EPISTEMIC FOUNDATIONS OF SOLUTION CONCEPTS IN GAME THEORY: AN INTRODUCTION

We give an introduction to the literature on the epistemic foundations of solution concepts in game theory. Only normal-form games are considered. The solution concepts analyzed are rationalizability, strong rationalizability, correlated equilibrium and Nash equilibrium. The analysis is carried out locally in terms of properties of the belief hierarchies. Several examples are used throughout to illustrate definitions and concepts.

Dynamic unawareness and rationalizable behavior

We define generalized extensive-form games which allow for mutual unawareness of actions. We extend Pearce's (1984) notion of extensive-form (correlated) rationalizability to this setting, explore its properties and prove existence.Unawareness, extensive-form games, extensive-form rationalizability

Beyond Normal Form Invariance : First Mover Advantage in Two-Stage Games with or without Predictable Cheap Talk

Von Neumann (1928) not only introduced a fairly general version of the extensive form game concept. He also hypothesized that only the normal form was relevant to rational play. Yet even in Battle of the Sexes, this hypothesis seems contradicted by players' actual behaviour in experiments. Here a refined Nash equilibrium is proposed for games where one player moves first, and the only other player moves second without knowing the first move. The refinement relies on a tacit understanding of the only credible and straightforward perfect Bayesian equilibrium in a corresponding game allowing a predictable direct form of cheap talk.

Game theory

game theory

Robert Aumann's and Thomas Schelling's Contributions to Game Theory: Analyses of Conflict and Cooperation

Advanced information on the Bank of Sweden Prize in Economic Sciences in Memory of Alfred Nobel 2005.Game Theory;

Variational optimization of probability measure spaces resolves the chain store paradox

In game theory, players have continuous expected payoff functions and can use fixed point theorems to locate equilibria. This optimization method requires that players adopt a particular type of probability measure space. Here, we introduce alternate probability measure spaces altering the dimensionality, continuity, and differentiability properties of what are now the game's expected payoff functionals. Optimizing such functionals requires generalized variational and functional optimization methods to locate novel equilibria. These variational methods can reconcile game theoretic prediction and observed human behaviours, as we illustrate by resolving the chain store paradox. Our generalized optimization analysis has significant implications for economics, artificial intelligence, complex system theory, neurobiology, and biological evolution and development.Comment: 11 pages, 5 figures. Replaced for minor notational correctio