Multi-player, Multi-prize, Imperfectly Discriminating Contests

Abstract

This paper models success probability in imperfectly discriminating contests involving multiple players and multiple prizes. This, in fact, turns out to be a generalization of Tullock’s contest success function to a multi-player, multiple prizes. The model can be used to analyze efforts exerted by individuals in various real-life situations, like obtaining seats in congested public transportation vehicles or obtaining admission into elite educational institutes. We propose a “holistic” probability model, derive the equilibrium efforts exerted, and analyze those efforts, the associated total costs and total dissipation, and explore pricing and number of ‘seats’. The derivation provides a new rational for the multinomial Logit Model. It also derives formula for rent dissipation. We also discuss two extensions of the model.