We study finite normal-form games in which payoffs are subject to random perturbations and players face uncertainty about how these shocks co-move across actions, an ambiguity that naturally arises when only realized (not counterfactual) payoffs are observed. We introduce the Statistical Equilibrium of Optimistic Beliefs (SE-OB), inspired by discrete choice theory. We model players as \textit{optimistic better responders}: they face ambiguity about the dependence structure (copula) of payoff perturbations across actions and resolve this ambiguity by selecting, from a belief set, the joint distribution that maximizes the expected value of the best perturbed payoff. Given this optimistic belief, players choose actions according to the induced random-utility choice rule. We define SE-OB as a fixed point of this two-step response mapping. SE-OB generalizes the Nash equilibrium and the structural quantal response equilibrium. We establish existence under standard regularity conditions on belief sets. For the economically important class of marginal belief sets, that is, the set of all joint distributions with fixed action-wise marginals, optimistic belief selection reduces to an optimal coupling problem, and SE-OB admits a characterization via Nash equilibrium of a smooth regularized game, yielding tractability and enabling computation. We characterize the relationship between SE-OB and existing equilibrium notions and illustrate its empirical relevance in simulations, where it captures systematic violations of independence of irrelevant alternatives that standard logit-based models fail to explain.

翻译：我们研究具有随机扰动收益的有限标准形式博弈，其中玩家面临关于这些冲击在不同行动间如何共同变动的模糊性，这种模糊性在仅观察到已实现（而非反事实）收益时自然产生。受离散选择理论启发，我们引入统计均衡的乐观信念（SE-OB）。我们将玩家建模为乐观的优化响应者：他们面临关于收益扰动在不同行动间的依赖结构（连接函数）的模糊性，并通过从信念集中选择使最佳扰动收益期望值最大化的联合分布来解决这一模糊性。给定这一乐观信念，玩家根据诱导的随机效用选择规则选择行动。我们将SE-OB定义为这一两阶段响应映射的不动点。SE-OB推广了纳什均衡和结构量化响应均衡。我们在信念集满足标准正则性条件下证明了存在性。对于边际信念集这一重要经济类别——即所有具有固定行动边际分布的联合分布集合——乐观信念选择简化为一个最优耦合问题，且SE-OB可通过光滑正则化博弈的纳什均衡进行刻画，从而具有可处理性并支持计算。我们刻画了SE-OB与现有均衡概念的关系，并通过模拟说明其经验相关性——该模型能够捕捉标准基于logit的模型无法解释的无关替代品独立性系统性违背现象。