Mediated Contests and Strategic Foundations for Contest Success Functions

This paper examines the foundations of arbitrary contest success functions (CSFs) in two distinct types of contests – unmediated and mediated contests. In an unmediated contest, CSFs arise as the (interim) players’ equilibrium beliefs of a two-stage game – the gun-butter game – in which players choose an activity (appropriative vs. productive) in the first stage, and apply effort to their activity in the second stage. In this view a CSF is rationalizable if a contest is induced on the equilibrium path of the gun-butter game. In the second approach, a CSF is the result of the optimal design of an administrator. Here, the designer seeks to maximize his utility by implementing a probability distribution on the set of contestants. However, he is curbed by a disutility term which represents the underlying institutional constraints or the designer’s preferences. Both approaches provide foundations for arbitrary CSFs with no restrictions on the number of contestants.