A Sufficient Condition for General Decentralized Cooperative Stochastic Differential Games

Abstract

Martingale techniques are applied to derive sufficient decentralized optimality conditions for general stochastic differential games, with multiple Decision Makers (DMs), who aim at optimizing a common pay-off, based on the notion of decentralized Person-by-Person (PbP) optimality. The methodology utilizes the value processes of each one of the DMs of the game, and relates them to solutions of backward stochastic differential equations (SDEs). The sufficient conditions for decentralized PbP optimality are expressed in terms of conditional Hamiltonians, conditioned on the information structures of the DMs. The mathematical models are generalizations of the ones considered in [1], while the decentralized PbP optimality conditions of this paper degenerate to the ones derived in [1] via the stochastic maximum principle.