Bertrand模型与超模博弈

将近年来博弈论中出现的一种新的研究方法--超模博弈理论应用于Bertrand寡头博弈中,对于具有一般成本函数的差异产品的Bertrand寡头博弈,当企业的策略只是选择价格水平时,比较了博弈为超模和对数超模博弈的充分条件,表明虽然一个对数超模博弈一定是拟超模的,因而较超模博弈的适用范围更广泛,但二者的充分条件之间不具备可比性,即不能由其中一个推出另外一个.同时既使该博弈既不是超模的也不是对数超模的,仍可能存在对利润函数的其它单调转换使博弈成为超模的.当边际生产成本为常数时,给出了具体的反例.当企业的策略为同时选择价格和广告水平,且企业的边际生产成本为常数时,表明在一般的假设下博弈为超模博弈,从而说明了为什么通常情况下较高的广告水平对应着较高的价格.

Bertrand Model and the Theory of Supermodular Games

A new analysis method in game theory, supermodular game, is used in Bertrand model, for differentiated-product Bertrand oligopoly with general cost functions, when the strategy variable is price ato ne, the sufficient conditions are comparedfor supermodular and log-supermodular game.Although a logsupermodular game is a quasi-supermodular one, which is more general than a supermodular one, the corresponding sufficient conditions placed on the firms' profit functions are shown not to be comparable, that is one cant get one from another.When the game is neither a log-supermodular nor a supermodular one, a new monotone transformations of the firms' profit functions may make the game a supermodular one.For the special case of constant marginal production cost, counterexamples are provided.When the strategy variables are pricing and advertising effort, under usual assumptions and constant marginal production cost, the game is a supermodular one and this explains why higher prices are always associated with higher advertising levels.