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On the computation of stable sets for bimatrix games

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  • Vermeulen, Dries
  • Jansen, Mathijs

Abstract

In this paper it is shown how to compute stable sets, defined by Mertens (1989), inthe context of bimatrix games only using linear optimization techniques.
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Suggested Citation

  • Vermeulen, Dries & Jansen, Mathijs, 2005. "On the computation of stable sets for bimatrix games," Journal of Mathematical Economics, Elsevier, vol. 41(6), pages 735-763, September.
  • Handle: RePEc:eee:mateco:v:41:y:2005:i:6:p:735-763
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    References listed on IDEAS

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    1. Wilson, Robert, 1992. "Computing Simply Stable Equilibria," Econometrica, Econometric Society, vol. 60(5), pages 1039-1070, September.
    2. Srihari Govindan & Robert Wilson, 2002. "Maximal stable sets of two-player games," International Journal of Game Theory, Springer;Game Theory Society, vol. 30(4), pages 557-566.
    3. John Hillas & Dries Vermeulen & Mathijs Jansen, 1996. "On the Finiteness of Stable Sets," Game Theory and Information 9605003, EconWPA, revised 15 Jun 1996.
    4. Blume, Lawrence E & Zame, William R, 1994. "The Algebraic Geometry of Perfect and Sequential Equilibrium," Econometrica, Econometric Society, vol. 62(4), pages 783-794, July.
    5. Talman, A.J.J. & van den Elzen, A.H., 1991. "A procedure for finding Nash equilibria in bi-matrix games," Other publications TiSEM 14df3398-1521-43ad-8803-a, Tilburg University, School of Economics and Management.
    6. Jansen M. J. M. & Jurg A. P. & Borm P. E. M., 1994. "On Strictly Perfect Sets," Games and Economic Behavior, Elsevier, vol. 6(3), pages 400-415, May.
    7. Vermeulen, Dries & Jansen, Mathijs, 2005. "On the computation of stable sets for bimatrix games," Journal of Mathematical Economics, Elsevier, vol. 41(6), pages 735-763, September.
    8. Mathijs Jansen & Dries Vermeulen, 2001. "On the computation of stable sets and strictly perfect equilibria," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 17(2), pages 325-344.
    9. Hillas, John, 1990. "On the Definition of the Strategic Stability of Equilibria," Econometrica, Econometric Society, vol. 58(6), pages 1365-1390, November.
    10. Vermeulen, A. J. & Jansen, M. J. M., 2000. "Ordinality of solutions of noncooperative games," Journal of Mathematical Economics, Elsevier, vol. 33(1), pages 13-34, February.
    11. Talman, A.J.J. & Yang, Z., 1994. "A simplicial algorithm for computing proper Nash equilibria of finite games," Discussion Paper 1994-18, Tilburg University, Center for Economic Research.
    12. Kohlberg, Elon & Mertens, Jean-Francois, 1986. "On the Strategic Stability of Equilibria," Econometrica, Econometric Society, vol. 54(5), pages 1003-1037, September.
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    Cited by:

    1. Balkenborg, Dieter & Vermeulen, Dries, 2014. "Universality of Nash components," Games and Economic Behavior, Elsevier, vol. 86(C), pages 67-76.
    2. Vermeulen, Dries & Jansen, Mathijs, 2005. "On the computation of stable sets for bimatrix games," Journal of Mathematical Economics, Elsevier, vol. 41(6), pages 735-763, September.

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