Necessary and Sufficient Conditions for Pareto Optimality in Infinite Horizon Cooperative Differential Games

In this article we derive necessary and sufficient conditions for the existence of Pareto optimal solutions for an $N$ player cooperative infinite horizon differential game. Firstly, we write the problem of finding Pareto solutions as solving $N$ constrained optimal control subproblems. We derive some weak sufficient conditions which entail one to find all Pareto solutions by solving a weighted sum optimal control problem. Further, we observe that these sufficient conditions are related to transversality conditions of the associated subproblems. We consider games defined by nonautonomous and discounted autonomous systems.