Bertrand模型与超模博弈
发布时间：2018-12-12 03:14
【摘要】：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。
[Abstract]:The supermodel game theory, a new research method in game theory in recent years, is applied to the Bertrand oligopoly game. For the Bertrand oligopoly game with different products with general cost function, when the firm's strategy is only to choose the price level, The sufficient conditions for the game to be supermodule and logarithmic supermodule are compared. It is shown that although a logarithmic supermodule game must be quasi-supermodule, so it has a wider range of application than supermodel game, but the sufficient conditions between them are not comparable. That is, one cannot launch the other. At the same time, even if the game is neither hypermodule nor logarithmic supermodule, there may be other monotonic transformations of the profit function that make the game supermodule. When the marginal production cost is constant, a concrete counterexample is given. When the strategy of the enterprise is to select both the price and the advertising level, and the marginal production cost of the enterprise is constant, it is shown that the game is supermodel game under the general assumption. This explains why higher advertising levels usually correspond to higher prices.
【作者单位】： 华中科技大学控制科学与工程系;
【基金】：国家自然科学基金资助项目(60674083)
【分类号】：C931
，
本文编号：2373794
[Abstract]:The supermodel game theory, a new research method in game theory in recent years, is applied to the Bertrand oligopoly game. For the Bertrand oligopoly game with different products with general cost function, when the firm's strategy is only to choose the price level, The sufficient conditions for the game to be supermodule and logarithmic supermodule are compared. It is shown that although a logarithmic supermodule game must be quasi-supermodule, so it has a wider range of application than supermodel game, but the sufficient conditions between them are not comparable. That is, one cannot launch the other. At the same time, even if the game is neither hypermodule nor logarithmic supermodule, there may be other monotonic transformations of the profit function that make the game supermodule. When the marginal production cost is constant, a concrete counterexample is given. When the strategy of the enterprise is to select both the price and the advertising level, and the marginal production cost of the enterprise is constant, it is shown that the game is supermodel game under the general assumption. This explains why higher advertising levels usually correspond to higher prices.
【作者单位】： 华中科技大学控制科学与工程系;
【基金】：国家自然科学基金资助项目(60674083)
【分类号】：C931
，
本文编号：2373794
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