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Dynamic Games and Applications

, Volume 9, Issue 4, pp 1076–1099 | Cite as

Generalized Cops and Robbers: A Multi-player Pursuit Game on Graphs

  • Ath. KehagiasEmail author
Article
  • 36 Downloads

Abstract

We introduce and study the Generalized Cops and Robbers (GCR) game, 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 nonpositional ones. We also study the capturing properties of GCR Nash equilibria in connection with 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

N-player game Pursuit Cops and robbers 

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Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Aristotle University of ThessalonikiThessalonikiGreece

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