Cooperative and non-cooperative Nash solution for linear supply function equilibrium game

Abstract

In this paper, the competition among suppliers in an oligopolistic market is studied using supply function equilibrium model. Since the decision of each supplier affects other suppliers’ profit, we have a game problem rather than optimization. In the proposed supply function equilibrium game, both of the cooperative and non-cooperative behaviors of the players are studied. In non-cooperative case, the Nash equilibrium point of the game is obtained for n-player in constant and price sensitive demand cases. In cooperative game, the concept of Nash bargaining solution is utilized to study the collusive behavior of the suppliers. The convexity and closeness of the players’ payoff set in supply function equilibrium model is proved as the necessary and sufficient condition for existence and uniqueness of the solution and then, the mathematical formulation of Nash bargaining solution is derived. In addition, the cooperative and non-cooperative behavior of players is compared over a wide range of parameters in a case study.