Abstract
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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Haimanko, O. Bayesian Nash equilibrium existence in (almost continuous) contests. Econ Theory 71, 1231–1258 (2021). https://doi.org/10.1007/s00199-021-01358-5
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DOI: https://doi.org/10.1007/s00199-021-01358-5
Keywords
- Contests
- Tullock lottery
- Bayesian Nash equilibrium
- Equilibrium existence
- Absolute continuity of information
- Continuum of types