A New Approach To Tikhonov Well-Posedness For Nash Equilibria^∗

^∗This work has been supported by MURST and CNR (Italy).

Abstract

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 ∊ equilibrium also that of being ∊ 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.

Keywords:

• Approximate Nash Equilibria
• Tikhonov Well-Posedness
• Ordinality in Games

^∗This work has been supported by MURST and CNR (Italy).

^∗This work has been supported by MURST and CNR (Italy).

Notes

^∗This work has been supported by MURST and CNR (Italy).