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

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  • Ath. Kehagias

    (Aristotle University of Thessaloniki)

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.

Suggested Citation

  • Ath. Kehagias, 2019. "Generalized Cops and Robbers: A Multi-player Pursuit Game on Graphs," Dynamic Games and Applications, Springer, vol. 9(4), pages 1076-1099, December.
    • Handle: RePEc:spr:dyngam:v:9:y:2019:i:4:d:10.1007_s13235-018-0288-0
    DOI: 10.1007/s13235-018-0288-0
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    Cited by:

    1. Athanasios Kehagias & Georgios Konstantinidis, 2021. "Some Game-Theoretic Remarks on Two-Player Generalized Cops and Robbers Games," Dynamic Games and Applications, Springer, vol. 11(4), pages 785-802, December.

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