Language of game theory : putting epistemics into the mathematics of games / Adam Brandenburger.

Includes bibliographical references and indexes.

1. An Impossibility Theorem on Beliefs in Games;
2. Hierarchies of Beliefs and Common Knowledge;
3. Rationalizability and Correlated Equilibria;
4. Intrinsic Correlation in Games;
5. Epistemic Conditions for Nash Equilibrium;
6. Lexicographic Probabilities and Choice under Uncertainty;
7. Admissibility in Games;
8. Self-Admissible Sets.

This book 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 what players believe about a game a central feature of the theory. The program - now called epistemic game theory - extends the classical definition of a game model to include not only the game matrix or game tree, but also what each player believes about how the game will be played, and even higher-order beliefs. With this richer mathematical framework, it becomes possible to determine what different configurations of beliefs among the players imply 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.