Optimal Allocation for Multiple Objects with Costly Verification and Limited Punishments

Description

Consider a principal who have multiple objects to allocate among a finite number of agents. Each agent values receiving an object and has private information regarding the payoff to the principal of selecting him. The principal can verify an agent' private information at a cost and punish the agent who receives an object by destroying a certain fraction of his surplus.There are no monetary transfers. There are several important economic environments roughly corresponding to this model. The head of personnel for an organization may need to choose several applicants from many applicants to fill multiple jobs with predetermined salaries, and each applicant has private information about his/her ability. A development aid agency may need to allocate multiple grants among several local organizations to serve some beneficiary groups, and each local organization privately knows its management ability. A funding agency may have multiple grants to allocate among several researchers, and each researcher privately knows the intellectual merit of his/her project. In many of these situations, monetary transfers are not practical or not used.In these settings, the principal can verify the agents' private information, but the verification process is often costly. The principal can also punish an agent who makes a false statement, but punishment is severely limited. The head of personnel can monitor an employee's performance and fire him after the probationary period, but cannot ask him to pay back the salary or other employment benefits. The development aid agency can evaluate a recipient's management ability by reviewing its expenditure report and disbar it from future grant application, but cannot recover the funds allocated to the organization. The funding agency can first provide support of a project for an initial specified period of time, then review the project and provide additional support only if the accomplishments achieved warrant further support.In this project, I study the design of optimal mechanisms in the environments described above and the properties of optimal mechanisms. Three earlier papers including one of the PI’s have studied this problem when there is a single object. In this project, instead of considering the allocation of a single object, I would consider a more general environment allowing for multiple and heterogeneous objects. These theoretical exercises would help us understand how some important parameters (e.g., verification cost, sustainability/complementarity between different agents) affect the characteristics of optimal mechanisms and provide guidance for the use of different mechanisms in practice.