Contest success functions with(out) headstarts

Hao Yu

Papers from arXiv.org

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.

Date: 2025-08, Revised 2026-03
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