Decentralized sufficient & necessary optimality conditions for cooperative stochastic differential decision problems

In this paper we derive necessary and sufficient Person by Person and Global (team) decentralized optimality conditions, for stochastic differential decision problems with multiple Decision Makers (DMs) or Agents aimed at optimizing a common pay-off. These consist of forward and backward stochastic differential equations, and a set of conditional variational Hamiltonians with respect to the information structures of the DMs.