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An Alternating Direction Method for Nash Equilibrium of Two-Person Games with Alternating Offers

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Abstract

In this paper, we propose a method for finding a Nash equilibrium of two-person games with alternating offers. The proposed method is referred to as the inexact proximal alternating direction method. In this method, the idea of alternating direction method simulates alternating offers in the game, while the inexact solutions of subproblems can be matched to the assumptions of incomplete information and bounded individual rationality in practice. The convergence of the proposed method is proved under some suitable conditions. Numerical tests show that the proposed method is competitive to the state-of-the-art algorithms.

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Acknowledgements

This work was supported by the Natural Science Foundation of China (61170308), the Natural Science Foundation of FuJian Province (2011J01008), and FuJian Province Education Department (JA11033). The authors are very grateful to the editor and two anonymous referees for their constructive comments which helped improving the quality of the manuscript greatly.

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Authors and Affiliations

  1. College of Mathematics and Computer Science, Fuzhou University, Fuzhou, 350108, China

    Zheng Peng

  2. Center of Discrete Mathematics and Theoretical Computer Science, Fuzhou University, Fuzhou, 350108, China

    Wenxing Zhu

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  1. Zheng Peng
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  2. Wenxing Zhu
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Correspondence to Zheng Peng.

Additional information

Communicated by Liqun Qi.

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Peng, Z., Zhu, W. An Alternating Direction Method for Nash Equilibrium of Two-Person Games with Alternating Offers. J Optim Theory Appl 157, 533–551 (2013). https://doi.org/10.1007/s10957-012-0165-8

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  • DOI: https://doi.org/10.1007/s10957-012-0165-8

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