I examine when, how, and which conventions arise in N-player games. Each player draws a random sample of strategies used in the recent past, and then chooses a strategy in response to this sample. A player’s response is determined by a behavioural rule, which maps from the set of recently used strategy profiles to a subset of his own strategy set, and each element in the latter set is chosen with positive probability. A random sample of strategies is monomorphic if it contains only one distinct strategy for each of the other players. The behavioural rule of a player is responsive if, on drawing a monomorphic sample, there is a positive probability of playing a best-response to the other players’ strategy profile that is induced by their respective strategies in that sample; in addition, if the said induced strategy profile supports a strict Nash equilibrium, then a strategy played by him in the recent past is chosen with the complementary probability. A game is weakly acyclic if there exists a ‘best-response path’ from each outcome that is not a strict Nash equilibrium to a strict Nash equilibrium. I show that: (i) a convention forms whenever the players’ behavioural rules are responsive, and the game is weakly acyclic, (ii) in bi-matrix games, individuals described by the behavioural rule of extreme optimism—whereby, conditional on the random sample, they play a best-response to the most optimistic belief about the other player’s strategy choice—perform better than individuals described by any other responsive behavioural rule in the sense that the convention that is most preferred by the former is always in the stochastically stable set, and (iii) in bi-matrix pure coordination games, the said convention is the uniquely stochastically stable state if the other player’s behavioural rule is ‘mildly different’ from extreme optimism.

我研究了在N玩家游戏中何时，如何以及哪些惯例出现。每个参与者随机抽取最近使用的策略样本，然后根据该样本选择策略。玩家的反应是由行为规则决定的，该行为规则从最近使用的策略配置文件集映射到他自己的策略集的子集，并且以正概率选择后者集中的每个元素。如果策略样本中的每个其他参与者仅包含一个不同的策略，则它是单态的。玩家的行为规则具有响应能力如果在抽取一个单形样本时，有一个最佳的可能性对其他参与者的策略配置文件做出最佳响应，而该响应是由该样本中他们各自策略引起的；另外，如果所述诱导的策略概况支持严格的纳什均衡，则以互补的概率选择他近来所扮演的策略。如果存在从非严格的纳什均衡到严格的纳什均衡的每个结果的“最佳响应路径”，则博弈是弱非周期性的。我证明：（i）每当玩家的行为规则做出反应并且游戏弱循环时，就会形成惯例；（ii）在双矩阵游戏中，被极端乐观的行为规则描述的个体（因此，以随机样本为条件，他们对其他参与者的策略选择的最乐观信念表现出最佳反应），其表现要优于其他任何反应性行为规则所描述的个人，因为在这种情况下，最受惯例欢迎的惯例是前者始终处于随机稳定状态，而且（iii）在双矩阵纯协调游戏中，如果其他玩家的行为规则与极端乐观主义“略有不同”，则上述约定就是唯一的随机稳定状态。