The incentive effect of coarsening the competition structure in a tournament

The incentive effect of coarsening the competition structure in a tournament is studied. By coarsening the competition structure, we mean that coarser performance measure is used while finer information is available. Examples include letter grades or grade classes when finer numeric grades are available. Coarsening the competition structure has two countervailing incentive effects. While it reduces the likelihood that marginal effort changes the result, the reward change will be bigger once the result is changed. We provide a sufficient condition on the performance distribution for the reduction of work incentive by coarsening; log-concavity of the density.