Optimal Orchestration of Rewards and Punishments in Rank-Order Contests

58 Pages Posted: 17 Apr 2020 Last revised: 22 Dec 2022

See all articles by Bin Liu

Bin Liu

The Chinese University of Hong Kong, Shenzhen

Jingfeng Lu

National University of Singapore (NUS) - Department of Economics

Date Written: December 20, 2022

Abstract

We allow negative prizes and investigate effort-maximizing prize design in rank-order contests with incomplete information. Endogenous participation arises due to less-efficient types' incentive to avoid punishments. The optimum features winner-take-all for the best performer and at most one punishment for the worst performer among all potential contestants, whenever they enter the competition. Based on this, we then (1) provide a necessary and sufficient condition for the optimality of pure winner-take-all without punishment; and (2) show that the optimal entry threshold increases with the total number of contestants and converges to the Myerson cutoff in the limit. Finally, we characterize the optimal entry-dependent prize structure, allowing the prize sequence to vary with the number of entrants. The optimal design must entail endogenous entry, and it harmonically integrates both winner-take-all and egality.

Keywords: All-pay auction, Cross-rank/scenario transfer, Incomplete information, Negative prize, Optimal contest.

JEL Classification: D44, D72, D82

Suggested Citation

Liu, Bin and Lu, Jingfeng, Optimal Orchestration of Rewards and Punishments in Rank-Order Contests (December 20, 2022). Available at SSRN: https://ssrn.com/abstract=3565671 or http://dx.doi.org/10.2139/ssrn.3565671

Bin Liu (Contact Author)

The Chinese University of Hong Kong, Shenzhen ( email )

Jingfeng Lu

National University of Singapore (NUS) - Department of Economics ( email )

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