Abstract: The paper brings forward four game models under quadratic game:static state-static state game,static state-dynamic state game,dynamic state-static state game and dynamic state-dynamic state game,analyzes the equilibrium under the four game models,at last calculates a mixed strategy Nash equilibrium through an example,and by contrast to the cost under quadratic game and simple game draws a conclusion that under normal condition the cost of supplier,retailer and supply chain under simple game is lower than that under quadratic game.

Key words: supply chain, quadratic game, quantity discount policy, mixed strategy Nash equilibrium