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.
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References
Margiocco, M., Patrone, F., and Pusillo Chicco, L., A New Approach to Tikhonov Well-Posedness for Nash Equilibria, Optimization, Vol. 40, pp. 385–400, 1997.
Furi, M., and Vignoli, A., About Well-Posed Optimization Problems for Functionals on Metric Spaces, Journal of Optimization Theory and Applications, Vol. 5, pp. 225–229, 1970.
Cavazzuti, E., and Morgan, J., Well-Posed Saddle-Point Problems, Optimization Theory and Algorithms, Edited by J. B. Hiriart-Urruty, W. Oettli, and J. Stoer, Lecture Notes in Pure and Applied Mathematics, M. Dekker, New York, New York, Vol. 86, pp. 61–76, 1983.
Patrone, F., Well-Posed Minimum Problems for Preorders, Rendiconti del Seminario Matematico dell'Università di Padova, Vol. 84, pp. 109–121, 1990.
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Margiocco, M., Patrone, F. & Chicco, L.P. Metric Characterizations of Tikhonov Well-Posedness in Value. Journal of Optimization Theory and Applications 100, 377–387 (1999). https://doi.org/10.1023/A:1021738420722
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DOI: https://doi.org/10.1023/A:1021738420722