This paper studies an n-player non-cooperative game where each player has expected-value payoff function and chance-constrained strategy set. We consider the case where the row vectors defining the constraints are independent random vectors whose probability distributions are not completely known and belong to a certain distributional uncertainty set. The chance-constrained strategy sets are defined using a distributionally robust framework. We consider one density based uncertainty set and four two-moments based uncertainty sets. One of the considered uncertainty sets is based on a nonnegative support. Under the standard assumptions on the players’ payoff functions, we show that there exists a Nash equilibrium of a distributionally robust chance-constrained game for each uncertainty set. As an application, we study Cournot competition in electricity market and perform the numerical experiments for the case of two electricity firms.

本文研究的ñ玩家非合作游戏，其中每个玩家都有期望值支付功能和机会受限的策略集。我们考虑以下情况：定义约束的行向量是独立的随机向量，其概率分布不完全已知，并且属于某个分布不确定性集。机会受限的策略集是使用分布稳健的框架定义的。我们考虑一个基于密度的不确定性集合和四个基于两个矩的不确定性集合。所考虑的不确定性集合之一基于非负支持。在关于玩家收益函数的标准假设下，我们表明对于每个不确定性集，存在一个分布鲁棒的机会受限游戏的纳什均衡。作为应用，