Best-response sets (Pearce [1984]) characterize the epistemic condition of “rationality and common belief of rationality.” When rationality incorporates a weak-dominance (admissibility) requirement, the self-admissible set (SAS) concept (Brandenburger, Friedenberg, and Keisler [2008])...

AbstractJohn F. Nash, Jr., submitted his Ph. D. dissertation entitled Non-Cooperative Games to Princeton University in 1950. Read it 58 years later, and you will find the germs of various later developments in game theory. Some of these are presented below, followed by a discussion of dynamic...

AbstractAn elementary proof, based on linear duality, is provided for the existence of correlated equilibria in finite games. The existence result is then extended to infinite games, including some that possess no Nash equilibria.

We discuss the unity between the two standard approaches to noncooperative solution concepts for games. The decision-theoretic approach starts from the assumption that the rationality of the players is common knowledge. This leads to the notion of correlated rationalizability. It is shown that...

AbstractWe study the problem of reaching a pure Nash equilibrium in multi-person games that are repeatedly played under the assumption of uncoupledness: every player knows only his own payoff function. We consider strategies that can be implemented by finite-state automata, and characterize the...

Correlations arise naturally in noncooperative games, e.g., in the equivalence between undominated and optimal strategies in games with more than two players. But the noncooperative assumption is that players do not coordinate their strategy choices, so where do these correlations come from? The...

A paradox of self-reference in beliefs in games is identified, which yields a game-theoretic impossibility theorem akin to Russell's Paradox. An informal version of the paradox is that the following configuration of beliefs is impossible:Ann believes that Bob assumes thatAnn believes that Bob's...

In the present essay, we develop at first a model of choice by actors to show how a society can take decisions on specific issues according to how flexible or rigid it is in new ideas and trends. Then, by utilizing game theory we explain how the Athenian society abandoned war in favour of a...

Game theorists typically assume that changing a game’s payoff levels—by adding the same constant to, or subtracting it from, all payoffs—should not affect behavior. While this invariance is an implication of the theory when payoffs mirror expected utilities, it is an empirical question...