  Peer review (e.g., grading assignments in Massive Open Online Courses
(MOOCs), academic paper review) is an effective and scalable method to evaluate
the products (e.g., assignments, papers) of a large number of agents when the
number of dedicated reviewing experts (e.g., teaching assistants, editors) is
limited. Peer review poses two key challenges: 1) identifying the reviewers'
intrinsic capabilities (i.e., adverse selection) and 2) incentivizing the
reviewers to exert high effort (i.e., moral hazard). Some works in mechanism
design address pure adverse selection using one-shot matching rules, and pure
moral hazard was addressed in repeated games with exogenously given and fixed
matching rules. However, in peer review systems exhibiting both adverse
selection and moral hazard, one-shot or exogenous matching rules do not link
agents' current behavior with future matches and future payoffs, and as we
prove, will induce myopic behavior (i.e., exerting the lowest effort) resulting
in the lowest review quality.
  In this paper, we propose for the first time a solution that simultaneously
solves adverse selection and moral hazard. Our solution exploits the repeated
interactions of agents, utilizes ratings to summarize agents' past review
quality, and designs matching rules that endogenously depend on agents'
ratings. Our proposed matching rules are easy to implement and require no
knowledge about agents' private information (e.g., their benefit and cost
functions). Yet, they are effective in guiding the system to an equilibrium
where the agents are incentivized to exert high effort and receive ratings that
precisely reflect their review quality. Using several illustrative examples, we
quantify the significant performance gains obtained by our proposed mechanism
as compared to existing one-shot or exogenous matching rules.
