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Contests with discontinuous payoffs

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  • Duvocelle, Benoit
  • Mourmans, Niels

Abstract

We consider a contest model with non-monotonic payoff and cost functions as introduced by Siegel (2014b). In this paper we generalize this set-up to also allow for cases in which payoffs and costs of the players can have some kind of discontinuities. Relevant real-life examples include open markets where firm decisions lead to discontinuous costs and competitions where, for instance, an extra reward is allocated to the contestant when a particular performance threshold is reached. Players compete by investing some effort in order to win one of several identical prizes. We show that one can relax the assumptions in Siegel (2009, 2014b) so that the Payoff Equivalence Theorem of Siegel still holds with the aforementioned discontinuities. We present relevant examples which show that the relaxed assumptions are indispensable, and therefore one cannot expect to refine the assumptions of Siegel more than the ones presented in this paper.

Suggested Citation

  • Duvocelle, Benoit & Mourmans, Niels, 2022. "Contests with discontinuous payoffs," Journal of Mathematical Economics, Elsevier, vol. 98(C).
    • Handle: RePEc:eee:mateco:v:98:y:2022:i:c:s0304406821001221
    DOI: 10.1016/j.jmateco.2021.102559
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    References listed on IDEAS

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    7. Ron Siegel, 2014. "Asymmetric Contests with Head Starts and Nonmonotonic Costs," American Economic Journal: Microeconomics, American Economic Association, vol. 6(3), pages 59-105, August.
    8. Philippe Bich & Rida Laraki, 2017. "On the Existence of approximative Equilibria and Sharing Rule Solutions in Discontinuous Games," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) hal-01396183, HAL.
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