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

Author

Listed:
  • Dennis Epple

    (Carnegie Mellon University)

  • Richard Romano

    (University of Florida)

  • Holger Sieg

    (University of Pennsylvania)

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.

Suggested Citation

  • Dennis Epple & Richard Romano & Holger Sieg, 2025. "A sharp characterization of equilibria in a tournament with performance and distinction standards," Economic Theory Bulletin, Springer;Society for the Advancement of Economic Theory (SAET), vol. 13(1), pages 125-143, April.
  • Handle: RePEc:spr:etbull:v:13:y:2025:i:1:d:10.1007_s40505-024-00284-8
    DOI: 10.1007/s40505-024-00284-8
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    More about this item

    Keywords

    Academic tournaments; Graduation standards; Academic prizes; Student effort; Optimal effort structure;
    All these keywords.

    JEL classification:

    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • I21 - Health, Education, and Welfare - - Education - - - Analysis of Education

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