Some Game-Theoretic Remarks on Two-Player Generalized Cops and Robbers Games
Dyn. Games Appl.(2021)
摘要
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.
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关键词
Cops and robbers, Pursuit evasion
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