After a brief survey of iterative algorithms for general stochastic games, we concentrate on finite-step algorithms for two special classes of stochastic games. They are Single-Controller Stochastic Games and Perfect Information Stochastic Games. In the case of single-controller games, the transition probabilities depend on the actions of the same player in all states. In perfect information st...

In stochastic games with perfect information, in each state at most one player has more than one action available. We propose two algorithms which find the uniform optimal strategies for zero-sum two-player stochastic games with perfect information. Such strategies are optimal for the long term average criterion as well. We prove the convergence for one algorithm, which presents a higher comple...

We analyze reputation games where a strategic long-lived player acts in a repeated game against a collection of short-lived (myopic) Bayesian players. The running assumption in our model is that the information at the short-lived players is nested in that of the long-lived player in a causal fashion. Under this setup, we show that the set of perfect Bayesian equilibria coincide with a properly ...

We solve large two-player zero-sum extensive-form games with perfect recall. We propose a new algorithm based on fictitious play that significantly reduces memory requirements for storing average strategies. The key feature is exploiting imperfect recall abstractions while preserving the convergence rate and guarantees of fictitious play applied directly to the perfect recall game. The algorith...

The knowledge-based rational decision model (KBR-model) offers an approach to rational decision making in a non-probabilistic setting, e.g., in perfect information games with deterministic payoffs. The KBR-model uses standard game-theoretical assumptions and suggests following a strategy yielding the highest payoff which the agent can secure to the best of his knowledge. In this report, we prov...

We use a universal, extensive form interactive beliefs system to provide an epistemic characterization of a weak and a strong notion of rationalizability with independent beliefs. The weak solution concept is equivalent to backward induction in generic perfect information games where no player moves more than once in any play. The strong solution concept is related to explicability (Reny, 1992)...

We study perfect information games with an infinite horizon played by an arbitrary number of players. This class of games includes infinitely repeated perfect information games, repeated games with asynchronous moves, games with long and short run players, games with overlapping generations of players, and canonical non-cooperative models of bargaining. We consider two restrictions on equilibri...

We study perfect information games with an infinite horizon played by an arbitrary number of players. This class of games includes infinitely repeated perfect information games, repeated games with asynchronous moves, games with long and short run players, games with overlapping generations of players, and canonical non-cooperative models of bargaining. We consider two restrictions on equilibri...