Bayesian Nash equilibrium existence in (almost continuous) contests

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We prove the existence of a behavioral-strategy Bayesian Nash equilibrium in contests where each contestant’s probability to win is continuous in efforts outside the zero-effort profile, monotone in his own effort, and greater that 1/2 if that contestant is the only one exerting positive effort. General type spaces, and in particular a continuum of information types, are allowed. As a corollary, the existence of a pure-strategy Bayesian Nash equilibrium is established in generalized Tullock contests, where the probability to win is strictly concave in one’s own effort for any non-zero effort profile of other players.

Original languageEnglish
Pages (from-to)1231-1258
Number of pages28
JournalEconomic Theory
Issue number3
StatePublished - 1 Apr 2021


  • Absolute continuity of information
  • Bayesian Nash equilibrium
  • Contests
  • Continuum of types
  • Equilibrium existence
  • Tullock lottery

All Science Journal Classification (ASJC) codes

  • Economics and Econometrics


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