Pursuit-Evasion Games with Incomplete Information in Discrete Time

TL;DR

This paper proves that pursuit-evasion games with incomplete information and nonnegative payoffs have a well-defined, uniform value, and introduces epsilon-optimal strategies that work throughout the game.

Contribution

It establishes the existence of a uniform value in pursuit-evasion games with incomplete information and nonnegative payoffs, extending to leavable games.

Findings

Games admit a uniform value despite incomplete information

Epsilon-optimal strategies are effective in any long enough prefix

Nonnegativity of payoffs is essential for the results

Abstract

Pursuit-Evasion Games (in discrete time) are stochastic games with nonnegative daily payoffs, with the final payoff being the cumulative sum of payoffs during the game. We show that such games admit a value even in the presence of incomplete information and that this value is uniform, i.e. there are epsilon-optimal strategies for both players that are epsilon-optimal in any long enough prefix of the game. We give an example to demonstrate that nonnegativity is essential and expand the results to leavable games.