Equilibrium Analysis Of Cournot Game And Stackelberg Game Based On Price Discrimination

Price discrimination is a common phenomenon in the market.Based on the Cournot game and Stackelberg game of many manufacturers,this paper introduces the price discrimination.The manufacturer sells the same product to different consumer groups at different prices.First of all,the effects of price discrimination on monopoly cooperation and Cournot game equilibrium's output,profit and market average price are studied.The trigger strategy of repeated game of two manufacturers is given.Then the manufacturers,competing with Stackelberg game,its only subgame perfect Nash equilibrium is given by a backward induction and implicit function extremum method.And the relationship between the subgame and the number of manufacturers and consumer groups is given.Finally,the Nash equilibrium of two Cournot manufacturers with different degree of price discrimination based on nonlinear price function is studied.Regardless of price discrimination,the output provided by each Cournot oligopoly is higher than the output of each cooperative oligopoly.The average price of homogeneous products of monopoly cooperation is higher than that in Cournot competition.Then,the trigger strategy of repeated game is constructed,and the optimal response of each manufacturer to the trigger strategy is given.In the Stackelberg game,the optimal output of the first-mover is independent of the number of consumer groups and manufacturers regardless of price discrimination in the market.The average selling price of the back-movers has no relation with the number of groups,although the selling price of the back-movers is different for different groups.When the number of group is increased,the net increase effect of the profit of all oligarchs obeys the law of diminishing margin.When the number of group is small,the profit improvement brought by price discrimination is the most obvious,and the profit of Cournot is also subject to this law.Based on nonlinear price function,introducing the price discrimination,the profit for the Cournot oligopoly that provides products to both high and low consumer groups is less profit than that without price discrimination.The Cournot oligopoly that provides the product only to the high consumer group can make more profit than it's earning without price discrimination.When price discrimination of different degree is carried out,the average market price is smaller than that without price discrimination.