Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Contest success functions with(out) headstarts

Hao Yu

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.

Contest success functions with(out) headstarts

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.

Paper Structure

This paper contains 23 sections, 16 theorems, 84 equations.

Table of Contents

  1. Introduction
  2. Axiomatization
  3. Standard axioms
  4. Relative homogeneity of counterfactual deviation
  5. Axiom comparison
  6. The main theorem
  7. More specifications with headstarts
  8. Two fairness axioms
  9. No advantageous reallocation
  10. Dummy consistency and non-headstart specifications
  11. A generalized model allowing partial allocation
  12. Concluding remarks
  13. Proofs
  14. Proof of Theorem \ref{['thm:main']}
  15. Three lemmata
  16. ...and 8 more sections

Key Result

Lemma 1

SM and LCA hold if and only if for all $i\in M\subseteq N$, for some strictly increasing function $f_j(x_j)\geq 0$ for all $j\in N$.

Theorems & Definitions (22)

  • Definition 1
  • Lemma 1
  • Theorem 1
  • proof : Sketch of proof
  • Corollary 1
  • Theorem 2
  • Corollary 2
  • Theorem 3
  • Lemma 2: clark1998
  • Proposition 1
  • ...and 12 more