Fair and consistent prize allocation in competitions

Given the ranking of competitors, how should the prize endowment be allocated? This paper introduces and axiomatically studies the prize allocation problem. We focus on consistent prize allocation rules satisfying elementary solidarity and fairness principles. In particular, we derive several families of rules satisfying anonymity, order preservation, and endowment monotonicity, which all fall between the equal division rule and the winner-takes-all rule. Our results may help organizers to select the most suitable prize allocation rule for rank-order competitions.