Existence of Mixed Strategy Equilibria in a Class of Discontinuous Games with Unbounded Strategy Sets

We prove existence of mixed strategy equilibria for a class of discontinuous two-player games with non-compact strategy sets. As a corollary of our main results, we obtain a continuum of mixed strategy equilibria for the first- and second-price two-bidder auctions with toeholds. We also find Klemperer’s (2000) result about the existence of mixed strategy equilibria in the classical Bertrand duopoly
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