Contest success functions with(out) headstarts

TL;DR

This paper axiomatizes contest success functions with headstarts, extending classic models and exploring fairness, dummy consistency, and the impact of inactive contestants on allocation rules.

Contribution

It introduces new axioms and extends existing models to incorporate headstarts and draws in contest success functions.

Findings

Axiomatization of CSFs with headstarts

Connection to CSFs allowing draws

Introduction of dummy consistency

Abstract

Contest success function (CSF) maps contestants' efforts to their winning probability. This paper provides axiomatizations of CSFs with headstarts. The results extend the classic axiomatization of the Tullock CSF and connect to CSFs that allow for draws. The central axiom is relative homogeneity of counterfactual deviation, which requires the pairwise influence of one contestant's effort on opponent's probabilistic allocation to be scale-invariant. Two fairness axioms and no advantageous reallocation further restrict the admissible functional forms with headstarts. We also introduce dummy consistency, requiring allocations to be consistent with and without inactive contestants, to clarify the relationship with earlier axiomatic work that rules out headstarts. Finally, we discuss an extension that drops the assumption of full allocation.