Complementarity formulation of games with random payoffs

We consider an n-player non-cooperative game where the payoff function of each player follows a multivariate distribution. This formulation is adopted to model a zonal electricity market in which generators operate by running conventional and renewable-based plants. The players in the market compete as in a Cournot model. We formulate this problem as a chance-constrained game by defining the payoff function of each player using a chance constraint. A full empirical analysis has been conducted on the Italian electricity market to test the impact of renewable genera- tors in the light of decarbonization of the market and the impact of the volatility of the cost of conventional plants, mainly related to the volatility of gas prices. We finally test the robustness of the chance constraint formulation with an out of sample analysis.