Strategic complexity in repeated extensive games

Strategic Complexity in Repeated Extensive Games by Nozomu Muto

Strategic Irrationality in Extensive Games

Most standard solution concepts of extensive games are history-insensitive in the sense that no matter at which information set one is, it is assumed that each player believes that everybody else is rational. In reality, each history of moves reveals certain traits of the players to one another. It is argued in this paper that solution concepts ought to make use of this fact. An example of such...

An Approach to Bounded Rationality

A central question in game theory, learning, and other elds is how a rational intelligent agent should behave in a complex environment, given that it cannot perform unbounded computations. We study strategic aspects of this question by formulating a simple model of a game with additional costs (computational or otherwise) for each strategy. While a zero-sum game with strategy costs is no longer...

Computational complexity of correlated equilibria for extensive games

Correlated equilibria are more general than Nash equilibria. For games in strategic form, they are also easier to compute. This no longer holds when the game is given in extensive form. We show that for an extensive twoplayer game with perfect recall, even without chance moves, it is computationally difficult (NP-hard) to find a correlated equilibrium with maximum payoff sum. Even with a modifi...

Lecture Notes on Game Theory

1. Extensive form games with perfect information 3 1.1. Chess 3 1.2. Definition of extensive form games with perfect information 4 1.3. The ultimatum game 5 1.4. Equilibria 5 1.5. The centipede game 6 1.6. Subgames and subgame perfect equilibria 6 1.7. Backward induction, Kuhn’s Theorem and a proof of Zermelo’s Theorem 7 2. Strategic form games 10 2.1. Definition 10 2.2. Nash equilibria 10 2.3....