Optimal Contest Design with Entry Restriction

2025-02-13

AI Summary

This paper studies optimal contest design under a fixed budget constraint, jointly optimizing the entry cap and prize structure to maximize either individual effort or aggregate effort. Methodologically, it fully characterizes the symmetric Bayesian Nash equilibrium in an n-player symmetric Bayesian game with entry restrictions, enabling derivation of the unique optimal mechanism for each objective. The analysis reveals a fundamental trade-off: maximizing aggregate effort necessitates allocating the entire budget to a single high-value prize, whereas maximizing individual effort requires precisely calibrating the entry cap and adopting a graded multi-prize structure. Integrating tools from game theory, mechanism design, and optimization, the study yields closed-form analytical solutions that explicitly quantify the tension between budget allocation efficiency and participation incentives.

Technology Category

• Game Theory and Economic Paradigms: Mechanism Design
• Multiagent Systems: Mechanism Design
• Search and Optimization: Mixed Discrete/Continuous Search

Application Category

• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• User Modeling, Personalization and Recommendation: Metrics for user behavior and evaluating success

Abstract

This paper explores the design of contests involving $n$ contestants, focusing on how the designer decides on the number of contestants allowed and the prize structure with a fixed budget. We characterize the unique symmetric Bayesian Nash equilibrium of contestants and find the optimal contests design for the maximum individual effort objective and the total effort objective.

Problem

• Optimal contest design with entry restriction
• Characterize symmetric Bayesian Nash equilibrium
• Determine optimal design for maximum and total effort

Innovation

• Optimal contest design
• Entry restriction strategy
• Bayesian Nash equilibrium