Best-Effort Strategies for Losing States

Computer Science – Computer Science and Game Theory

Scientific paper

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Technical report derived from the GAMES'07 talk "Games you cannot win"

Scientific paper

We consider games played on finite graphs, whose goal is to obtain a trace belonging to a given set of winning traces. We focus on those states from which Player 1 cannot force a win. We explore and compare several criteria for establishing what is the preferable behavior of Player 1 from those states. Along the way, we prove several results of theoretical and practical interest, such as a characterization of admissible strategies, which also provides a simple algorithm for computing such strategies for various common goals, and the equivalence between the existence of positional winning strategies and the existence of positional subgame perfect strategies.

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