Markov games with frequent actions and incomplete information

TL;DR

This paper analyzes a two-player zero-sum stochastic game with incomplete information, where players can act more frequently, and characterizes the limit value as actions become continuous, using advanced mathematical tools.

Contribution

It introduces a framework for Markov games with frequent actions and incomplete information, establishing the existence and characterization of the limit value as actions become continuous.

Findings

Existence of a limit value as the time between actions vanishes

Characterization of the limit value via an auxiliary optimization problem

Solution of a Hamilton-Jacobi equation for the limit value

Abstract

We study a two-player, zero-sum, stochastic game with incomplete information on one side in which the players are allowed to play more and more frequently. The informed player observes the realization of a Markov chain on which the payoffs depend, while the non-informed player only observes his opponent's actions. We show the existence of a limit value as the time span between two consecutive stages vanishes; this value is characterized through an auxiliary optimization problem and as the solution of an Hamilton-Jacobi equation.