PRIZE ALLOCATION IN TUG-OF-WAR WITH FINITE ROUNDS OF PLAY

Abstract

In this paper we analyze the effort-maximizing prize structure for a tug-of-war contest with five states and at most three rounds of competition. The contest consists of a sequence of one shot competition in which the stage-winner is determined by a Tullock contest success function. The contest organizer selects a prize structure to maximize the aggregate effort exerted in the contest and faces a unit budget constraint. The optimal prize structure is characterized and it depends on the discriminatory parameter r, which captures the degree of luck in each round. The magnitude of the parameter affects the size of the momentum effect in the second round and thus imposes an essential impact on the optimal prize design problem. Our results suggest that when r is small, the momentum effect in the contest is small and the winner-take-all is the optimal prize scheme. When r is at an intermediate level, the momentum effect becomes significant and intermediate prizes are desirable. Our results confirm the intuition that momentum effect affects the equilibrium effort input in dynamic contests in an essential way and it should be addressed properly in order to elicit the highest aggregate effort.