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Abstract

We consider a tournament game in which each player is rewarded based on her rank in terms of the time of reaching a goal. We prove existence, uniqueness and stability of the game with in finitely many players, existence of an approximate equilibrium with finitely many players, and find an explicit characterization when players are homogeneous. In our setup we find that: (i) the welfare may be increasing in cost of effort; (ii) when the total pie is small, the aggregate effort may be increasing in prize inequality, unlike in Fang et al. (2018); (iii) the welfare may go up with a higher percentage of unskilled workers, as do the completion rates of the skilled and unskilled subpopulations. Our results lend support to
government subsidies for R&D, assuming the profi ts to be made are substantial.