A formal model is given of Harsanyi's infinite hierarchies of beliefs. It is shown that the model doses with some Bayesian game with incomplete information, and that any such game can be approximated by one with a finite number of states of world.

Covering both noncooperative and cooperative games, this comprehensive introduction to game theory also includes some advanced chapters on auctions, games with incomplete information, games with vector payoffs, stable matchings and the bargaining set. Mathematically oriented, the book presents every theorem alongside a proof. The material is presented clearly and every concept is illustrated with concrete examples from a broad range of disciplines. With numerous exercises the book is a thorough and extensive guide to game theory from undergraduate through graduate courses in economics, mathematics, computer science, engineering and life sciences to being an authoritative reference for researchers.

Abstract." We consider repeated two-person zero-sum games in which each player has only partial information about a chance move that takes place at the beginning of the game. Under some conditions on the information pattern it is proved that lira v, exists, v, being the value of the game with n repetin~c~ tions. Two functional equations are given for which lira v, is the only simultaneous solutions. We n~m also find the least upper bound for the error term Iv, -lira v,.

This document is the author's final manuscript accepted version of the journal article, incorporating any revisions agreed during the peer review process. Some differences between this version and the published version may remain. You are advised to consult the publisher's version if you wish to cite from it. Leadership Games with Convex Strategy Sets AbstractA basic model of commitment is to convert a two-player game in strategic form to a "leadership game" with the same payoffs, where one player, the leader, commits to a strategy, to which the second player always chooses a best reply. This paper studies such leadership games for games with convex strategy sets. We apply them to mixed extensions of finite games, which we analyze completely, including nongeneric games. The main result is that leadership is advantageous in the sense that, as a set, the leader's payoffs in equilibrium are at least as high as his Nash and correlated equilibrium payoffs in the simultaneous game. We also consider leadership games with three or more players, where most conclusions no longer hold.

Three leading experts have produced a landmark work based on a set of working papers published by the Center for Operations Research and Econometrics (CORE) at the Université Catholique de Louvain in 1994 under the title 'Repeated Games', which holds almost mythic status among game theorists. Jean-François Mertens, Sylvain Sorin and Shmuel Zamir have significantly elevated the clarity and depth of presentation with many results presented at a level of generality that goes far beyond the original papers - many written by the authors themselves. Numerous results are new, and many classic results and examples are not to be found elsewhere. Most remain state of the art in the literature. This book is full of challenging and important problems that are set up as exercises, with detailed hints provided for their solutions. A new bibliography traces the development of the core concepts up to the present day.