Asymmetry and revenue in second-price auctions: a majorization approach

Abstract

Bidder asymmetries are common in certain auctions where heterogeneous bidders coexist. In this paper, we employ the tool of majorization to study the effect of bidder asymmetry on revenue in second-price auctions. As a preorder on vectors of real components, the majorization is used to rank the asymmetry of bid distributions from different auctions. Our analysis indicates that bidders’ asymmetries may raise revenue under certain classes of value distributions (e.g., proportional reversed hazard rate models) and may not in others (e.g., proportional hazard rate models). These results are further validated through supportive evidence that is based on simulated three-bidder auctions. The use of majorization allows us to extend and strengthen the results obtained in the existing literature under more general conditions. This study adds to the literature a useful analytical technique for future research on asymmetric auctions.