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

Overview & Synopsis

We study an n-player random game with random payoffs and continuous strategy profiles sets. The payoff function of each player is defined by its expected value and the strategy set of each player is defined by a linear joint chance constraint. The random constraint vectors defining the joint chance constraint are independent and follow normal mean-variance mixture distributions. We propose a reformulation of the joint chance constraint of each player. We prove the existence of Nash equilibrium of this game by using the Kakutani fixed-point theorem under mild assumptions. Keywords Chance-constrained game • Normal mean-variance mixture • Nash equilibrium.