耦合不动点（或最佳邻近点）在寡头市场均衡中的应用
Application of Coupled Fixed (or Best Proximity) Points in Market Equilibrium in Oligopoly Markets
摘要：
本文给出了循环映射与耦合不动点的序偶概念的一种可能的推广及其在寡头垄断市场均衡模型中的应用。在完全度量空间（一致凸巴拿赫空间）中，我们得到了不动点（或最佳邻近点）存在唯一的充分条件。我们得到固定（或最佳邻近）的误差估计，只要我们使用连续迭代序列。我们说明了一个可能的应用程序的结果，建立一个务实的模型，在寡头垄断市场的竞争。为了实现这一目标，我们使用的方法的基础上研究的响应函数的每个市场参与者，从而使之有可能解决古诺和贝特朗产业结构与统一的形式化方法。与双寡头均衡的限制性理论结构相比，我们的研究能够解释现实世界的限制，如最低可持续生产水平和独家获得某些资源。我们证明并表明，通过使用精心构造的响应函数，它是可能的，以建立和校准一个模型，反映了不同的竞争战略，在极端集中的市场。响应函数方法还可以考虑不同的进入壁垒。通过对响应函数的拟合而不是对支付函数的利润最大化问题的拟合，将经典的最优化问题转化为一个耦合不动点问题，其优点是可以跳过角点最优、角点平衡和支付函数的凸性条件。
英文摘要：
We present a possible kind of generalization of the notion of ordered pairs of cyclic maps and coupled fixed points and its application in modelling of equilibrium in oligopoly markets. We have obtained sufficient conditions for the existence and uniqueness of fixed (or best proximity) points in complete metric spaces (uniformly convex Banach spaces). We get an error estimates of the fixed (or best proximity), provided that we have used sequences of successive iterations. We illustrate one possible application of the results by building a pragmatic model on competition in oligopoly markets. To achieve this goal, we use an approach based on studying the response functions of each market participant, thus making it possible to address both Cournot and Bertrand industrial structures with unified formal method. In contrast to the restrictive theoretical constructs of duopoly equilibrium, our study is able to account for real-world limitations like minimal sustainable production levels and exclusive access to certain resources. We prove and demonstrate that by using carefully constructed response functions it is possible to build and calibrate a model that reflects different competitive strategies used in extremely concentrated markets. The response functions approach makes it also possible to take into consideration different barriers to entry. By fitting to the response functions rather than the profit maximization of the payoff functions problem we alter the classical optimization problem to a problem of coupled fixed points, which has the benefit that considering corner optimum, corner equilibria and convexity condition of the payoff function can be skipped.
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