Optimal Prize Design in Parallel Rank-order Contests
Xiaotie Deng, Ningyuan Li, Weian Li, Qi Qi
TL;DR
The paper addresses optimal prize design in a setting with $m$ parallel rank-order contests and $n$ contestants who both choose which contest to enter and exert costly effort. It develops a two-stage model where designers commit prize structures within budgets and contestants respond with contest selection and deterministic effort, yielding a symmetric Bayesian Nash equilibrium (sBNE) analysis for the contestants and optimality results for designer objectives. The main contributions are: (i) a full characterization of the contestant sBNE via a one-dimensional cumulative choice strategy and a deterministic effort function, (ii) a demonstration that winner-takes-all prize structures are dominant for broad effort-based designer objectives, and (iii) that for participation objectives the optimal prize structure is a simple contest, with efficient computation of designer equilibria when thresholds are common. These results extend single-contest insights to multi-contest environments and provide practical guidance for designing parallel contests in platforms and conferences, preserving tractability and strategic predictability.
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.