| In the production mode of modern enterprises,multi-agent(team)coproduction is commonly used as a mode of production,so the efficiency of multi-agent has naturally become the focus of attention.How to effectively motivate agents to reduce ”free redder” behavior or to contribute more to the team has likewise become a major problem for the principal.For this,many scholars have conducted a large number of studies,or based on the classical assumption of complete rationality or the assumption of incomplete rationality in behavioral economics,have obtained some meaningful and guiding conclusions.However,most of the studies are performed within a single-period or discrete-time framework.Obviously,the production process or investment process is more reasonable in a continuous time frame,and in real life,if the principal provides a continuous payment contract,it also needs to be analyzed in a continuous time.In this thesis,the optimal incentive contract problem of multi-agent is studied under the continuous time frame.We assume that a principal employs multiple agents to jointly manage multiple production projects(or manage multiple venture capital projects),and assume that the principal and all agents are risk averse.We analyzed the optimal incentive problems of multiple agents under different information structures.Specifically,this thesis mainly studies the following aspects:Firstly,under full information,we transform the multi-agent problem into a risk-sharing problem,and get the explicit form of the agents’ optimal contract.According to our analysis,at the optimal effort value of the agent,the expected output is equal to the marginal substitution rate of the agent’s salary and effort.If we assume that the principal is risk neutral and the agents are risk averse,the optimal result is that the agents get a contract that is independent of the final output.On the contrary,if the principal is risk averse and the agents are risk neutral,the principal get a fixed income.In both cases,the conclusion of multi-agent contract is the same as that of single agent contract problem.Secondly,in the case of moral hazard,we assume that agents are not completely rational.Specifically,we assume that the agents will compare wages with each other,which can bring a gain-loss utility to agents.Therefore,in this problem,the agents’ utility function is divided into two parts,one is the traditional material utility function(the utility of wages and effort costs),and the other is the behavior utility function(the utility of the wage gap).Under this utility function,we analyze how the principal designs an incentive mechanism when the agents have loss aversion,and how the principal’s utility will be affected when agents compare their salary.Under some reasonable assumptions,we get the explicit solution of optimal incentive contract and optimal effort,and illustrate the influence of agents’ loss aversion on incentive mechanism by numerical simulation.Thirdly,in the moral hazard problem,we prove that the agents’ optimal efforts are Nash equilibrium efforts.However,in some special cases(such as when the principal is risk-neutral),there may be a ”prisoner’s dilemma” between the agents(the Nash equilibrium may not be optimal).Therefore,we analyze the Pareto optimal effort between agents in the moral hazard problem.Our research shows that when agents cooperate,the agents choose Pareto optimal effort is the agents’ optimal choice.Further,we analyzed that the expected utility of the agents and the principal can be improved when the agents collaborate.On this basis,we assume that the principal hires an agent as the planner to manage the total utility of the agents.Fifthly,under full information and moral hazard,we analyze a principalagent problem with inconsistent time preferences.In this problem,we prove the necessary and sufficient conditions for the existence of equilibrium incentive contracts.To be specific,first we assume that the utility function of the principal is linearly additive and the agents are independent of each other,so we can translate the multi-agent problem into the incentive problem of the principal facing one agent.Then,by establishing an extended HJB equation and subgame perfect Nash equilibrium strategy,we obtain the optimal incentive contract provided by the principal and the optimal effort provided by the agent under full information and moral hazard.Finally,in the adverse selection problem,we assume that both agents have different types,the types of agents only know by themselves,and the principal and colleagues only know the prior distribution of the types of agents.Under this assumption,we obtain the conditions satisfied by the optimal incentive contract and the optimal effort.Furthermore,in the case of moral hazard and adverse selection,we studied the multi-agent’s incentive problem.We obtained that,depending on the proportion of agent types in the labor market,the principal can choose to provide different types of optimal incentive contracts.The mode in this thesis is a generalization of the continuous time single agent principal-agent model.The research conclusions not only provide meaningful reference and guidance for the design of the optimal incentive mechanism in the labor market,but also have certain reference value for the further research and application of principal-agent theory. |
