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Theory and Decision

, Volume 85, Issue 3–4, pp 435–453 | Cite as

Asymmetric endogenous prize contests

  • Damian S. Damianov
  • Shane Sanders
  • Anil Yildizparlak
Article

Abstract

We consider a two-player contest in which one contestant has a headstart advantage, but both can exert further effort. We allow the prize to depend on total performance in the contest and consider the respective cases in which efforts are productive and destructive of prize value. When the contest success function takes a logit form, and marginal cost is increasing in effort, we show that a Nash equilibrium exists and is unique both in productive and destructive endogenous prize contests. In equilibrium, the underdog expends more resources to win the prize, but still his probability of winning remains below that of the favorite. In a productive contest, the underdog behaves more aggressively and wins the prize more often in comparison to a fixed-value contest. Thus, the degree of competitive balance—defined as the level of uncertainty of the outcome—depends upon the (fixed or endogenous) prize nature of the contest.

Keywords

Endogenous prize contests Productive and destructive effort Competitive balance 

Notes

Acknowledgements

We thank Jürgen Eichberger, Jörg Oechssler, seminar participants at the University of Heidelberg and the audience at the 5th World Congress of the Game Theory Society in Maastricht for their helpful comments and suggestions.

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Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  • Damian S. Damianov
    • 1
  • Shane Sanders
    • 2
  • Anil Yildizparlak
    • 1
  1. 1.Department of Economics and FinanceDurham UniversityDurhamUK
  2. 2.Department of Sport Management, Falk CollegeSyracuse UniversitySyracuseUSA

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