We study stochastic games with an infinite horizon and sequential moves played by an arbitrary number of players. We assume that social memory is finite—every player, except possibly one, is finitely lived and cannot observe events that are sufficiently far back in the past. This class of games includes games between a long-run player and a sequence of short-run players and games with overlappi...

We study stochastic games with an infinite horizon and sequential moves played by an arbitrary number of players. We assume that social memory is finite—every player, except possibly one, is finitely lived and cannot observe events that are sufficiently far back in the past. This class of games includes games between a long-run player and a sequence of short-run players and games with overlappi...

A stochastic graph game is played by two players on a game graph with probabilistic transitions. We consider stochastic graph games with ω-regular winning conditions specified as Rabin or Streett objectives. These games are NP-complete and coNP-complete, respectively. The value of the game for a player at a state s given an objective Φ is the maximal probability that the player can guarantee th...

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 ...

We consider zero-sum repeated games with incomplete information on both sides, where the states privately observed by each player follow independent Markov chains. It generalizes the model, introduced by Aumann and Maschler in the sixties and solved by Mertens and Zamir in the seventies, where the private states of the players were fixed. It also includes the model introduced in Renault [20], o...

We describe applications and theoretical results for a new class of two-player planning games. In these games, each player plans in a separate Markov Decision Process (MDP), but the costs associated with a policy in one of the MDPs depend on the policy selected by the other player. These costpaired MDPs represent an interesting and computationally tractable subset of adversarial planning proble...

Learning Automata (LA) were recently shown to be valuable tools for designing Multi-Agent Reinforcement Learning algorithms. One of the principal contributions of LA theory is that a set of decentralized, independent learning automata is able to control a finite Markov Chain with unknown transition probabilities and rewards. This result was recently extended to Markov Games and analyzed with th...

We study coalition formation in “real time”, a situation in which coalition formation is intertwined with the ongoing receipt of pay-offs. Agreements are assumed to be permanently binding: They can only be altered with the full consent of existing signatories. For characteristic function games we prove that equilibrium processes—whether or not these are history dependent—must converge to effici...

The present study focuses on a class of games with reinforcement-learning agents that adaptively choose their actions to locally maximize their rewards. By analyzing a limit model with a special type of learning, previous studies suggested that dynamics of games with learners may become chaotic. We evaluated the generality of this model by analyzing the consistency of this limit model in compar...

We show existence of an optimal control and a saddlepoint for the zero-sum games associated with payoff functionals of mean-field type, under a dynamics driven by a class of Markov chains of mean-field type.