Usually, to apply game-theoretic methods, we must specify utilities precisely, and we run the risk that the solutions we compute are not robust to errors in this specification. Ordinal games provide an attractive alternative: they require specifying only which outcomes are preferred to which other ones. Unfortunately, they provide little guidance for how to play unless there are pure Nash equilibria; evaluating mixed strategies appears to fundamentally require cardinal utilities. In this paper, we observe that we can in fact make good use of mixed strategies in ordinal games if we consider settings that allow for folk theorems. These allow us to find equilibria that are robust, in the sense that they remain equilibria no matter which cardinal utilities are the correct ones -- as long as they are consistent with the specified ordinal preferences. We analyze this concept and study the computational complexity of finding such equilibria in a range of settings.

翻译：通常，应用博弈论方法时，我们必须精确设定效用函数，这导致我们计算出的解可能对设定误差缺乏鲁棒性。序数博弈提供了一种有吸引力的替代方案：它仅需设定哪些结果优于其他结果。遗憾的是，除非存在纯纳什均衡，否则序数博弈几乎无法为策略选择提供指导——评估混合策略似乎本质上需要基数效用。本文指出，若考虑允许民间定理成立的场景，我们实际上可以在序数博弈中有效利用混合策略。这使得我们能够找到具有鲁棒性的均衡，即无论实际基数效用函数如何（只要与指定的序数偏好一致），这些均衡始终保持均衡性质。我们分析了这一概念，并在多种场景下研究了寻找此类均衡的计算复杂性。