Selfish Cops and Passive Robber: Qualitative Games

TL;DR

This paper introduces a new variant of the cops and robbers game where two selfish cops aim to catch a passive robber, analyzing its strategic properties and providing algorithms for optimal play.

Contribution

It defines the Selfish Cops and Passive Robber (SCPR) game, proves the existence of value and optimal strategies, and develops algorithms for both sequential and concurrent versions.

Findings

Existence of game value and optimal strategies for SCPR.

Algorithms for computing optimal strategies in SCPR.

Analysis of sequential and concurrent game variants.

Abstract

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.