Recently, Associate Professor Gao Lei and Professor Wang Zhewei from the School of Economics, in collaboration with Professor Lü Jingfeng from the National University of Singapore, published their paper The Effort-Maximizing Move Order in Tullock Contests in Volume 158 of Games and Economic Behavior (GEB), a leading international journal specializing in game theory. Focusing on the issue of move order within the Tullock contest framework, this research systematically investigates the optimal action scheme that maximizes participants’ total effort, offering new theoretical foundations for mechanism design in various real-world competitions.
A wide range of competitive activities in socioeconomic operations, including R&D rivalry, talent selection, job promotion, sports tournaments, and rent-seeking contests, essentially feature contest attributes. Competition designers aim to fully stimulate participants’ input incentives through rational rule formulation. During the 15th Five-Year Plan period, China is advancing high-level self-reliance and strength in science and technology to foster new quality productive forces, prioritizing breakthroughs in original innovation and core key technologies while integrating the development of education, science, technology and talent. Against this strategic backdrop, exploring how to maximize innovators’ effort via optimal move order design carries profound theoretical value and practical significance.
Based on a two-player Tullock contest model, this study explores how competition designers can select among three modes—“strong player moves first”, “weak player moves first”, or simultaneous moves—according to specific contest environments and contestants’ ability endowments to achieve the goal of aggregate effort maximization. In this model, the parameter r measures contest accuracy: a smaller/larger r implies stronger/weaker randomness in the contest, meaning effort exerts a weaker/stronger influence on competition outcomes. Most prior relevant studies were confined to the special lottery contest scenario where contest accuracy \(r = 1\), concluding that letting the strong player move first is always the optimal choice for maximizing total effort. Breaking this limitation, the present research extends contest accuracy r to the full range from zero to positive infinity, while accounting for arbitrary degrees of asymmetry in contestants’ capabilities. It compares the incentive effects of two sequential-move game formats (strong-first and weak-first) and the simultaneous-move game format.
The research conclusions overturn conventional wisdom: a strong-player-first sequence is not universally optimal, as all three action arrangements can be optimal under distinct conditions. When contest accuracy is low and random factors dominate competition, the strong-player-first rule becomes optimal by effectively motivating strong contestants to increase their inputs. When contest accuracy is relatively high, a strong-player-first order significantly boosts strong players’ effort; even though it dampens weak players’ subsequent motivation to invest, the increment in strong players’ effort suffices to maximize total effort, rendering this arrangement optimal. However, when contest accuracy falls within an intermediate interval, the weak-player-first or simultaneous-move format delivers the best performance.
The above conclusions rest on a counterintuitive core finding: a weak-player-first sequence is not inherently inefficient. When the ability gap between weak and strong competitors is not excessively wide and contest accuracy lies within a certain intermediate range, the weak player can preempt the strong player’s subsequent effort by expending high upfront effort—such weak-first contests may instead yield the highest aggregate effort. The underlying economic intuition is straightforward: to preempt the strong rival, the weak player must devote substantial effort, and this high level of investment makes the weak-first design optimal within specific parameter regions. In summary, the optimal move order of a contest is jointly determined by two core factors: contest accuracy and the disparity in contestants’ capabilities.
This achievement serves as a follow-up to the trio’s 2025 paper published in Games and Economic Behavior, Move Orders in Contests: Equilibria and Winning Chances, which systematically characterized and solved equilibrium structures under sequential-move Tullock contests and analyzed how move order impacts winning probabilities from the contestants’ perspective. By contrast, the current study adopts the competition designer’s viewpoint and centers on total effort maximization.
Gao Lei earned his PhD in Finance from Washington University in St. Louis, USA, in 2010. His research outputs have appeared in authoritative international journals including Games and Economic Behavior, Journal of Economics, and Journal of Systems Science and Complexity. He has participated in multiple national-level research projects.
Wang Zhewei, Distinguished Young and Middle-Aged Scholar of Shandong University and Young Taishan Scholar of Shandong Province, obtained his PhD in Economics from the University of Edinburgh, UK, in 2010. He has published over 20 papers in domestic and international top journals such as Games and Economic Behavior, Journal of Economic Behavior & Organization, and Management World. He presides over several national research projects and participates in major national research initiatives; he works as a reviewer for project initiation and final assessment of the National Natural Science Foundation of China and the National Social Science Fund of China. He is a member of the textbook editorial committee for core courses under the Ministry of Education’s “101 Plan”. His honors include Excellent Postdoctoral Researcher of Shandong Province, Excellent Teacher of Shandong University, and Provincial Teaching Achievement Award of Shandong Province.
