Cops and Robbers, Game Theory and Zermelo's Early Results

TL;DR

This paper develops a game theoretic framework for cops and robbers, linking it to early mathematical work and exploring strategic and capture time concepts in pursuit games.

Contribution

It introduces a formal game theoretic model for CR, connecting it to Zermelo's early results and related reachability games.

Findings

Established a formal framework for CR and pursuit games.

Linked CR concepts to Zermelo's and Konig's early work.

Discussed strategic and capture time assumptions in pursuit scenarios.

Abstract

We provide a game theoretic framework for the game of cops and robbers (CR). Within this framework we study certain assumptions which underlie the concepts of optimal strategies and capture time. We also point out a connection of these concepts to early work by Zermelo and D. Konig. Finally, we discuss the relationship between CR and related pursuit games to reachability games.