Extractive contest design

TL;DR

This paper analyzes contest success functions (CSFs) that extract contestants' prize values across different information settings, identifying conditions for their existence and providing explicit examples where possible.

Contribution

It characterizes the existence of extractive CSFs in various value settings and explicitly constructs such functions when they exist.

Findings

Extractive CSFs exist in common-value cases in equilibrium.

In observable-private-value cases, extractive CSFs exist in some equilibria; always if three or more contestants or homogeneous values.

No extractive CSFs exist in unobservable-private-value cases.

Abstract

We consider contest success functions (CSFs) that extract contestants' prize values. In the common-value case, there exists a CSF extractive in any equilibrium. In the observable-private-value case, there exists a CSF extractive in some equilibrium; there exists a CSF extractive in any equilibrium if and only if the number of contestants is greater than or equal to three or the values are homogeneous. In the unobservable-private-value case, there exists no CSF extractive in some equilibrium. When extractive CSFs exist, we explicitly present one of them.