李沛瑜,林贵华.求解一类广义Nash均衡问题[J].数学研究及应用,2013,33(3):372~378
求解一类广义Nash均衡问题
Solving a Class of Generalized Nash Equilibrium Problems
投稿时间:2012-03-11  最后修改时间:2013-04-12
DOI:10.3770/j.issn:2095-2651.2013.03.013
中文关键词:  广义纳什均衡问题  正则均衡  正则稳定性  可分离性
英文关键词:generalized Nash equilibrium problem  normalized equilibrium  normalized stationarity  separability.
基金项目:国家自然科学基金 (Grant No.11071028).
作者单位
李沛瑜 大连理工大学数学科学学院, 辽宁 大连 116024 
林贵华 上海大学管理学院, 上海 200444 
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中文摘要:
      广义纳什均衡问题(GNEP)是具有重要应用背景的一类问题.然而, GNEP通常多解,有时甚至存在无穷多均衡解,如何选择合适的均衡解并非易事.本文研究一类具有分离结构的GNEP.我们首先将正则均衡解推广至稳定点的情形,然后提出一种将GNEP转化为单一优化问题的求解途径,并进一步讨论了其在相似产品市场中的应用.
英文摘要:
      Generalized Nash equilibrium problem (GNEP) is an important model that has many applications in practice. However, a GNEP usually has multiple or even infinitely many Nash equilibrium points and it is not easy to choose a favorable solution from those equilibria. This paper considers a class of GNEP with some kind of separability. We first extend the so-called normalized equilibrium concept to the stationarity sense and then, we propose an approach to solve the normalized stationary points by reformulating the GNEP as a single optimization problem. We further demonstrate the proposed approach on a GNEP model in similar product markets.
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