Selfish cops and passive robber: Qualitative games

Several variants of the cops and robbers (CR) game have been studied in the past. In this paper we examine a novel variant, which is played between two cops, each one independently trying to catch a " passive robber ". We will call this the Selfish Cops and Passive Robber (SCPR) game. In short, SCPR is a stochastic two-player, zero-sum game where the opponents are the two cop players. We study sequential and concurrent versions of the SCPR game. For both cases we prove the existence of value and optimal strategies and present algorithms for the computation of these.