Optimal Prize Design in Parallel Rank-order Contests

TL;DR

This paper models and analyzes the strategic design of prizes in multiple parallel contests, revealing that winner-takes-all structures are optimal for effort objectives and simple contests for participation goals, with tractable equilibrium analysis.

Contribution

It provides a full characterization of equilibrium in multi-contest settings and identifies optimal prize structures under different designer objectives.

Findings

Winner-takes-all prizes are optimal for effort maximization.

Simple contests are optimal for maximizing participation.

Equilibrium analysis is computationally tractable with shared thresholds.

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.