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The von Neumann–Morgenstern stable sets for the mixed extension of 2×2 games

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Listed:
  • Inarra, E.
  • Larrea, C.
  • Saracho, A.

Abstract

This paper studies the von Neumann–Morgenstern (vNM) stable sets for the mixed extension of 2×2 games when only single profitable deviations are allowed. We show that games with a strict Nash equilibrium have infinite vNM stable sets, and games without a strict Nash equilibrium have just a unique vNM stable set. A characterization of the strategy profiles that belong to the vNM stable sets is provided. We also show that in games without a strict Nash equilibrium the vNM stable set always contains a Pareto optimal strategy profile.

Suggested Citation

  • Inarra, E. & Larrea, C. & Saracho, A., 2014. "The von Neumann–Morgenstern stable sets for the mixed extension of 2×2 games," Economics Letters, Elsevier, vol. 125(1), pages 70-73.
    • Handle: RePEc:eee:ecolet:v:125:y:2014:i:1:p:70-73
    DOI: 10.1016/j.econlet.2014.07.025
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    References listed on IDEAS

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    1. Fabrizio Germano, 2006. "On some geometry and equivalence classes of normal form games," International Journal of Game Theory, Springer;Game Theory Society, vol. 34(4), pages 561-581, November.
    2. Xiao Luo, 2009. "On the foundation of stability," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 40(2), pages 185-201, August.
    3. Noritsugu Nakanishi, 2001. "On the existence and efficiency of the von Neumann-Morgenstern stable set in a n-player prisoners' dilemma," International Journal of Game Theory, Springer;Game Theory Society, vol. 30(2), pages 291-307.
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    Cited by:

    1. Bloch, Francis & van den Nouweland, Anne, 2021. "Myopic and farsighted stable sets in 2-player strategic-form games," Games and Economic Behavior, Elsevier, vol. 130(C), pages 663-683.

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    More about this item

    Keywords

    Non-cooperative games; von Neumann and Morgenstern stable sets; Nash equilibrium;
    All these keywords.

    JEL classification:

    • C7 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory

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