The value of Repeated Games with an informed controller

TL;DR

This paper studies zero-sum repeated games where one player is fully informed and controls state transitions, proving the existence of a uniform value and extending previous results in the field.

Contribution

It generalizes the existence of the uniform value in zero-sum stochastic games with an informed controller, including cases with pure strategies.

Findings

Existence of the uniform value in the general model.

Preliminary results for games with pure strategies.

Extension of prior literature on stochastic games.

Abstract

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.