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.

翻译：标准博弈论解概念——纳什均衡——假设所有参与者均理性行事。若遵循纳什均衡策略而对手非理性（或遵循不同纳什均衡的策略），则可能获得极低收益。另一方面，最大最小策略假设所有对手均以最小化我方收益为目标（即使此举不符合其自身利益），虽能保证最坏情况下的最大可能收益，但会导致过度保守的博弈行为。本文提出一种名为安全均衡的新解概念：该模型以特定概率假设对手理性行事，并以剩余概率假设其可能采取任意行为。我们证明在任意策略式博弈中（对于所有可能的理性参数取值）安全均衡均存在，并证明其计算复杂度为PPAD难。针对双人博弈与$n$人博弈，我们分别提出了计算安全均衡的精确算法，以及可扩展的近似算法。