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Minimax Theory and its Applications 01 (2016), No. 1, 145--161
Copyright Heldermann Verlag 2016

Characterizations of Vector Equilibria Subject to Explicit Constraints

Adela Capata
Dept. of Mathematics, Technical University, Str. Memorandumului 28, 400114 Cluj-Napoca, Romania

Gábor Kassay
Faculty of Mathematics and Computer Science, Babes-Bolyai University, Str. M. Kogalniceanu 1, 400084 Cluj-Napoca, Romania

We investigate weak vector equilibrium problems subject to explicit constraints and provide necessary and sufficient conditions for the existence of their solutions. Two different approaches are used by means of two separation results. As a byproduct, we deduce sufficient conditions for the existence of weak saddle points for generalized Nash two-person noncooperative games, where the payoff function is vector-valued. Our results recover earlier statements from the literature.

Keywords: Equilibrium problems, optimality conditions, separation theorem, cone constraints.

MSC: 49K35, 90C46

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