An N-person non-cooperative discounted vector-valued dynamic game with a metric space (Q1095817)

An N-person non-cooperative discounted vector-valued game with a metric space is investigated. We define a D-convex equilibrium point and prove that a D-convex equilibrium point exists in this game system. A modified version of the original game system is formulated so that an equilibrium point of the modified version is a D-convex equilibrium point of the original game system. Under appropriate conditions, the converse holds in the sense that a D-convex equilibrium point is also an equilibrium point of the modified game system.