Real populations are seldom found at the Nash equilibrium strategy. The present work focuses on how population size can be a relevant evolutionary force diverting the population from its expected Nash equilibrium. We introduce the concept of insuperable strategy, a strategy that guarantees that no other player can have a larger payoff than the player that adopts it. We show that this concept is different from the rationality assumption frequently used in game theory and that for small populations the insuperable strategy is the most probable evolutionary outcome for any dynamics that equal game payoff and reproductive fitness. We support our ideas with several examples and numerical simulations. We finally discuss how to extend the concept to multiplayer games, introducing, in a limited way, the concept of game reduction.

翻译：现实种群很少处于纳什均衡策略。本研究聚焦于种群规模如何作为一种相关进化力量，使种群偏离预期的纳什均衡。我们引入不可超越策略的概念，即保证其他参与者无法获得高于采用该策略者收益的策略。我们证明这一概念不同于博弈论中常用的理性假设，并表明对于小规模种群，在任何将博弈收益等同于繁殖适应度的动态过程中，不可超越策略都是最可能的进化结果。我们通过多个实例与数值模拟验证了这些观点。最后探讨了如何将该概念扩展至多人博弈，并有限度地引入了博弈约简的概念。