并行奇偶对策的有限理性
Bounded Rationality in Concurrent Parity Games
摘要：
我们考虑在有限状态空间上进行无限回合的2人博弈。游戏是并行的：在每一轮中，两个玩家同时选择他们的动作;当前状态和动作决定继任者。我们认为欧米茄经常获胜的条件作为平价目标。我们考虑的定性分析问题：几乎肯定和有限肯定获胜的状态集的计算，其中玩家1可以确保赢得概率1和概率任意接近1，分别。一般来说，几乎肯定和有限肯定获胜策略需要无限记忆和无限精度。本文研究了并发奇偶博弈定性分析的有限理性问题，其中策略集参与人1被限制为有限资源策略。就精度而言，策略可以是确定性的、均匀的、有限精度的或无限精度的;就记忆而言，策略可以是无记忆的、有限记忆的或无限记忆的。我们提出了一个精确和完整的定性获胜集的所有组合类的策略的特征。特别是，我们表明，统一的无记忆策略是强大的有限精度的无限记忆策略，和无限精度的无记忆策略是强大的无限精度的有限记忆策略。我们证明了获胜集可以在O（n^{2d+3}）时间内计算，其中n是游戏的大小，2d是优先级的数量，并且我们的算法是符号的。在NP cap coNP中可以判定一个状态是否属于获胜集的成员问题。虽然这种复杂性是相同的简单类的回合制游戏，其中在每个状态下，只有一个玩家有一个选择的动作，我们的算法，这是通过表征的胜利集作为μ演算公式，是相当多的参与。
英文摘要：
We consider 2-player games played on a finite state space for infinite rounds. The games are concurrent: in each round, the two players choose their moves simultaneously; the current state and the moves determine the successor. We consider omega-regular winning conditions given as parity objectives. We consider the qualitative analysis problems: the computation of the almost-sure and limit-sure winning set of states, where player 1 can ensure to win with probability 1 and with probability arbitrarily close to 1, respectively. In general the almost-sure and limit-sure winning strategies require both infinite-memory and infinite-precision. We study the bounded-rationality problem for qualitative analysis of concurrent parity games, where the strategy set player 1 is restricted to bounded-resource strategies. In terms of precision, strategies can be deterministic, uniform, finite-precision or infinite-precision; and in terms of memory, strategies can be memoryless, finite-memory or infinite-memory. We present a precise and complete characterization of the qualitative winning sets for all combinations of classes of strategies. In particular, we show that uniform memoryless strategies are as powerful as finite-precision infinite-memory strategies, and infinite-precision memoryless strategies are as powerful as infinite-precision finite-memory strategies. We show that the winning sets can be computed in O(n^{2d+3}) time, where n is the size of the game and 2d is the number of priorities, and our algorithms are symbolic. The membership problem of whether a state belongs to a winning set can be decided in NP cap coNP. While this complexity is the same as for the simpler class of turn-based games, where in each state only one of the players has a choice of moves, our algorithms, that are obtained by characterization of the winning sets as mu-calculus formulas, are considerably more involved.
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