Distribution-Free Equilibrium in Search Contests

2026-03-21

AI Summary

This study investigates strategic behavior in sequential search contests where participants incur a cost per draw, draws are memoryless and unlimited in number, and the highest score wins. Using game-theoretic and sequential search models, the paper establishes the existence of a unique symmetric equilibrium whose acceptance threshold depends solely on the number of contestants, the search cost, and the prize—remarkably independent of the underlying score distribution. The key contribution lies in demonstrating this distribution-free property of equilibrium strategies and showing that total expected expenditure exactly equals the prize value. The analysis extends these insights to settings with multiple prizes and hierarchical team competitions. Furthermore, equilibrium efficiency is shown to be governed by the hazard rate of the score distribution, and under finite horizons, the selective effect can dominate the discouragement effect when search costs are sufficiently low.

Technology Category

• Game Theory and Economic Paradigms: Equilibrium
• Search and Optimization: Learning to Search
• Multiagent Systems: Mechanism Design

Application Category

• Economics, Online Markets and Human Computation: Uses of LLMs and GenAI for marketplace design, bidding, and strategic interactions
• Search and Retrieval-Augmented AI: Efficiency and scalability of Web search engines
• Security and Privacy: Large-scale security measurements

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.

Problem

• search contests
• distribution-free equilibrium
• sequential search
• contest efficiency
• hazard rate

Innovation

• distribution-free equilibrium
• search contests
• hazard rate
• no recall
• symmetric equilibrium