The Language of Game Theory Putting Epistemics Into the Mathematics of Games

This volume contains eight papers written by Adam Brandenburger and his co-authors over a period of 25 years. These papers are part of a program to reconstruct game theory in order to make how players reason about a game a central feature of the theory. The program OCo now called epistemic game theory OCo extends the classical definition of a game model to include not only the game matrix or game tree, but also a description of how the players reason about one another (including their reasoning about other players' reasoning). With this richer mathematical framework, it becomes possible to determine the implications of how players reason for how a game is played. Epistemic game theory includes traditional equilibrium-based theory as a special case, but allows for a wide range of non-equilibrium behavior. Sample Chapter(s). Foreword (39 KB). Introduction (132 KB). Chapter 1: An Impossibility Theorem on Beliefs in Games (299 KB). Contents: An Impossibility Theorem on Beliefs in Games (Adam Brandenburger and H Jerome Keisler); Hierarchies of Beliefs and Common Knowledge (Adam Brandenburger and Eddie Dekel); Rationalizability and Correlated Equilibria (Adam Brandenburger and Eddie Dekel); Intrinsic Correlation in Games (Adam Brandenburger and Amanda Friedenberg); Epistemic Conditions for Nash Equilibrium (Robert Aumann and Adam Brandenburger); Lexicographic Probabilities and Choice Under Uncertainty (Lawrence Blume, Adam Brandenburger, and Eddie Dekel); Admissibility in Games (Adam Brandenburger, Amanda Friedenberg and H Jerome Keisler); Self-Admissible Sets (Adam Brandenburger and Amanda Friedenberg). Readership: Graduate students and researchers in the fields of game theory, theoretical computer science, mathematical logic and social neuroscience."