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

Athanasios Kehagias () and Georgios Konstantinidis
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Athanasios Kehagias: Aristotle University Thessaloniki
Georgios Konstantinidis: Aristotle University Thessaloniki

Dynamic Games and Applications, 2021, vol. 11, issue 4, No 6, 785-802

Abstract: 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.

Keywords: Cops and robbers; Pursuit evasion (search for similar items in EconPapers)
Date: 2021
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DOI: 10.1007/s13235-021-00385-0

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