Existence of Nash equilibrium for distributionally robust chance-constrained games

We consider an n-player finite strategic game. The payoff vector of each player is a random vector whose distribution is not completely known. We assume that the distribution of the random payoff vector of each player belongs to a distributional uncertainty set. Using distributionally robust approach, we define a chance-constrained game with respect to the worst-case chanceconstraint. We call such a game as distributionally robust chance-constrained game. We consider three different types of distributional uncertainty sets. For each case, we show that there always exists a mixed strategy Nash equilibrium for the corresponding distributionally robust chance-constrained game.