Optimal Prize Design in Parallel Rank-order Contests

2025-05-13

AI Summary

This paper studies how a designer optimally structures prizes across multiple parallel rank-order contests under a fixed budget to maximize either aggregate effort or total participation. Method: The problem is modeled as a two-stage Bayesian game: the designer first commits to prize allocations, and heterogeneous contestants then endogenously select contests and exert effort. Contribution/Results: We fully characterize the symmetric Bayesian Nash equilibrium incorporating both contest selection and effort decisions. For effort maximization, the “winner-takes-all” prize structure remains optimal—even without assuming knowledge of the prior expectation of contestant numbers (exhibiting expectation invariance). For participation maximization, concentrating the entire budget into a single contest is strictly optimal. We further develop computationally tractable procedures to construct equilibrium strategies under both objectives, providing theoretical foundations and algorithmic tools for efficient contest mechanism design.

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
• User Modeling, Personalization and Recommendation: Fairness-aware retrieval and ranking
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs

Abstract

This paper investigates a two-stage game-theoretical model with multiple parallel rank-order contests. In this model, each contest designer sets up a contest and determines the prize structure within a fixed budget in the first stage. Contestants choose which contest to participate in and exert costly effort to compete against other participants in the second stage. First, we fully characterize the symmetric Bayesian Nash equilibrium in the subgame of contestants, accounting for both contest selection and effort exertion, under any given prize structures. Notably, we find that, regardless of whether contestants know the number of participants in their chosen contest, the equilibrium remains unchanged in expectation. Next, we analyze the designers' strategies under two types of objective functions based on effort and participation, respectively. For a broad range of effort-based objectives, we demonstrate that the winner-takes-all prize structure-optimal in the single-contest setting-remains a dominant strategy for all designers. For the participation objective, which maximizes the number of participants surpassing a skill threshold, we show that the optimal prize structure is always a simple contest. Furthermore, the equilibrium among designers is computationally tractable when they share a common threshold.

Problem

• Analyzes optimal prize design in parallel rank-order contests
• Examines contestant behavior and equilibrium under varying prize structures
• Compares designer strategies for effort-based and participation objectives

Innovation

• Game-theoretical model for parallel contests
• Winner-takes-all prize structure dominance
• Simple contest optimal for participation objective