Random games under normal mean-variance mixture distributed independent linear joint chance constraints

In this paper, we study an n player game where the payoffs as well as the strategy sets are defined using random variables. The payoff function of each player is defined using expected value function and his/her strategy set is defined using a linear joint chance constraint. The random constraint vectors defining the joint chance constraint are independent and follow normal mean-variance mixture distributions. For each player, we reformulate the joint chance constraint in order to prove the existence of a Nash equilibrium using the Kakutani fixed-point theorem under mild assumptions. We illustrate our theoretical results by considering a game between two competing firms in financial market.