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Nash refinement of equilibria


A method for choosing equilibria in strategic form games is proposed and axiomatically characterized. The method as well as the axioms are inspired by the Nash bargaining theory. The method can be applied to existing refinements of Nash equilibrium (e.g., perfect equilibrium) and also to other equilibrium concepts, like correlated equilibrium.

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  1. 1.

    Nash, J. F.,Noncooperative Games, Annals of Mathematics, Vol. 54, pp. 286–295, 1951.

  2. 2.

    Van Damme, E. E. C.,Stability and Perfection of Nash Equilibria, Springer Verlag, Berlin, Germany, 1987.

  3. 3.

    Harsanyi, J. C., andSelten, R.,A Generalized Nash Solution for Two-Person Bargaining Games with Incomplete Information, Management Science, Vol. 18, pp. 80–106, 1972.

  4. 4.

    Guth, W., andKalkofen, B.,Unique Solutions for Strategic Games: Equilibrium Selection Based on Resistance Avoidance, Springer Verlag, Berlin, Germany, 1989.

  5. 5.

    Aumann, R. J.,Subjectivity and Correlation in Randomized Strategies, Journal of Mathematical Economics, Vol. 1, pp. 67–96, 1974.

  6. 6.

    Aumann, R. J.,Correlated Equilibrium as an Expression of Bayesian Rationality Econometrica, Vol. 55, pp. 1–18, 1987.

  7. 7.

    Selten, R.,Reexamination of the Perfectness Concept for Equilibrium Points in Extensive Games, International Journal of Game Theory, Vol. 4, pp. 25–55, 1975.

  8. 8.

    Myerson, R. B.,Refinements of the Nash Equilibrium Concept, International Journal of Game Theory, Vol. 7, pp. 73–80, 1978.

  9. 9.

    Kalai, E., andSamet, D.,Persistent Equilibria in Strategic Games, International Journal of Game Theory, Vol. 13, pp. 129–144, 1984.

  10. 10.

    Peters, H., andVrieze, K.,Nash Equilibria, Report M91-02, University of Limburg, 1991.

  11. 11.

    Nash, J. F.,The Bargaining Problem, Econometrica, Vol. 18, pp. 155–162, 1950.

  12. 12.

    Harsanyi, J. C., andSelten, R.,A General Theory of Equilibrium Selection in Games, MIT Press, Cambridge, Massachusetts, 1988.

  13. 13.

    Tedeschi, P.,Bargained-Correlated Equilibria, Instituto di Economia Politica, Università Commerciale Luigi Bocconi, Milano, Italy, 1990.

  14. 14.

    Aumann, R. J.,An Axiomatization of the Nontransferable Utility Value, Econometrica, Vol. 53, pp. 599–612, 1985.

  15. 15.

    Griesmer, J. H., Hofmann, A. J., andRobinson, A.,On Symmetric Bimatrix Games, Research Paper RC-959, IBM Watson Research Center, Yorktown Heights, New York, 1963.

  16. 16.

    Jansen, M. J. M., Potters, J. A. M., andTijs, S. H.,Symmetrizations of Two-Person Games, Methods of Operations Research, Vol. 54, pp. 385–402, 1986.

  17. 17.

    Heuer, G. A., andMillham, C. B.,On Nash Subsets and Mobility Chains in Bimatrix Games, Naval Research Logistics Quarterly, Vol. 23, pp. 311–319, 1976.

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The authors thank the reviewers for their comments, which led to an improvement of the paper.

Communicated by G. P. Papavassilopoulos

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Peters, H., Vrieze, K. Nash refinement of equilibria. J Optim Theory Appl 83, 355–373 (1994).

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Key Words

  • Noncooperative games
  • Nash equilibrium
  • Nash bargaining solution
  • refinements