  Dynamic contracts with multiple agents is a classical decentralized
decision-making problem with asymmetric information. In this paper, we extend
the single-agent dynamic incentive contract model in continuous-time to a
multi-agent scheme in finite horizon and allow the terminal reward to be
dependent on the history of actions and incentives. We first derive a set of
sufficient conditions for the existence of optimal contracts in the most
general setting and conditions under which they form a Nash equilibrium. Then
we show that the principal's problem can be converted to solving
Hamilton-Jacobi-Bellman (HJB) equation requiring a static Nash equilibrium.
Finally, we provide a framework to solve this problem by solving partial
differential equations (PDE) derived from backward stochastic differential
equations (BSDE).
