The Effect of Cross Ownership on Competition in Auction Markets

We consider a model where bidders in an auction own passive partial claims over their rivals’ auction profits. While the cross ownership confers no ability to directly affect bidding behavior, the claims on rival profits dampen bidding competition. It is not uncommon for enforcement agencies to investigate such an arrangements as a possible violation of antitrust laws. When bidders hold the same aggregate level of shares in rival bidders in a first-price independent private-value auction, we find that such cross ownership has an effect similar to reducing the number of bidders while holding constant the distribution of the highest value in the auction. A similar decrease in competition occurs in independent private-value second-price auctions with two bidders and in first-price complete information auctions. In each of these cases, the competitive effect disappears as the level of cross ownership goes to zero. English auctions in complete information environments, however, generate strikingly different outcomes. There, for any positive level of cross ownership, the unique subgame perfect equilibrium generates the same result as the perfectly collusive outcome: the highest valued bidder wins the object at the lowest possible price