Theoretical Economics, Volume 18, Number 2 (May 2023)

Theoretical Economics 18 (2023), 481–502


Equilibrium existence in games with ties

Wojciech Olszewski, Ron Siegel

Abstract


We provide conditions that simplify applying Reny's (1999) better-reply security to Bayesian games, and use these conditions to prove the existence of equilibria for classes of games in which payoff discontinuities arise only at "ties." These games include a general version of all-pay contests, first-prize auctions with common values, and Hotelling models with incomplete information.

Keywords: Equilibrium existence, discontinuous games, better-reply security

JEL classification: D82, D44, C72, L13

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