Multi-player, Multi-prize, Imperfectly Discriminating Contests

This paper models success probability in imperfectly discriminating contests involving multiple players and multiple prizes. This turns out to be a generalization of Tullock's contest success function to a multiplayer, multi-prize situation. The model can be used to analyse e orts 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 e orts exerted, and analyse those e orts, the associated total costs and total dissipation, and also pricing and the optimal number of 'seats'. We also discuss extensions of the model.