基于Cournot模型的四种市场三度价格歧视博弈分析

Analysis on Third-degree Price Discrimination in All Four Kinds of Markets by Game Theory Based on Cournot Model

对m个厂商n元市场的最一般情形用完全信息静态博弈的方法分析了实施三度价格歧视情形和统一定价情形的均衡产量,均衡价格和均衡总收益的统一的计算公式,并研究了这两种情形三个指标之间的关系。结果显示,在n个子市场的需求函数为线性需求的条件下,统一定价的市场均衡产量等于歧视定价的市场均衡产量;统一定价的均衡价格是歧视定价时n个子市场均衡价格的加权平均;统一定价的市场均衡总收益小于歧视定价的市场均衡总收益。同时,还研究清楚了各均衡量随着厂商数m变化的规律,以及随着子市场数n变化的规律。

The unified formula of equilibrium output,equilibrium price and equilibrium total revenue in case of implementing third-degree price discrimination and unified pricing are analyzed under the most common circumstances of m enterprises with n sub markets by complete information static game method,and the relationship between the three indexes of the two cases are studied.The results show that:(1)under the condition of linear demand functions of the nsub markets,the equilibrium output of unified pricing is equal to the equilibrium output of discriminative pricing;(2)the equilibrium price of unified pricing is weighted average of the equilibrium prices of nsub markets while discriminative pricing;(3)the equilibrium total revenue of unified pricing is less than the equilibrium total revenue of discriminative pricing.At the same time,the laws are researched too of equilibrium indexes varying with numbers of enterprises varying,and with numbers of sub markets varying.