This is the second article in our new Guest Author Series, which gives affiliates the opportunity to share their research with the social science community. 

The Cournot (1838) theory of complements shows that the subdivision of a good into many essential, monopolized components drives down production and raises prices.  In this setting, the buyer must assemble the aggregate good.  Since all sellers must agree to transact, each seller has an incentive to "holdout," demanding the highest price possible.

A leading example of this "holdout problem" arises in land assembly.  Often, there is a large plot of land, owned in pieces by many individual landowners, which is valuable to prospective buyers only in its entirety.  The landowners can be seen as sellers of land parcels which are perfect complements--the parcels assemble to form an aggregate good, the entire plot.  This extreme complementary may arise for physical reasons.  For example, when a government attempts to build a public work such as a highway, there are scale and geographic restrictions which must be satisfied.

The holdout problem may also emerge when land is explicitly collectively owned, as in the Mexican ejido system, where consent of all members of a community is required for any land in that community to be sold.  Additionally, holdout may result from social, cultural, and political factors, as in Rio de Janeiro where an informal system of property has led to a paucity of development in land on the beautiful hillsides overlooking the city and bay.

Landowners’ incentives to holdout are often offered (Merrill, 1986; Posner, 2005) as a rationale for the policy of "eminent domain." This policy of property takings is written into the Fifth Amendment to the US Constitution: governments may take "private property ... for public use", but only after "just compensation" has been paid.

In practice, compensation for land takings tends to be far below the minimum price at which landowners would be willing to sell their lands. Indeed, eminent domain procedures typically follow a period in which the lands’ property values have fallen following a declaration of "blight," and takees’ legal recourse is increasingly limited following a recent Supreme Court decision (Kelo v. City of New London, Connecticut, 2005) which dramatically expanded the number of (and the controversy surrounding) takings.  The current eminent domain system abrogates nearly all landowners’ property rights and allows inefficient transfers.  However, even if the government were bound to pay the landowners’ valuations directly, as in a decentralized purchase of the plots, the Cournot (1838) theory of complements indicates that eliciting landowners’ true valuations is difficult--each individual landowner has an incentive to holdout by stating an exaggerated valuation, in hopes of capturing all the gains from trade. With such a decentralized purchase mechanism, landowner property rights are completely preserved but even efficient land transfers would never occur. 

A good eminent domain mechanism must balance the dual concerns of efficiency and property rights, hence clever market design is required.

E. Glen Weyl and I have developed a rigorous model of the holdout problem which encompasses land takings and a host of other applications such as corporate acquisitions, mutual relations between firms, and patent pool formation.  We propose a Concordance principle, inspired by the Cournot (1838) theory of concours de producteurs: each seller should receive, at worst, a pre-determined, objective share of the buyer’s offer whenever a sale takes place.*   Using the objective share information as a "pivot," we can adapt standard auction procedures to the setting of complementary goods.  This allows protection of collective, and approximate individual, property rights while solving the holdout problem and, asymptotically, achieving full efficiency.

We develop several Concordance mechanisms for solving the holdout problem.  We compare these mechanisms to the natural X-plurality mechanism which generalizes all mechanisms that we know of that have been proposed or implemented in practice to solve the holdout problem (including weighted-majority voting and the current eminent domain system).  We show that Concordance mechanisms surpass X-plurality mechanisms in terms of efficiency, while preserving property rights.  Especially attractive is a straightforward mechanism based upon the Vickrey (1961)-Clarke (1971)-Groves (1973) rule and augmented by a Pigouvian tax refund that helps balance the budget and deter collusion.

Scott Duke Kominers is a PhD candidate in the Harvard University joint PhD program in Business Economics.  Most of his research focuses on market design, with an eye towards interactions with law and computer science.  This article discusses Scott’s current joint work with E. Glen Weyl (Harvard Society of Fellows) on the holdout problem.

References

• Clarke, Edward H., "Multipart Pricing of Public Goods," Public Choice, 1971, 11 (1), 17-33.
• Cournot, A. Augustin, Recherches sur les Principes Mathematiques de la Theorie des Richess, Paris, 1838.
• Groves, Theodore, "Incentives in Teams," Econometrica, 1973, 41 (4), 617-631.
• Kelo v. City of New London, Connecticut, (04-108), 2005, 545 U.S. (469).
• Merrill, Thomas W., "The Economics of Public Use," Cornell Law Review, 1986, 72 (1), 61-116.
• Posner, Richard A., "Foreword: A Political Court," Harvard Law Review, 2005, 119 (1), 31-102.
• Vickrey, William, "Counterspeculation, Auctions and Competitive Sealed Tenders," Journal of Finance, 1961, 16 (1), 8-37.

*Patents on the Concordance principle, and on all the Concordance mechanisms discussed, are currently pending.