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

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  • Zheng Peng

    (Fuzhou University)

  • Wenxing Zhu

    (Fuzhou University)

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.

Suggested Citation

  • Zheng Peng & Wenxing Zhu, 2013. "An Alternating Direction Method for Nash Equilibrium of Two-Person Games with Alternating Offers," Journal of Optimization Theory and Applications, Springer, vol. 157(2), pages 533-551, May.
    • Handle: RePEc:spr:joptap:v:157:y:2013:i:2:d:10.1007_s10957-012-0165-8
    DOI: 10.1007/s10957-012-0165-8
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    References listed on IDEAS

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    1. B. S. He & H. Yang & S. L. Wang, 2000. "Alternating Direction Method with Self-Adaptive Penalty Parameters for Monotone Variational Inequalities," Journal of Optimization Theory and Applications, Springer, vol. 106(2), pages 337-356, August.
    2. Orbay, Hakan, 2009. "Computing Cournot equilibrium through maximization over prices," Economics Letters, Elsevier, vol. 105(1), pages 71-73, October.
    3. Jianzhong Zhang & Biao Qu & Naihua Xiu, 2010. "Some projection-like methods for the generalized Nash equilibria," Computational Optimization and Applications, Springer, vol. 45(1), pages 89-109, January.
    4. Ray, Isha & Williams, Jeffrey, 2002. "Locational asymmetry and the potential for cooperation on a canal," Journal of Development Economics, Elsevier, vol. 67(1), pages 129-155, February.
    5. Diskin, Abraham & Felsenthal, Dan S., 2007. "Individual rationality and bargaining," LSE Research Online Documents on Economics 24233, London School of Economics and Political Science, LSE Library.
    6. Steffan Berridge & Jacek Krawczyk, "undated". "Relaxation Algorithms in Finding Nash Equilibrium," Computing in Economics and Finance 1997 159, Society for Computational Economics.
    7. Francisco Facchinei & Christian Kanzow, 2010. "Generalized Nash Equilibrium Problems," Annals of Operations Research, Springer, vol. 175(1), pages 177-211, March.
    8. Martin J. Osborne & Ariel Rubinstein, 1994. "A Course in Game Theory," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262650401, December.
    9. G. De Marco & J. Morgan, 2008. "Slightly Altruistic Equilibria," Journal of Optimization Theory and Applications, Springer, vol. 137(2), pages 347-362, May.
    10. Von Stengel, Bernhard, 2002. "Computing equilibria for two-person games," Handbook of Game Theory with Economic Applications, in: R.J. Aumann & S. Hart (ed.), Handbook of Game Theory with Economic Applications, edition 1, volume 3, chapter 45, pages 1723-1759, Elsevier.
    11. Sergiu Hart, 1985. "Nonzero-Sum Two-Person Repeated Games with Incomplete Information," Mathematics of Operations Research, INFORMS, vol. 10(1), pages 117-153, February.
    12. Francisco Facchinei & Veronica Piccialli & Marco Sciandrone, 2011. "Decomposition algorithms for generalized potential games," Computational Optimization and Applications, Springer, vol. 50(2), pages 237-262, October.
    13. Abraham Diskin & Dan Felsenthal, 2007. "Individual rationality and bargaining," Public Choice, Springer, vol. 133(1), pages 25-29, October.
    14. Han, Deren & Zhang, Hongchao & Qian, Gang & Xu, Lingling, 2012. "An improved two-step method for solving generalized Nash equilibrium problems," European Journal of Operational Research, Elsevier, vol. 216(3), pages 613-623.
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