Extreme Nash equilibrium of polymatrix games in electricity market

Game theoretical approaches are widely used for the analysis of oligopolistic electricity markets. Nash equilibrium is a solution concept of game theoretical approaches. Due to existence of mixed strategy equilibrium and large number of multiple players, finding Nash equilibrium for problems in electricity market is a difficult task. To resolve these difficulties, this paper proposes a simplified approach for finding extreme Nash equilibrium, based on payoff matrix approach and mixed integer linear programming (MILP). To illustrate the proposed approach, a practical case study of Cournot poly-matrix game is considered. Eliminating constraints are appended on the proposed approach to find a global optimal solution. Obtained results show the strength of proposed approach, in terms of simplicity and computational time.