Existence of Nash equilibrium for chance-constrained games

We consider an nn-player strategic game with finite action sets and random payoffs. We formulate this as a chance-constrained game by considering that the payoff of each player is defined using a chance constraint. We consider that the components of the payoff vector of each player are independent normal/Cauchy random variables. We also consider the case where the payoff vector of each player follows a multivariate elliptically symmetric distribution. We show the existence of a Nash equilibrium in both cases.