外部性商品的定价模型研究
Pricing Model with Network Externalities
DOI: 10.12677/AAM.2018.72023, PDF,  被引量    国家自然科学基金支持
作者: 徐汇成：浙江师范大学数理与信息工程学院，浙江 金华
关键词: 社会网络；外部性影响；定价模型；NP难；近似比；Social Network； Externality； Pricing Model； NP-Hard； Approximation
摘要: 本文主要研究商品的定价问题，在给定的社会网络图G中，我们希望商家的收益最大化。商品的总价值取决于两个因素：①该商品对于消费者的固有价值；②不断变化的外部性影响。在图G中，商品的固定价值以及外部性影响都是给定的，其中外部影响包括负外部性影响和正外部性影响，在这样的完全信息网络中，我们得出：找到最优的交互式定价策略是NP-难的。在星状网络图中，我们给出了最优的定价方案以及最大收益，并且证明了，通过单一定价能得到近似比为2的定价策略。
Abstract: In a given social network G, we study the problems of iterative pricing a product to consumers. We hope to maximize the revenue for seller. The value of product is determined by two factors: Con-sumer’s intrinsic value and the variable externalities. The consumer’s intrinsic value is fixed and the variable externality is negative or positive. In complete information network, we find that it is NP-hard to find an optimal iterative pricing. This paper gives the optimal strategies and revenues for the star network. We also proved that single pricing works well with 2-approximation for it.
文章引用：徐汇成. 外部性商品的定价模型研究[J]. 应用数学进展, 2018, 7(2): 189-194. https://doi.org/10.12677/AAM.2018.72023

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