The Contest Game for Crowdsourcing Reviews

We consider a contest game modelling a contest where reviews for $m$ proposals are crowdsourced from $n$ strategic agents} players. Player $i$ has a skill $s_{i\ell}$ for reviewing proposal $\ell$; for her review, she strategically chooses a quality $q \in \{ 1, 2, \ldots, Q \}$ and pays an effort ${\sf f}_{q} \geq 0$, strictly increasing with $q$. For her effort, she is given a strictly positive payment determined by a payment function, which is either player-invariant, like, e.g., the popular proportional allocation function, or player-specific; for a given proposal, payments are proportional to the corresponding efforts and the total payment provided by the contest organizer is 1. The cost incurred to player $i$ for each of her reviews is the difference of a skill-effort function $\Lambda (s_{i},{ \sf f}_{q})$ minus her payment. Skills may vary for arbitrary players and arbitrary proposals. A proposal-indifferent player $i$ has identical skills: $s_{i\ell} = s_{i}$ for all $\ell$; anonymous players means $s_{i} = 1$ for all players $i$. In a pure Nash equilibrium, no player could unilaterally reduce her cost by switching to a different quality. We present algorithmic results for computing pure Nash equilibria.