Hold-Up and Durable Trading Opportunities

This paper examines a contractual setting with unverifiable investment and a durable trading opportunity, in which trade can take place in any one of an infinite number of periods. The contractual setting features cross-investment, meaning that the seller’s investment affects the buyer’s benefit of trade. Two different trade technologies are studied, one in which the seller has the individual action that consummates trade and one in which the buyer has the action that consummates trade. The set of outcomes supported in the durability setting is shown to be equivalent to the set supported in the related setting without durability. Thus, rather than durability, it is the technology of investment and trade — in particular, whether investment and trade actions are divided or unified (Buzard and Watson 2009) — that plays the critical role in determining whether the seller can be induced to invest at the efficient level. The issue of multiple equilibrium is analyzed and it is shown that particular non-stationary contracts can achieve unique implementation. The modeling exercise thus qualifies the recent view that durability may contribute to the hold-up problem.