Cops and Robber Game on Infinite Chessboard

We consider two variants of the Cops and Robbers game on an infinite chessboard that is a graph giving a regular partition of the plane into squares. Heuristic and precise definitions of a winning initial state for a pursuer and a winning initial state for an evader are formulated. Criteria for determining if a given initial state is winning for a pursuer or evader are given.

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