Asymmetric Optimal Auction Design with Loss-Averse Bidders

We study optimal auctions with expectation-based loss-averse bidders. For ex-ante identical bidders, we establish sufficient conditions under which optimal mechanisms must be asymmetric. While symmetric designs are optimal for bidders with expected-utility preferences, we show that if the degree of loss aversion is sufficiently large relative to valuation variation, a one-bidder optimal design (an extreme form of asymmetry) yields higher expected revenue than any symmetric design with multiple bidders. To address the challenges posed by non-standard preferences, we develop a novel method for deriving the optimal auction. First, we employ the reduced-form auction framework to reformulate the revenue maximization problem as a tractable optimal control problem. We then use the ironing technique of Toikka (2011) to address the monotonicity constraint on the allocation rule, as Myerson’s ironing method is not applicable in our setting. Applying our method to a two-bidder setting with uniformly distributed valuations, we derive the optimal auction in closed form. The resulting mechanism modifies Myerson (1981) to reduce auction outcome uncertainty.