To verify the robustness of a program or protocol, it is common in the computer science community to rely on the theoretical framework of game theory. In particular, if one seeks to enforce a desired property, or specification, despite an unpredictable environment, a useful abstraction is to model the situation as a two-player zero-sum game. The goal is then to find a strategy for the system that guarantees the specification against any strategy of the environment. However, to model more complex situations, such as multiple systems with different objectives or an environment composed of various agents, the richer framework of multiplayer games must be considered. In this setting, a natural question is to identify equilibria, i.e., strategy profiles that are robust in the sense that no player has an incentive to deviate. The most well-known equilibrium concept is the Nash equilibrium, but several alternatives exist. We study five such notions and, for each of them, we provide complexity results for the constrained existence problem, which consists of deciding whether a given game contains an equilibrium that ensures each player a payoff within a specified interval.

翻译：为验证程序或协议的鲁棒性，计算机科学界通常依赖博弈论理论框架。具体而言，若要在不可预测环境下强制执行所需属性（即规范），一种有效的抽象方法是将该情形建模为双人零和博弈，其目标是找到系统策略，使其在任何环境策略下均能保证规范成立。然而，为建模更复杂的场景（例如含有多元目标的多个系统，或由不同智能体构成的环境），必须采用更丰富的多人博弈框架。在此设定下，一个自然问题是识别均衡——即所有参与者均无动机偏离的鲁棒策略组合。最著名的均衡概念是纳什均衡，但存在多种替代方案。我们研究了五种此类概念，并针对每种概念提供约束存在性问题的复杂度结果，该问题旨在判定给定博弈是否存在确保所有参与者收益位于指定区间内的均衡。