Pareto optimality of stochastic cooperative differential game with general delays in finite horizon

Abstract

The Pareto optimality of stochastic cooperative differential game with a discrete delay, a moving-average delay and a noisy memory process is studied. We establish two sets of equivalent necessary and sufficient conditions for Pareto efficient strategies. The first set comes from reduction to a discrete delayed Pareto optimality, while the second set given by Malliavin derivative is derived by the decomposition of the adjoint equation and the relationship between two Hamiltonian functions. As applications, we use the theoretical results to an indefinite linear quadratic (LQ) Pareto game with general delays.