Optimal Common Contract with Heterogeneous Agents

Abstract

We consider the principal-agent problem with heterogeneous agents. Previous works assume that the principal signs independent incentive contracts with every agent to make them invest more efforts on the tasks. However, in many circumstances, these contracts need to be identical for the sake of fairness. We investigate the optimal common contract problem. To our knowledge, this is the first attempt to consider this natural and important generalization. We first show this problem is NP-complete. Then we provide a dynamic programming algorithm to compute the optimal contract in O(n 2 m) time, where n, m are the number of agents and actions, under the assumption that the agents' cost functions obey increasing difference property. At last, we generalize the setting such that each agent can choose to directly produce a reward in [0, 1]. We provide an O(log n)-approximate algorithm for this generalization.

Contracts under Moral Hazard and Adverse Selection

“…Another such line of work studies the problem of learning optimal contracts in a repeated setting Ho et al [2016]. In Xiao et al [2019], the authors prove computational results for agents with multiple types (analogous to the results we show in Section B) but for the restricted setting where the principal can contract directly on the agents' actions (we additionally show an APX-hardness result over the NP-hardness result in their paper).…”