Games with distributionally robust joint chance constraints

• DOI: 10.1007/s11590-021-01700-9
• Publication Date: 2021-01-19T14:03:01Z
• Authors: Shen Peng; Abdel Lisser; Vikas Vikram Singh; Nalin Gupta; Eshan Balachandar
• Keywords: Stochastic game; Robust Optimization

This paper studies an n-player non-cooperative game where each player has expected-value payoff function and chance-constrained strategy set. We consider the case where the row vectors defining the constraints are independent random vectors whose probability distributions are not completely known and belong to a certain distributional uncertainty set. The chance-constrained strategy sets are defined using a distributionally robust framework. We consider one density based uncertainty set and four two-moments based uncertainty sets. One of the considered uncertainty sets is based on a nonnegative support. Under the standard assumptions on the players’ payoff functions, we show that there exists a Nash equilibrium of a distributionally robust chance-constrained game for each uncertainty set. As an application, we study Cournot competition in electricity market and perform the numerical experiments for the case of two electricity firms.