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**A new approach to Tikhonov well-posedness for Nash equilibria.**
*(English)*
Zbl 0881.90136

Summary: It is suggested a new approach to Tikhonov well-posedness for Nash equilibria. Loosely speaking, Tikhonov well-posedness of a problem means that approximate solutions converge to the true solution when the degree of approximation goes to zero.

The novelty of our approach consists in a suitable definition of what could be considered an approximate solution of a Nash equilibrium problem. We add to the requirement of being an \(\varepsilon\)-equilibrium also that of being \(\varepsilon\) close in value to some Nash equilibrium. In this way, we can get rid of some problems which affect Tikhonov well-posedness when the last condition is not taken into account, like the usual lack of uniqueness for Nash equilibria. Furthermore, it can be proved that this property of well-posedness is preserved under monotonic transformations of the payoffs: a result which is relevant in view of economic interpretation.

The novelty of our approach consists in a suitable definition of what could be considered an approximate solution of a Nash equilibrium problem. We add to the requirement of being an \(\varepsilon\)-equilibrium also that of being \(\varepsilon\) close in value to some Nash equilibrium. In this way, we can get rid of some problems which affect Tikhonov well-posedness when the last condition is not taken into account, like the usual lack of uniqueness for Nash equilibria. Furthermore, it can be proved that this property of well-posedness is preserved under monotonic transformations of the payoffs: a result which is relevant in view of economic interpretation.

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\textit{M. Margiocco} et al., Optimization 40, No. 4, 385--400 (1997; Zbl 0881.90136)

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