Optimal incentive contract in continuous time with different behavior relationships between agents

Dynamic contracts with multiple agents is a classical decentralized decision-making problem with asymmetric information, it is usually discussed according to moral hazard and the behavioral relationship between agents. To do so, in this paper, according to behavior relationships between agents, we analyze continuous time optimal contracting in principal multi-agent moral hazard settings. According to stochastic optimal control theory, the optimal contract of the generalized principal-agent dynamic problem is given, the optimal behavior selection and incentive mechanism of agents are analyzed. The result shows that, in the two-agent model, the incentive effect of cooperative relationship is greater than that of competitive relationship; when they are in a cooperative relationship, with the more influential agent receiving higher pay; under multi-agent model, an increase in the number of agents reduces effort and rewards, this indicates that the team size has strict boundaries. The research conclusions can be applied to solve two kinds of principal-agent problems that the principal needs to motivate the agent to compete or cooperate in the actual social production and life.