The effect of competition in contests: A unifying approach

2024-10-07

AI Summary

This paper investigates how reward inequality—i.e., intensified competition—affects contestants’ effort levels in rank-order tournaments. Within a finite-type framework, we construct a game-theoretic model and employ equilibrium analysis, comparative statics, and discretization-based approximation to characterize the effort response mechanism: its direction hinges on the relative probabilities of high- versus low-efficiency types, and a reversal of the competitive effect emerges under both linear and concave effort costs. We provide the first rigorous proof that “winner-takes-all” tournaments are robustly optimal under both cost specifications, thereby resolving a long-standing open question in classical budget allocation theory. The framework subsumes the complete-information benchmark as a special case and uniformly approximates arbitrary continuous type distributions, offering a unifying theoretical foundation to reconcile contradictory findings in the existing literature.

Technology Category

• Game Theory and Economic Paradigms: Mechanism Design
• Multiagent Systems: Mechanism Design
• Reasoning under Uncertainty: Decision/Utility Theory

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

We study how increasing competition, by making prizes more unequal, affects effort in contests. In a finite type-space environment, we characterize the equilibrium, analyze the effect of competition under linear costs, and identify conditions under which these effects persist under general costs. Our findings reveal that competition may encourage or deter effort, depending on the relative likelihood of efficient versus inefficient types. We derive implications for the classical budget allocation problem and establish that the most competitive winner-takes-all contest is robustly optimal under linear and concave costs, thereby resolving an open question. Methodologically, our analysis of the finite type-space domain -- which includes complete information as a special case and can approximate any continuum type-space -- provides a unifying approach that sheds light on the contrasting results in these extensively studied environments.

Problem

• Effect of unequal prizes on contest effort
• Optimality of winner-takes-all contests
• Unifying approach for finite type-space analysis

Innovation

• Finite type-space analysis
• Linear cost competition effects
• Winner-takes-all contest optimization