Deterministic Graphical Games Revisited

We revisit the deterministic graphical gamesof Washburn. A deterministic graphical game can be described as a simple stochastic game (a notion due to Anne Condon), except that we allow arbitrary real payoffs but disallow moves of chance. We study the complexity of solving deterministic graphical games and obtain an almost-linear time comparison-based algorithm for computing an equilibrium of such a game. The existence of a linear time comparison-based algorithm remains an open problem.

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