An ε-equilibrium point in an n-person game with constraints

Abstract

In this paper, an ε-noncooperative equilibrium point with ε ≥0 in a constrained n-person game is investigated. We show that there exists an ε-equilibrium point in the n-person game if and only if some set-valued mapping has a fixed point. Then, using Ekeland’s theorem, we shall discuss conditions under which there exists a fixed point of the extended contraction set-valued mapping.