Zero-sum Stochastic Games with Asymmetric Information

TL;DR

This paper develops a dynamic programming framework for zero-sum stochastic games with asymmetric information, providing a way to characterize or bound the game's value and compute equilibrium strategies.

Contribution

It introduces a general model for such games, derives conditions for the existence of the value, and applies the framework to games with asymmetric information, enabling equilibrium computation.

Findings

Dynamic programming characterizes the game value under certain information evolution conditions.

Bounds on the upper and lower values are provided when the game value does not exist.

The framework allows computation of equilibrium strategies for games with asymmetric information.

Abstract

A general model for zero-sum stochastic games with asymmetric information is considered. In this model, each player's information at each time can be divided into a common information part and a private information part. Under certain conditions on the evolution of the common and private information, a dynamic programming characterization of the value of the game (if it exists) is presented. If the value of the zero-sum game does not exist, then the dynamic program provides bounds on the upper and lower values of the game. This dynamic program is then used for a class of zero-sum stochastic games with complete information on one side and partial information on the other, that is, games where one player has complete information about state, actions and observation history while the other player may only have partial information about the state and action history. For such games, it is shown that the value exists and can be characterized using the dynamic program. It is further shown that for this class of games, the dynamic program can be used to compute an equilibrium strategy for the more informed player in which the player selects its action using its private information and the common information belief.