We present a new algorithm for polynomial time learning of near optimal behavior in stochastic games. This algorithm incorporates and integrates important recent results of Kearns and Singh [ 1998] in reinforcement learning and of Monderer and Tennenholtz [1997] in repeated games. In stochastic games we face an exploration vs. exploitation dilemma more complex than in Markov decision processes....

In this thesis we consider two-person zero-sum stochastic games with a special focus on how tools from the mathematical field of semi-algebraic geometry have been applied to these games. In the first of two parts of the thesis we introduce stochastic games and prove a complexity result about computing the value of a type of stochastic games called concurrent reachability games. We show that the...

Games on graphs provide a natural model for reactive non-terminating systems. In such games, the interaction of two players on an arena results in an infinite path that describes a run of the system. Different settings are used to model various open systems in computer science, as for instance turnbased or concurrent moves, and deterministic or stochastic transitions. In this paper, we are inte...

A large class of sequential decision making problems under uncertainty with multiple competing decision makers can be modeled as stochastic games. It can be considered that the stochastic games are multiplayer extensions of Markov decision processes (MDPs). In this paper, we develop a reinforcement learning algorithm to obtain average reward equilibrium for irreducible stochastic games. In our ...

Games on graphs provide a natural model for reactive non-terminating systems. In such games, the interaction of two players on an arena results in an infinite path that describes a run of the system. Different settings are used to model various open systems in computer science, as for instance turnbased or concurrent moves, and deterministic or stochastic transitions. In this paper, we are inte...

Shapley’s discounted stochastic games, Everett’s recursive games and Gillette’s undiscounted stochastic games are classical models of game theory describing two-player zero-sum games of potentially infinite duration. We describe algorithms for exactly solving these games. When the number of positions of the game is constant, our algorithms run in polynomial time.

Definable zero-sum stochastic games involve a finite number of states and action sets, reward and transition functions that are definable in an o-minimal structure. Prominent examples of such games are finite, semi-algebraic or globally subanalytic stochastic games. We prove that the Shapley operator of any definable stochastic game with separable transition and reward functions is definable in...

This paper presents a robust optimization model for n-person finite state/action stochastic games with incomplete information. We consider nonzero sum discounted stochastic games in which none of the players knows the true data of a game, and each player adopts a robust optimization approach to address the uncertainty. We call these games discounted robust stochastic games. Such games allow us ...

For n-person perfect inlbrmation stochastic games and for n-person stochastic games with Additive Rcwards and Additive Transitions (ARAT) we show the existence of pure limiting average equilibria. Using a similar approach we also derive the existence of limiting average e-equilibria for two-person switching control stochastic games. The orderfield property holds for each of the classes mentione...

In this paper, we initiate a study on optimal control problem for stochastic differential games under generalized expectation via backward stochastic differential equations and partial information. We first prove a sufficient maximum principle for zero-sum stochastic differential game problem. And then extend our approach to general stochastic differential games (nonzero–sum games), and obtain ...