Metric Characterizations of Tikhonov Well-Posedness in Value |
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Authors: | Margiocco M Patrone F Chicco L Pusillo |
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Institution: | (1) Department of Mathematics, University of Genova, Genova, Italy;(2) Department of Mathematics, University of Genova, Genova, Italy |
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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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Keywords: | Tikhonov well-posedness Nash equilibria metric characterizations |
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