We consider a two-player zero-sum game, given by a Markov chain over a finite set of states and a family of matrix games indexed by states. The sequence of states follows the Markov chain. At the beginning of each stage, only player 1 is informed of the current state, then the corresponding matrix game is played and the actions chosen are observed by both players before proceeding to the next stage. We call such a game a Markov chain game with lack of information on one side. This model generalizes the model of Aumann and Maschler of zero-sum repeated games with lack of information on one side (which corresponds to the case where the transition matrix of the Markov chain is the identity matrix). We generalize the proof of Aumann and Maschler and, from the definition and the study of appropriate "non revealing" auxiliary games with infinitely many stages, show the existence of the uniform value. An important difference with Aumann and Maschler's model is that here, the notions for player 1 of using the information and revealing a relevant information are distinct.
We investigate a limit value of an optimal control problem when the horizon converges to infinity. For this aim, we suppose suitable nonexpansive-like assumptions which does not imply that the limit is independent of the initial state as it is usually done in the literature.
Abstract. We consider dynamic programming problems with a large time horizon, and give sufficient conditions for the existence of the uniform value. As a consequence, we obtain an existence result when the state space is precompact, payoffs are uniformly continuous and the transition correspondence is nonexpansive. In the same spirit, we give an existence result for the limit value. We also apply our results to Markov decision processes and obtain a few generalizations of existing results.
We consider the general model of zero-sum repeated games (or stochastic games with signals), and assume that one of the players is fully informed and controls the transitions of the state variable. We prove the existence of the uniform value, generalizing several results of the literature. A preliminary existence result is obtained for a certain class of stochastic games played with pure strategies.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.