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非对称不确定策略下合作对偶均衡研究

罗桂美

罗桂美. 非对称不确定策略下合作对偶均衡研究[J]. 华南师范大学学报(自然科学版), 2022, 54(2): 101-107. doi: 10.6054/j.jscnun.2022032
引用本文: 罗桂美. 非对称不确定策略下合作对偶均衡研究[J]. 华南师范大学学报(自然科学版), 2022, 54(2): 101-107. doi: 10.6054/j.jscnun.2022032
LUO Guimei. Research on Cooperative Dual Equilibria with Asymmetric Uncertainty Strategy[J]. Journal of South China normal University (Natural Science Edition), 2022, 54(2): 101-107. doi: 10.6054/j.jscnun.2022032
Citation: LUO Guimei. Research on Cooperative Dual Equilibria with Asymmetric Uncertainty Strategy[J]. Journal of South China normal University (Natural Science Edition), 2022, 54(2): 101-107. doi: 10.6054/j.jscnun.2022032

非对称不确定策略下合作对偶均衡研究

doi: 10.6054/j.jscnun.2022032
基金项目: 

教育部人文社会科学规划基金项目 15YJA790043

详细信息
    通讯作者:

    罗桂美, Email: Luoguimei@gduf.edu.cn

  • 中图分类号: O225; O221.1

Research on Cooperative Dual Equilibria with Asymmetric Uncertainty Strategy

  • 摘要: 从参与者对手利益出发,研究对手成本最低的双人合作博弈问题:当博弈活动出现非理性现象及竞争者自身策略不确定情形时,假设竞争者自身支付矩阵能准确获知,对手策略落在混合策略集内,但自身策略集为一非对称有界闭集(混合策略集的子集),提出了合作对偶博弈模型。并采用鲁棒优化技术,研究了双人合作对偶博弈中均衡的求解问题,得到以下结论:当非对称不确定策略集中元素取l1∩∞- 范数时,使对方成本最低的问题可转化成一个线性规划问题,使双方成本同时最低的问题可转化成一个混合互补问题。最后用数值算例验证了模型的合理性和有效性。
  • 表  1  策略非对称不确定性下的鲁棒合作对偶均衡

    Table  1.   Robust cooperative dual equilibria with asymmetric strategy uncertainty

    Ω ${\mathit{\Upsilon}} $ zr yr yTrAzr yrTBzr
    0.1 0.1 (0, 1, 0) (0, 0.198 7, 0.801 3) 14.807 8 -9.801 3
    0.2 0.2 (0, 1, 0) (0, 0.085 7, 0.914 3) 15.485 8 -9.914 3
    0.3 0.3 (0, 1, 0) (0, 0, 1) 16 -10
    0.5 0.5 (0, 1, 0) (0, 0, 1) 16 -10
    0.8 0.8 (0.033 5, 0.962 1, 0.004 4) (0.005 1, 0.247, 0.747 9) 14.687 1 -9.568 8
    0.9 0.9 (0, 0.733 4, 0.266 6) (0, 0.2, 0.8) 22.051 5 -10.813 1
    1 1 (0, 1, 0) (0, 0, 1) 16 -10
    2 2 (0, 1, 0) (0, 0, 1) 16 -10
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出版历程
  • 收稿日期:  2020-10-14
  • 网络出版日期:  2022-05-12
  • 刊出日期:  2022-04-25

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