Monotonicity in asymmetric first-price auctions with affiliation

I study monotonicity of equilibrium strategies in first-price auctions with asymmetric bidders, risk-aversion, affiliated types, and interdependent values. I prove that every mixed-strategy equilibrium is outcome equivalent to a monotone pure strategy equilibrium under the “priority rule” for breaking ties. This provides a missing link to establish uniqueness in Milgrom and Weber (1982)’s “general symmetric model”. Non-monotone equilibria can exist under the “coin-flip rule” but they are distinguishable: all non-monotone equilibria have positive probability of ties whereas all monotone equilibria have zero probability of ties. This provides a justification for the standard empirical practice of restricting attention to monotone strategies. ∗E-mail: [email protected]. Post: MIT Sloan School of Management, E52-448, 50 Memorial Drive, Cambridge, MA 02142. I thank Eddie Dekel and Phil Reny for providing helpful comments at an early stage of this work and seminar participants at CalTech, Harvard/MIT, Northwestern, Princeton, and UC Berkeley for comments on a more recent version of the paper. This research has been supported by National Science Foundation grant #SES-0241468.