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Bayesian Nash equilibrium existence in (almost continuous) contests


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.

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Correspondence to Ori Haimanko.

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This article significantly benefited from comments and suggestions of three anonymous reviewers, to whom the author expresses his gratitude.

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Haimanko, O. Bayesian Nash equilibrium existence in (almost continuous) contests. Econ Theory 71, 1231–1258 (2021).

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

JEL Classification

  • C72
  • D72
  • D82