English

运筹学学报 ›› 2019, Vol. 23 ›› Issue (4): 59-70.doi: 10.15960/j.cnki.issn.1007-6093.2019.04.005

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带策略约束的区间数双矩阵博弈的双线性规划求解方法

肖燕1, 李登峰2,*   

  1. 1. 福州大学经济与管理学院, 福州 350108;
    2. 电子科技大学经济与管理学院, 成都 611731
  • 收稿日期:2018-08-11 发布日期:2019-09-09
  • 通讯作者: 李登峰 E-mail:lidengfeng@uestc.edu.cn
  • 基金资助:
    国家自然科学基金重点项目（No.71231003）

Bilinear programming method to solve interval bimatrix games with constrained strategy

XIAO Yan1, LI Dengfeng2,*   

  1. 1. School of Economics and Management, Fuzhou University, Fuzhou 350108, China;
    2. School of Management and Economics, University of Electronic Science and Technology of China, Chengdu 611731, China
  • Received:2018-08-11 Published:2019-09-09

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摘要： 传统区间数双矩阵博弈理论研究局中人支付值为区间数的策略选择问题，但没有考虑局中人策略选择可能受到各种约束.创建一种求解局中人策略选择受约束且支付值为区间数的双矩阵博弈（简称带策略约束的区间数双矩阵博弈）的简单、有效的双线性规划求解方法.首先，将局中人的博弈支付看作支付值区间中数值的函数.通过证明这种函数具有单调性，据此利用支付值区间的上、下界，构造了一对辅助双线性规划模型，可分别用于显式地计算任意带策略约束的区间数双矩阵博弈中局中人区间数博弈支付的上、下界及其相应的最优策略.最后，利用考虑策略约束条件下企业和政府针对发展低碳经济策略问题的算例，通过比较其与不考虑策略约束情形下的结果，说明了提出的模型和方法的有效性、优越性及可应用性.

关键词: 非合作博弈, 策略约束, 优化方法, 模糊集, 不确定信息

Abstract: Traditional interval bimatrix game theory is used to study players. strategy selection problems with interval payoff; however, such a theory does not consider players.strategy selection which may be subjected to various constraints. The purpose of this paper is to develop a simple and an effective bilinear programming method to solve the bimatrix game in which players. strategy selection is constrained, and the payoffs are intervals, which is called the interval bimatrix game with constrained strategy. Firstly, the values of players are regarded as functions of the values in the payoff intervals, which are of monotonicity. Therefore, we construct a pair of auxiliary bilinear programming models, which are used to explicitly compute the upper and lower bounds of the interval values of players in any interval bimatrix game by respectively using the lower and upper bounds of the payoff intervals and corresponding optimal strategies. Finally, based on a case of enterprise and government in developing a low-carbon economy in the situation that their strategies are constrained. The effectiveness, advantages, and applicability of the models and methods proposed in this paper are illustrated by comparing these results with those without considering strategic constraints.

Key words: non-cooperative game, strategy constraint, optimization method, fuzzy set, uncertain information

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