Asymmetric Optimal Auction Design with Loss-Averse Bidders *

Abstract

We study optimal auctions with expectation-based loss-averse bidders. First, we consider the case of ex-ante identical bidders and establish sufficient conditions under which optimal mechanisms must be asymmetric. While symmetric designs are optimal for bidders with expected-utility preferences, expected revenues are higher in a onebidder optimal design (an extreme form of asymmetric design) than in any symmetric design with multiple bidders if the degree of loss aversion is sufficiently large relative to valuation variations. Second, we explicitly derive the optimal auction in a two-bidder setting. For ex-ante identical bidders, the optimal auction excludes one bidder if the degree of loss aversion is sufficiently large relative to valuation variations; otherwise, Myerson's symmetric two-bidder design is optimal. For ex-ante heterogeneous bidders, the optimal auction is modified from Myerson (1981) to reduce outcome uncertainty.

Keywords: JEL Classification: D03, D44, D81, D82, D84 Asymmetric Auctions, Optimal Auctions, Reference Dependence, Expectationbased Loss Aversion

JEL Classification: D03, D44, D81, D82, D84