Random Games Under Elliptically Distributed Dependent Joint Chance Constraints

• DOI: 10.1007/s10957-022-02077-0
• Publication Date: 2022-09-09T12:37:36Z
• Authors: Hoang Nam Nguyen; Abdel Lisser; Vikas Vikram Singh
• Keywords: Elliptical distribution; 0209 industrial biotechnology; 02 engineering and technology; [MATH]Mathematics [math]; Chance-constrained game; Archimedean copulas Mathematics Subject Classification (2000) MSC 90C15; Nash equilibrium; 90C25; 90C59

We study an n-player game with random payoffs and continuous strategy sets. The payoff function of each player is defined by its expected value and the strategy set of each player is defined by a joint chance constraint. The random constraint vectors defining the joint chance constraint are dependent and follow elliptically symmetric distributions. The Archimedean copula is used to capture the dependence among random constraint vectors. We propose a reformulation of the joint chance constraint of each player. Under mild assumptions on the players' payoff functions and 1-dimensional spherical distribution functions, we show that there exists a Nash equilibrium of the game.