Nash and Correlated Equilibria for Pursuit-Evasion Games Under Lack of Common Knowledge

Abstract

The majority of work in pursuit-evasion games assumes perfectly rational players who are omnipotent and have complete knowledge of the environment and the capabilities of other agents and, consequently, are correct in their assumption of the game that is played. This is rarely the case in practice. More often than not, the players have different knowledge about the environment either because of sensing limitations or because of prior experience. In this paper, we wish to relax this assumption and consider pursuit-evasion games in a stochastic setting, where the players involved in the game have different perspectives regarding the transition probabilities that govern the world dynamics. We show the existence of a (Nash) equilibrium in this setting and discuss the computational aspects obtaining such an equilibrium. We also investigate a relaxation of this problem employing the notion of correlated equilibria. Finally, we demonstrate the approach using a grid-world example with two players in the presence of obstacles.