We consider the class of two-person ordinal potential games where each player has the same number of actions $K$. Each game in this class admits at least one pure Nash equilibrium and the best-response dynamics converges to one of these pure Nash equilibria; which one depends on the starting point. So, each pure Nash equilibrium has a basin of attraction. We pick uniformly at random one game from this class and we study the joint distribution of the sizes of the basins of attraction. We provide an asymptotic exact value for the expected basin of attraction of each pure Nash equilibrium, when the number of actions $K$ goes to infinity.

翻译：我们考虑一类双人序数势博弈，其中每位玩家具有相同数量的行动$K$。该类博弈中的每个游戏至少存在一个纯纳什均衡，且最佳响应动态会收敛至其中一个纯纳什均衡；具体收敛至哪一个取决于起始点。因此，每个纯纳什均衡都具有一个吸引域。我们以均匀分布方式从该类别中随机选取一个博弈，并研究各吸引域规模的联合分布。当行动数量$K$趋于无穷大时，我们给出了每个纯纳什均衡吸引域期望值的渐近精确值。