We consider an n-player non-cooperative game where each player has expected value payoff function and her strategy set is defined by a joint chance constraint. The random constraint vectors are independent. We propose a subset of probability distributions from elliptical family of distributions. We consider the case when the probability distribution of each random constraint vector belong to the subset as well as the case when it is a finite mixture of the probability distributions from the subset. We propose a convex reformulation for the joint chance constraint of each player and derive the bounds for players' confidence levels and weights used in the mixture distributions. Then, we show that there exists a Nash equilibrium of the game, under mild conditions on the players' payoff functions, when the players' confidence levels and the weights used in the mixture distributions are within the derived bounds.