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Metric Characterizations of Tikhonov Well-Posedness in Value

Author

Listed:
  • M. Margiocco

    (University of Genova)

  • F. Patrone

    (University of Genova)

  • L. Pusillo Chicco

    (University of Genova)

Abstract

In this paper, we discuss and give metric characterizations of Tikhonov well-posedness in value for Nash equilibria. Roughly speaking, Tikhonov well-posedness of a problem means that approximate solutions converge to the true solution when the degree of approximation goes to zero. If we add to the condition of ∈-equilibrium that of ∈-closeness in value to some Nash equilibrium, we obtain Tikhonov well-posedness in value, which we have defined in a previous paper. This generalization of Tikhonov well-posedness has the remarkable property of ordinality; namely, it is preserved under monotonic transformations of the payoffs. We show that a metric characterization of Tikhonov well-posedness in value is not possible unless the set of Nash equilibria is compact and nonempty.

Suggested Citation

  • M. Margiocco & F. Patrone & L. Pusillo Chicco, 1999. "Metric Characterizations of Tikhonov Well-Posedness in Value," Journal of Optimization Theory and Applications, Springer, vol. 100(2), pages 377-387, February.
    • Handle: RePEc:spr:joptap:v:100:y:1999:i:2:d:10.1023_a:1021738420722
    DOI: 10.1023/A:1021738420722
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    Cited by:

    1. J. W. Peng & S. Y. Wu, 2011. "The Well-Posedness for Multiobjective Generalized Games," Journal of Optimization Theory and Applications, Springer, vol. 150(2), pages 416-423, August.
    2. M. Margiocco & F. Patrone & L. Pusillo, 2002. "On the Tikhonov Well-Posedness of Concave Games and Cournot Oligopoly Games," Journal of Optimization Theory and Applications, Springer, vol. 112(2), pages 361-379, February.
    3. Francisco Facchinei & Christian Kanzow, 2010. "Generalized Nash Equilibrium Problems," Annals of Operations Research, Springer, vol. 175(1), pages 177-211, March.
    4. Fang, Ya-Ping & Huang, Nan-Jing & Yao, Jen-Chih, 2010. "Well-posedness by perturbations of mixed variational inequalities in Banach spaces," European Journal of Operational Research, Elsevier, vol. 201(3), pages 682-692, March.

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