Chance-constrained games with mixture distributions

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 a joint chance constraint. The constraint vectors are independent. We case when probability distribution vector belongs to subset elliptical distributions as well it finite mixture from subset. propose convex reformulation derive bounds for players’ confidence levels weights used in distributions. Under mild conditions on functions, show that there exists Nash equilibrium within derived bounds. As application these games, competition between two investment firms same portfolios. use best response algorithm compute equilibria randomly generated games different sizes.