Generalized Cops and Robbers: A Multi-Player Pursuit Game on Graphs
Abstract
We introduce and study the Generalized Cops and Robbers game (GCR), an N-player pursuit game in graphs. The two-player version is essentially equivalent to the classic Cops and Robbers (CR) game. The three-player version can be understood as two CR games played simultaneously on the same graph; a player can be at the same time both pursuer and evader. The same is true for four or more players. We formulate GCR as a discounted stochastic game of perfect information and prove that, for three or more players, it has at least two Nash Equilibria: one in positional deterministic strategies and another in non-positional ones. We also study the capturing properties of GCR Nash Equilibria in connection to the cop-number of a graph. Finally, we briefly discuss GCR as a member of a wider family of multi-player graph pursuit games with rather interesting properties.
Keywords
Cite
@article{arxiv.1807.08500,
title = {Generalized Cops and Robbers: A Multi-Player Pursuit Game on Graphs},
author = {Athanasios Kehagias},
journal= {arXiv preprint arXiv:1807.08500},
year = {2018}
}