Cooperative n Player Differential Games

Abstract

In contrast to the theory of cooperative games introduced by John von Neumann, this chapter is devoted to deterministic differential games with n players behaving exclusively cooperatively. Such games can be described as vector optimization problems. After some basic remarks on the cooperation concept we present necessary and sufficient conditions for optimal and weakly optimal controls concerning a system of ordinary differential equations. In the last section we discuss a special cooperative differential game with a linear differential equation in a Hilbert space.