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Distribution-Free Equilibrium in Search Contests

Murat Erkurt, Emre Ozdenoren

Abstract

We study contests in which players sequentially search for a high score at a cost per draw, with unlimited opportunities, no recall, and the best score wins a prize. In the unique symmetric equilibrium, the acceptance probability depends only on the number of players, the cost, and the prize, not on the distribution, and total expenditure equals the prize. These properties extend to multiple prizes and hierarchical team competition. Efficiency relative to a planner is determined by the hazard rate of the distribution. With a finite horizon, a selectivity effect can dominate the discouragement effect when search costs are low.

Distribution-Free Equilibrium in Search Contests

Abstract

We study contests in which players sequentially search for a high score at a cost per draw, with unlimited opportunities, no recall, and the best score wins a prize. In the unique symmetric equilibrium, the acceptance probability depends only on the number of players, the cost, and the prize, not on the distribution, and total expenditure equals the prize. These properties extend to multiple prizes and hierarchical team competition. Efficiency relative to a planner is determined by the hazard rate of the distribution. With a finite horizon, a selectivity effect can dominate the discouragement effect when search costs are low.
Paper Structure (20 sections, 9 theorems, 27 equations)

This paper contains 20 sections, 9 theorems, 27 equations.

Table of Contents

  1. Introduction
  2. Model
  3. Equilibrium
  4. Derivation
  5. Uniqueness
  6. Distribution-Free Property
  7. Comparative Statics
  8. Multiple Prizes
  9. Finite Horizon
  10. The Two-Draw Contest
  11. Selectivity versus Discouragement
  12. Illustration
  13. Hierarchical Competition
  14. Welfare
  15. The Planner's Problem
  16. ...and 5 more sections

Key Result

Proposition 1

Assume $Nc<W$.

Theorems & Definitions (18)

  • Proposition 1
  • proof
  • Remark 1: Asymmetric equilibria for $N\geq 3$
  • Proposition 2
  • Corollary 1
  • Remark 2: Boundary cases
  • Proposition 3
  • proof
  • Remark 3: Special cases
  • Proposition 4
  • ...and 8 more