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Bayesian equilibria for uncertain bimatrix game with asymmetric information

Author

Listed:
  • Xiangfeng Yang

    (Renmin University of China
    Tsinghua University)

  • Jinwu Gao

    (Renmin University of China)

Abstract

In an uncertain bimatrix game, there are two solution concepts of $$(\alpha ,\beta )$$ ( α , β ) -optimistic equilibrium strategy and $$(u,v)$$ ( u , v ) -maximum chance equilibrium strategy. This paper goes further by assuming that the confidence levels $$\alpha , \beta $$ α , β and payoff levels $$u, v$$ u , v are private information. Then, the so-called uncertain bimatrix game with asymmetric information is investigated. Two solution concepts of Bayesian optimistic equilibrium strategy and Bayesian maximum chance equilibrium strategy as well as their existence theorems are presented. Moreover, sufficient and necessary conditions are given for finding the Bayesian equilibrium strategies. Finally, a two-firm advertising problem is analyzed for illustrating our modelling idea.

Suggested Citation

  • Xiangfeng Yang & Jinwu Gao, 2017. "Bayesian equilibria for uncertain bimatrix game with asymmetric information," Journal of Intelligent Manufacturing, Springer, vol. 28(3), pages 515-525, March.
    • Handle: RePEc:spr:joinma:v:28:y:2017:i:3:d:10.1007_s10845-014-1010-8
    DOI: 10.1007/s10845-014-1010-8
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    References listed on IDEAS

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    2. John C. Harsanyi, 1967. "Games with Incomplete Information Played by "Bayesian" Players, I-III Part I. The Basic Model," Management Science, INFORMS, vol. 14(3), pages 159-182, November.
    3. R. G. Cassidy & C. A. Field & M. J. L. Kirby, 1972. "Solution of a Satisficing Model for Random Payoff Games," Management Science, INFORMS, vol. 19(3), pages 266-271, November.
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    Cited by:

    1. Boyang Dai & Xiangfeng Yang & Xiaoyue Liu, 2022. "Shapley Value of Uncertain Coalitional Game based on Hurwicz Criterion with Application to Water Resource Allocation," Group Decision and Negotiation, Springer, vol. 31(1), pages 241-260, February.

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