We study two-player games on finite graphs. Turn-based games have many nice properties, but concurrent games are harder to tame: e.g. turn-based stochastic parity games have positional optimal strategies, whereas even basic concurrent reachability games may fail to have optimal strategies. We study concurrent stochastic parity games, and identify a local structural condition that, when satisfied at each state, guarantees existence of positional optimal strategies for both players.

翻译：我们研究有限图上的双人博弈。回合制博弈具有诸多优良性质，而并发博弈则更难驾驭：例如，回合制随机奇偶博弈存在位置最优策略，但即使是最基本的并发可达性博弈也可能缺乏最优策略。本文研究并发随机奇偶博弈，并识别出一种局部结构条件——当每个状态均满足该条件时，可保证两位玩家均存在位置最优策略。