Repeated Matching Mechanism Design with Moral Hazard and Adverse Selection

In crowdsourcing systems, the mechanism designer aims to repeatedly match a set of tasks of varying qualities (high quality tasks generate high revenue), which are known to the designer, to a set of agents of varying qualities (high quality agents generate high revenue), which are unknown to the designer and to the agents themselves, such that the overall system performance (e.g. total revenue) is maximized. However, in any realistic system, the designer can only observe the output produced by an agent, which is stochastic, and not the actual quality of the agent. Thus, the designer needs to learn the quality of the agents and solve an adverse selection problem. Moreover, the expected values of agents' outputs depend not only on the qualities of the tasks and the qualities of the agents, but also on the efforts exerted by the agents. This is because agents are strategic and want to optimally balance the rewards and costs of exerting effort. Hence, the designer needs to simultaneously learn about the agents and solve a joint moral hazard and adverse selection problem. In this paper we develop a first mechanism that learns and repeatedly matches agents to tasks in a manner that mitigates both adverse selection and moral hazard. We compute the agents' equilibrium strategies that have a simple bang-bang structure and also enable the agents to learn their qualities. We prove that this mechanism achieves in equilibrium high long-run output by comparing to benchmarks that assume perfect knowledge of the qualities (no adverse selection) and no strategic behavior from the agents (no moral hazard). We also define a new metric of long-run stability for the repeated matching environment and show that our proposed matching is long-run stable.