A sharp characterization of equilibria in a tournament with performance and distinction standards

Dennis Epple, Richard Romano and Holger Sieg
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Dennis Epple: Carnegie Mellon University
Holger Sieg: University of Pennsylvania

Economic Theory Bulletin, 2025, vol. 13, issue 1, No 9, 125-143

Abstract: Abstract The objective of this paper is to provide a characterization of the equilibrium of an academic tournament model which highlights the relationship between minimum performance standards (graduation requirements) and distinction standards (academic prizes). We consider a generic effort game among a finite number of students that differ by ability in a single academic institution. The incentive mechanism combines a minimum performance standard with a tournament for prizes awarded based on relative performance rankings. We show that a high graduation requirement is necessary for the existence of a pure strategy equilibrium. It is characterized by the highest ability students obtaining the prizes. With a wide enough ability distribution, students in the tails of the distribution put forth low effort. For a lower graduation standard, equilibrium is in mixed strategies, but with just two students strictly randomizing in their effort choices. Interestingly, a top ability student exploits their ability advantage by randomly shirking, a lower ability student randomizes to perhaps beat out that student, and students of abilities between put in high effort to insure a prize. Finally, we consider a variety of extensions of the model.

Keywords: Academic tournaments; Graduation standards; Academic prizes; Student effort; Optimal effort structure (search for similar items in EconPapers)
JEL-codes: C72 I21 (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1007/s40505-024-00284-8

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