Stability in a general oligopoly model
Stability in a general oligopoly model
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DOI：
10.1002/nav.21829
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发表时间：
2019-01
期刊：
影响因子：
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通讯作者：
A. Federgruen;Ming Hu
中科院分区：
文献类型：
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作者：
A. Federgruen;Ming Hu
我们分析了寡头垄断的一般但节俭的价格竞争模型，在该模型中，每个公司提供任意数量的产品。需求量是整个价格向量的一般分段仿射函数，作为仿射函数基集的“正则”扩展而产生。与最常用的需求模型不同，该模型指定了产品类别以及它们的价格和需求量。我们确定了一个单调递增的完全最佳反应算子，当企业动态调整价格时，市场收敛到纳什均衡，作为对竞争对手价格的最佳反应，至少在两个价格区域之一开始时是这样。此外，在价格敏感度矩阵的附加条件下，对于任意起点，可以保证几何快速收敛到共同均衡。
We analyze a general but parsimonious price competition model for an oligopoly in which each firm offers any number of products. The demand volumes are general piecewise affine functions of the full price vector, generated as the “regular” extension of a base set of affine functions. The model specifies a product assortment, along with their prices and demand volumes, in contrast to most commonly used demand models. We identify a fully best response operator which is monotonically increasing so that the market converges to a Nash equilibrium, when firms dynamically adjust their prices, as best responses to their competitors' prices, at least when starting in one of two price regions. Moreover, geometrically fast convergence to a common equilibrium can be guaranteed for an arbitrary starting point, under an additional condition for the price sensitivity matrix.