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Some Game-Theoretic Remarks on Two-Player Generalized Cops and Robbers Games

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  • Athanasios Kehagias

    (Aristotle University Thessaloniki)

  • Georgios Konstantinidis

    (Aristotle University Thessaloniki)

Abstract

In this paper, we study the two-player generalized cops and robbers (GCR) games introduced by Bonato and MacGillivray. Our main goals are to provide: (a) a game-theoretic formulation of GCR and (b) a self-contained game-theoretic proof that GCR has a value and an optimal strategy profile. To achieve our goals, we first formulate GCR (and CR as a special case) as a zero-sum stochastic game. Then we study a Vertex Labeling (VL) algorithm and prove it computes the value of the GCR game (for every starting “condition”) and that the vertex labels can be used to specify a positional deterministic optimal strategy for each player. We also compare our game-theoretic analysis to some of the usual graph theoretic/combinatorial approaches to CR/GCR.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:dyngam:v:11:y:2021:i:4:d:10.1007_s13235-021-00385-0
    DOI: 10.1007/s13235-021-00385-0
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    References listed on IDEAS

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    1. Shravan Luckraz, 2019. "A Survey on the Relationship Between the Game of Cops and Robbers and Other Game Representations," Dynamic Games and Applications, Springer, vol. 9(2), pages 506-520, June.
    2. 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.
    Full references (including those not matched with items on IDEAS)

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    More about this item

    Keywords

    Cops and robbers; Pursuit evasion;

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