论文标题
安全平衡
Safe Equilibrium
论文作者
论文摘要
标准的游戏理论解决方案概念NASH平衡假设所有玩家都在合理地行事。如果我们遵循NASH平衡，并且对手是不合理的（或遵循来自不同NASH平衡的策略），那么我们可能会获得极低的收益。另一方面，最大值策略假设所有对立的代理商都在努力最小化我们的回报（即使这不符合他们的最大利益），并确保最大可能的最差收益可能会带来最大的收益，但会导致非常保守的比赛。我们提出了一个称为安全平衡的新解决方案概念，该概念将反对的人与指定的概率合理地行为，并具有剩余概率的可能任意行为。我们证明在所有战略形式游戏（对于理性参数的所有可能值）中都存在安全的平衡，并证明其计算是PPAD-HARD。我们提出了用于计算2和$ n $玩家游戏的安全平衡的精确算法，以及可扩展的近似算法。
The standard game-theoretic solution concept, Nash equilibrium, assumes that all players behave rationally. If we follow a Nash equilibrium and opponents are irrational (or follow strategies from a different Nash equilibrium), then we may obtain an extremely low payoff. On the other hand, a maximin strategy assumes that all opposing agents are playing to minimize our payoff (even if it is not in their best interest), and ensures the maximal possible worst-case payoff, but results in exceedingly conservative play. We propose a new solution concept called safe equilibrium that models opponents as behaving rationally with a specified probability and behaving potentially arbitrarily with the remaining probability. We prove that a safe equilibrium exists in all strategic-form games (for all possible values of the rationality parameters), and prove that its computation is PPAD-hard. We present exact algorithms for computing a safe equilibrium in both 2 and $n$-player games, as well as scalable approximation algorithms.
