Incomplete Information in Rent-seeking Contests

Abstract

We consider a variant of the Tullock lottery contest. Each player’s constant marginal cost of effort is drawn from a potentially different continuous distribution. In order to study the impact of incomplete information we compare three informational settings to each other: players are either completely informed, privately informed about their own costs, or ignorant of all cost realizations. For the first and the third setting we determine the unique pure-strategy Nash equilibrium. Under private information we prove existence of a pure-strategy Bayesian Nash equilibrium and identify a sufficient condition for uniqueness. Assuming that unit cost distributions all have the same mean, we show that under ignorance of all cost realizations ex ante expected aggregate effort is lower than under both private and complete information. Ex ante expected rent dissipation, however, is higher than in the latter settings if we focus on the standard lottery contest and assume costs are all drawn from the same distribution. Between complete and private information there is neither a general ranking in terms of effort nor in terms of rent dissipation.

Keywords: Rent-seeking, Contest, Incomplete Information, Private values

JEL Classification: D72, D74, D82, C72