Nash-type equilibrium theorems and competitive Nash-type equilibrium theorems. (English) Zbl 1103.91308

Summary: We consider two types of equilibrium problems. We study the constrained Nash-type equilibrium problems with multivalued payoff functions. We also study the competitive Nash-type equilibrium problems with multivalued payoff functions. In these two equilibrium problems, we want to find a strategy combination such that each player wishes to find a minimal loss from his multivalued payoff function. We use a fixed-point theorem of Park to prove the existence results of these two types of equilibrium problems.


91A10 Noncooperative games
91A44 Games involving topology, set theory, or logic
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