Asymmetric Optimal Auction Design with Loss-Averse Bidders

We study optimal auctions with expectation-based loss-averse bidders. We first consider when bidders are ex-ante identical. Although symmetric designs are optimal for bidders with expected-utility preferences, if the degree of loss aversion is sufficiently large relative to the variation in valuations, expected revenues are higher in the optimal design with one buyer than in any symmetric mechanism with multiple bidders. Further, we provide a sufficient condition under which optimal mechanisms are necessarily asymmetric. When bidders are ex-ante heterogeneous, the optimal degree of favoritism must be modified from the level in Myerson (1981) to reduce the uncertainty in auction outcomes. Not only the degree of the required modification but also the direction of the modification may not be monotone in the degree of loss aversion