Well-posedness for Nash equilibria and related topics. (English) Zbl 0849.90131

Patrone, F.

Lucchetti, Roberto (ed.) et al., Recent developments in well-posed variational problems. Dordrecht: Kluwer Academic Publishers. Math. Appl., Dordr. 331, 211-227 (1995).

This survey is in context of non-cooperative games in strategic form, and deals with concepts related with Nash equilibria. Specifically, Tykhonov’s well-posedness is considered for Nash equilibria (which amounts to require existence, uniqueness and also that approximate Nash equilibria converge to the true Nash equilibrium when the degree of approximation goes to zero). Some emphasis is given also to problems arising whenever the attention is concentrated on preferences of the players, instead of their payoffs. The special case of zero-sum games and the problems of Stackelberg equilibria are also briefly discussed.
For the entire collection see [Zbl 0823.00006].

Reviewer: F.Patrone (Genova)

MSC:

91A10	Noncooperative games
91A65	Hierarchical games (including Stackelberg games)

Keywords:

survey; Tykhonov well-posedness; Nash equilibria; Stackelberg equilibria