Society.

Subgame perfect equilibrium in continuous games of perfect information: An elementary approach to existence and approximation by discrete games

Abstract This paper relates infinite-action (continuous) games of perfect information to finite-action approximations of such games and thereby obtains a new existence proof for subgame-perfect equilibrium (SPE) in the infinite-action case. Accumulation points of SPE paths of approximating finite-action games are shown to be SPE paths of the limiting infinite-action game. However, no such upper hemi-continuity property holds for SPE strategies. The discontinuity in strategies corresponds to a need for forward induction in the SPE construction for the infinite-action game, thus conflicting with the Harsanyi-Selten principle of subgame-consistency.

Rational Behaviour in Extensive-Form Games

It is argued that subgame perfect equilibrium behavior is not an inevitable consequence of common belief of rationality among players in noncooperative extensive-form games. The argument centers around a particular extensive-form game with perfect information. In the context of this game, it is argued that if rationality is not common belief throughout play of the game, then it can be perfectly rational to play contrary to subgame perfection, even if rationality is common belief at the beginning of the game. It is then shown that it is impossible for rationality to be common belief throughout every play of the game.

A Course in Game Theory

A Course in Game Theory presents the main ideas of game theory at a level suitable for graduate students and advanced undergraduates, emphasizing the theorys foundations and interpretations of its basic concepts. The authors provide precise definitions and full proofs of results, sacrificing generalities and limiting the scope of the material in order to do so. The text is organized in four parts: strategic games, extensive games with perfect information, extensive games with imperfect information, and coalitional games. It includes over 100 exercises.