We consider both discrete and continuous time finite state-action stochastic games. In discrete time stochastic games, it is known that a stationary BlackwellNash equilibrium (BNE) exists for a single controller additive reward (SC-AR) stochastic game which is a special case of a general stochastic game. We show that, in general, the additive reward condition is needed for the existence of a BN...

We consider four models of evolution and learning in games which rely on perturbations of payoffs, including stochastic fictitious play. In all cases, we establish global stability results for zerosum games, games with an interior ESS, potential games, and supermodular games.

We introduce the Lenient Multiagent Reinforcement Learning 2 (LMRL2) algorithm for independent-learner stochastic cooperative games. LMRL2 is designed to overcome a pathology called relative overgeneralization, and to do so while still performing well in games with stochastic transitions, stochastic rewards, and miscoordination. We discuss the existing literature, then compare LMRL2 against oth...

The synthesis of a reactive system with respect to an ωregular specification requires the solution of a graph game. Such games have been extended in two natural ways. First, a game graph can be equipped with probabilistic choices between alternative transitions, thus allowing the modeling of uncertain behavior. These are called stochastic games. Second, a liveness specification can be strengthe...

We consider a class of stochastic games with finite number of resource states, individual states and actions per states. At each stage, a random set of players interact. The states and the actions of all the interacting players determine together the instantaneous payoffs and the transitions to the next states. We study the convergence of the stochastic game with variable set of interacting pla...

A great deal of research has been recently focused on stochastic games. Stochastic games can generally model the interactions between multiple agents in an environment. One of the major challenges in stochastic games is the problem of learning a policy to play in such games. While lots of people have worked in this area and proposed various algorithms for that, there is no unique method which c...

This chapter provides an introductory exposition of stochastic games with imperfect monitoring. These are stochastic games in which the players imperfectly observe the play. We discuss at length a few basic issues, and describe selected contributions. Our objective in this chapter is to provide an introductory exposition of some recent work on zero-sum stochastic games with imperfect monitoring...

We are interested in the convergence of the value of n-stage games as n goes to infinity and the existence of the uniform value in stochastic games with a general set of states and finite sets of actions where the transition is commutative. This means that playing an action profile a1 followed by an action profile a2, leads to the same distribution on states as playing first the action profile ...

A stochastic game is a two-player game played on a graph, where in each state the successor is chosen either by one of the players, or according to a probability distribution. We survey stochastic games with limsup and liminf objectives. A real-valued reward is assigned to each state, and the value of an infinite path is the limsup (resp. liminf) of all rewards along the path. The value of a st...