结构等价并发奇偶对策的鲁棒性
Robustness of Structurally Equivalent Concurrent Parity Games
摘要：
我们考虑在有限状态空间上进行无限回合的两人随机博弈。游戏是并行的：在每一轮中，两个参与者（参与者1和参与者2）独立地并且同时地选择他们的移动;当前状态和两个移动确定在后继状态上的概率分布。我们还考虑了回合制随机游戏的重要特例，玩家轮流移动，而不是同时移动。我们研究了以ω-正则获胜条件为奇偶目标的并发博弈。参与人1的奇偶目标值是参与人能够保证满足对手所有策略的目标的最大概率。研究了在转移概率不精确的情况下，并发和回合制随机奇偶博弈中价值函数的连续性和鲁棒性问题。我们提出的价值函数的差异（在转移概率的不精确性方面）的定量界限，并显示了结构上等价的并发游戏（两个游戏是结构上等价的，如果支持的转移函数是相同的，概率不同）的价值连续性。我们还证明了结构等价的回合制随机奇偶博弈的最优策略的鲁棒性。最后，我们表明，价值连续性属性打破结构上等价的假设（即使是马尔可夫链），并表明我们的定量界是渐近最优的。因此，我们的结果是紧的（假设是必要的和充分的）和最优的（我们的定量界是渐近最优的）。
英文摘要：
We consider two-player stochastic games played on a finite state space for an infinite number of rounds. The games are concurrent: in each round, the two players (player 1 and player 2) choose their moves independently and simultaneously; the current state and the two moves determine a probability distribution over the successor states. We also consider the important special case of turn-based stochastic games where players make moves in turns, rather than concurrently. We study concurrent games with ω-regular winning conditions specified as parity objectives. The value for player 1 for a parity objective is the maximal probability with which the player can guarantee the satisfaction of the objective against all strategies of the opponent. We study the problem of continuity and robustness of the value function in concurrent and turn-based stochastic parity gameswith respect to imprecision in the transition probabilities. We present quantitative bounds on the difference of the value function (in terms of the imprecision of the transition probabilities) and show the value continuity for structurally equivalent concurrent games (two games are structurally equivalent if the support of the transition function is same and the probabilities differ). We also show robustness of optimal strategies for structurally equivalent turn-based stochastic parity games. Finally we show that the value continuity property breaks without the structurally equivalent assumption (even for Markov chains) and show that our quantitative bound is asymptotically optimal. Hence our results are tight (the assumption is both necessary and sufficient) and optimal (our quantitative bound is asymptotically optimal).
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
