In two-sided multi-unit auctions having a variety of payment rules,including uniform-price and discriminatory auctions,a monotone pure-strategy equilibrium (MPSE)exists when bidders are risk neutral with independent multi-dimensional types and interdependent values.In fact,all mixed-strategy equilibria are ex post allocation and interim expected payment equivalent to MPSE.Thus,for standard expected surplus/revenue analysis,there is no loss restricting attention to monotone strategies.
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