In this paper, we consider an n-player non-cooperative game where the random payoff function of each player is defined by its expected value and her strategy set is defined by a joint chance constraint. The random constraint vectors are independent. We consider the case when the probability distribution of each random constraint vector belongs to a subset of elliptical distributions as well as the case when it is a finite mixture of the probability distributions from the subset. We propose a convex reformulation of the joint chance constraint of each player and derive the bounds for players’ confidence levels and the weights used in the mixture distributions. Under mild conditions on the players’ payoff functions, we show that there exists a Nash equilibrium of the game when the players’ confidence levels and the weights used in the mixture distributions are within the derived bounds. As an application of these games, we consider the competition between two investment firms on the same set of portfolios. We use a best response algorithm to compute the Nash equilibria of the randomly generated games of different sizes.

在本文中，我们考虑一个n-玩家非合作博弈，其中每个玩家的随机收益函数由其期望值定义，而她的策略集由联合机会约束定义。随机约束向量是独立的。我们考虑每个随机约束向量的概率分布属于椭圆分布子集的情况以及它是该子集概率分布的有限混合的情况。我们提出了对每个玩家的联合机会约束的凸重构，并推导出玩家的置信水平和混合分布中使用的权重的界限。在玩家收益函数的温和条件下，我们表明，当玩家的置信水平和混合分布中使用的权重在派生边界内时，游戏存在纳什均衡。作为这些游戏的一个应用，我们考虑两个投资公司在同一投资组合上的竞争。我们使用最佳响应算法来计算随机生成的不同大小游戏的纳什均衡。