Metric Characterizations of Tikhonov Well-Posedness in Value

M. Margiocco, F. Patrone and L. Pusillo Chicco
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M. Margiocco: University of Genova
F. Patrone: University of Genova
L. Pusillo Chicco: University of Genova

Journal of Optimization Theory and Applications, 1999, vol. 100, issue 2, No 8, 377-387

Abstract: 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.

Keywords: Tikhonov well-posedness; Nash equilibria; metric characterizations (search for similar items in EconPapers)
Date: 1999
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DOI: 10.1023/A:1021738420722

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