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Approximate Calculation of Equilibria in the Nonlinear Stackelberg Oligopoly Model: A Linearization Based Approach
Automation and Remote Control ( IF 0.7 ) Pub Date : 2020-11-06 , DOI: 10.1134/s0005117920090064
M. I. Geraskin

The game-theoretic problem of choosing optimal strategies for oligopoly market agents with linear demand functions and nonlinear cost functions is considered. Necessary conditions for the existence of a solution of a system of nonlinear equations with power functions are established. The system of equations for the optimal responses of agents is linearized by expanding the power functions in Taylor series. As a result, the linearized system depends on the vector of linearization parameters, and the calculation of game equilibria is reduced finding fixed points of nonlinear mappings. The deviations of the approximate equilibrium from the exact solution are investigated. Analytical formulas for calculating equilibria in the game of oligopolists under an arbitrary level of Stackelberg leadership are derived. Analysis of duopoly and tripoly demonstrates that the game equilibrium is determined by two factors as follows. First, the concavity of the agent’s cost function (the positive scale effect) leads to an increase in his payoff compared to the agents with convex cost functions (the negative scale effect). Second, the agent’s payoff increases if he is a Stackelberg leader; however, the advantage of his environment by the type of cost function reduces the effect of the second factor.



中文翻译:

非线性Stackelberg寡头垄断模型中均衡的近似计算:基于线性化的方法

考虑了为具有线性需求函数和非线性成本函数的寡头市场代理商选择最优策略的博弈论问题。建立了具有幂函数的非线性方程组的解的存在的必要条件。通过扩展泰勒级数的幂函数,可以线性化用于代理最佳响应的方程组。结果,线性化系统取决于线性化参数的向量,减少了博弈均衡的计算,从而找到了非线性映射的固定点。研究了近似平衡与精确解之间的偏差。推导了在斯塔克尔贝格领导层任意水平下寡头垄断博弈均衡计算公式。对双头垄断和三头垄断的分析表明,博弈均衡由以下两个因素决定。首先,与具有凸成本函数的代理商(负规模效应)相比,代理人成本函数(正规模效应)的凹性导致其收益的增加。其次,如果代理人是Stackelberg领导者,代理人的收益会增加;但是,通过成本函数的类型所带来的环境优势降低了第二个因素的影响。

更新日期:2020-11-06
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