Monotonicity in Asymmetric First-Price Auctions with Affiliation
Posted: 14 Jan 2008
I study monotonicity of equilibrium strategies in first-price auctions with symmetric 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.
Keywords: Asymmetric First-price Auctions, Asymmetric Bidders, Mixed Strategy Equilibrium
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