General sum games with joint chance constraints

We consider an n-player non-cooperative game with continuous strategy sets. The strategy set of each player contains a set of stochastic linear constraints. We model the stochastic linear constraints of each player as a joint chance constraint. We assume that the row vectors of a matrix defining the stochastic constraints of each player are independent and each row vector follows a multivariate normal distribution. Under certain conditions, we show the existence of a Nash equilibrium for this game.