Optimal selling mechanisms with crossholdings
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Optimal selling mechanisms with crossholdings Gino Loyola1 Received: 18 January 2020 / Accepted: 19 October 2020 © Springer-Verlag GmbH Germany, part of Springer Nature 2020
Abstract We characterize the optimal selling mechanism when bidders have ownership links among them (crossholdings). This mechanism discriminates against bidders who enjoy a value comparative advantage resulting from the extent to which they appropriate their own surplus. It is shown that since crossholdings improve the seller’s ability to selectively extract surplus from bidders, expected seller revenue is increasing with the asymmetry in these stakes. The optimal mechanism is implemented by a hybrid procedure that combines an auction with price preferences and a possible exclusive deal. An alternative negotiation procedure replicates some properties of the optimal one, and revenue-dominates most commonly used auction formats. Keywords Optimal auction · Crossholding · Asymmetric auction · Negotiation · Private values JEL Classification C72 · D44 · D82 · G32 · G34
1 Introduction Many contests can in fact be considered as auctions with crossholdings, that is, auctions in which bidders have minority stakes in other bidders’ surplus. For instance, it is usual in some markets for competing firms to hold shares in one other, or for a fraction of a company’s ownership to belong to a non-controlling shareholder who also holds a controlling stake in a rival company.1 1 For the case of direct cross-ownership, Claessens et al. (1998) document the fact that other (non-affiliated)
companies constitute one of the most important corporate blockholders in various Asian countries. As regards indirect cross-ownership, Hansen and Lott (1996) report that the portfolios held by institutional investors in the U.S. include shares in competing firms in markets such as computers and automobiles. Similarly, Brunello et al. (2001) and Becht and Roell (1999) describe how pyramidal groups are very common in corporate ownership structures in Italy, France and Belgium.
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Gino Loyola [email protected] Department of Management Control and Information Systems, Faculty of Economics and Business, University of Chile, Diagonal Paraguay 257, Of. 1903, Santiago, Chile
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The presence of crossholdings introduces countervailing incentives for bidders in that they get a payoff not only when they win an auction, but also when they lose. Since the losing bidder appropriates a fraction of the winning surplus, he will care about the valuation and the price paid by the winning bidder. Thus, losing transforms a bidder with crossholdings into a minority buyer, which induces him to bid less aggressively. As a result, the typical bidder’s incentives to raise his bid in order to obtain the object under auction are now counteracted by this particular incentive to lose induced by crossholdings. Previous literature has shown that this less aggressive bidding induced by crossholdings breaks down the revenue equivalence between standard auctions (Myerson 1981; Riley and Sam
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