Auctions and shareholdings

This paper examines how shareholdings affect auctions' revenue and efficiency with independent private values. Two types of shareholdings are analyzed: vertical (resp: horizontal) toeholds cover situations in which bidders own a fraction of the seller's profit (resp: a share of their competitor's profit). Expected revenue is an increasing (resp: decreasing) function of vertical (resp: horizontal) toeholds. With both types of toeholds, auction formats are not revenue equivalent. Expected revenue is affected to a greater extent by the presence of toeholds in the second-price auction than in the first-price auction.