Cops Only Need Factual Knowledge to Catch Robbers

The cops and robber game is a well-studied model for investigating pursuit-evasion phenomena, among many others. Although many variants of this game have been studied in the literature, the epistemic assumptions underlying their game designs are often left implicit. In this work, we focus on the imperfect information version of the game and re-examine it from an epistemic perspective to explore the levels of player knowledge that are essential for playing the game. To facilitate our investigations on these knowledge levels, we discuss two kinds of strategies for the players, history-based and positional, and show what matters in this context. Our study eventually sheds light on the implicit assumptions prevalent in the existing literature in terms of player knowledge while playing the game, and provides a foundation for further studies on epistemically informed game structures.