Fair and consistent prize allocation in competitions

TL;DR

This paper develops and axiomatizes a range of fair and consistent prize allocation rules for competitions, bridging the gap between equal division and winner-takes-all approaches.

Contribution

It introduces the first axiomatic framework for prize allocation rules in rank-order competitions, ensuring fairness and consistency.

Findings

Characterization of rules satisfying fairness principles

Identification of rules between equal division and winner-takes-all

Development of axiomatic foundations for prize allocation

Abstract

Given the final ranking of a competition, how should the total prize endowment be allocated among the competitors? We study consistent prize allocation rules satisfying elementary solidarity and fairness principles. In particular, we axiomatically characterize 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. Specific characterizations of rules and subfamilies are directly obtained. To our knowledge, this paper is the first that develops and motivates prize allocation rules for rank-order competitions directly from axioms.