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On the Existence of Maximum Likelihood Nash Equilibria

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Abstract

Existence results for maximum likelihood Nash equilibria for random games were given by Borm, Cao and García-Jurado, and by Voorneveld. Here we discuss the relationship of those results with ordinary existence results for Nash equilibria, a traditional subject in game theory.

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References

  1. R. Aumann, Markets with a continuum of traders, Econometrica 32 (1964) 39-50.

    Google Scholar 

  2. E.J. Balder, On seminormality of integral functionals and their integrands, SIAM Journal on Control and Optimization 24 (1986) 95-121.

    Google Scholar 

  3. E.J. Balder, Unusual applications of a.e. convergence, in: Almost Everywhere Convergence, eds. G.A. Edgar and L. Sucheston (Academic Press, New York, 1989) pp. 31-53.

    Google Scholar 

  4. E.J. Balder, New sequential compactness results for spaces of scalarly integrable functions, Journal of Mathematical Analysis and Applications 151 (1990) 1-16.

    Google Scholar 

  5. E.J. Balder, Lectures on Young Measures, Cahiers du Centre de Recherche de Mathématiques de la Décision (CEREMADE) 9517 (Université Paris-Dauphine, Paris, 1995).

    Google Scholar 

  6. E.J. Balder, Comments on the existence of equilibrium distributions, Journal of Mathematical Economics 25 (1996) 307-323.

    Google Scholar 

  7. E.J. Balder, On the existence of optimal contract mechanisms for incomplete information principalagent models, Journal of Economic Theory 68 (1996) 133-148.

    Google Scholar 

  8. E.J. Balder, On the existence of Cournot-Nash equilibria in continuum games, Journal of Mathematical Economics 32 (1999) 207-223. 70 BALDER

    Google Scholar 

  9. E.J. Balder, A unifying pair of Cournot-Nash equilibrium results, Journal of Economic Theory 102 (2002) 437-470.

    Google Scholar 

  10. E.J. Balder,More on maximum likelihood equilibria for games with random payoffs and participation, Preprint No. 1169, Mathematical Institute, University of Utrecht (November 2000), forthcoming.

  11. E.J. Balder and C. Hess, Two generalizations of Komlós' theorem with lower closure-type applications, Journal of Convex Analysis 3 (1996) 25-44.

    Google Scholar 

  12. D.P. Bertsekas and S.E. Shreve, Stochastic Optimal Control: The Discrete Time Case (Academic Press, New York, 1978).

    Google Scholar 

  13. P.E.M. Borm, R. Cao and I. García-Jurado, Maximum likelihood equilibria of random games, Optimization 35 (1995) 77-84.

    Google Scholar 

  14. C. Castaing and M. Valadier, Convex Analysis and Measurable Multifunctions, Lecture Notes in Mathematics, Vol. 580 (Springer, Berlin, 1977).

    Google Scholar 

  15. C. Dellacherie and P.-A. Meyer, Probabilités et Potentiel (Hermann, Paris, 1975) (English translation: North-Holland, Amsterdam, 1978).

    Google Scholar 

  16. R.M. Dudley, Real Analysis and Probability (Wadsworth, Pacific Grove, CA, 1989).

    Google Scholar 

  17. W. Hildenbrand, Core and Equilibria of a Large Economy (Princeton University Press, Princeton, 1974).

    Google Scholar 

  18. J. Komlós, A generalization of a problem of Steinhaus, Acta Mathematica Hungarica 18 (1967) 217-229.

    Google Scholar 

  19. P.A. Meyer, Limites médiales, d'après Mokobodzki, in: Séminaire de Probabilités VII, Lecture Notes in Mathematics, Vol. 321 (Springer, 1973) pp. 198-204.

  20. D. Schmeidler, Equilibrium points of non-atomic games, Journal of Statistical Physics 7 (1973) 295-300.

    Google Scholar 

  21. L. Schwartz, Radon Measures (Oxford University Press, London, 1973).

    Google Scholar 

  22. M. Voorneveld, Potential games and interactive decisions with multiple criteria, Dissertation Series No. 61, Center for Economic Research, Tilburg University (1999).

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Balder, E.J. On the Existence of Maximum Likelihood Nash Equilibria. Annals of Operations Research 114, 57–70 (2002). https://doi.org/10.1023/A:1021049800653

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