Efficient Non-Contractible Investments in a Finite Economy*

Investors making complementary investments typically do not have in­ centives to invest efficiently when they cannot contract with each other prior to their decisions because of the hold-up problem: when they bargain over the surplus generated by their investments, they will usually not obtain the full fruits of the investment. Intuitively, the hold-up problem should be ameliorated if, in the bargaining stage, each agent has alternatives to the partner he is bargaining with. We characterize the matching and division of surplus in finite economies for any initial investment decisions. We provide conditions on those decisions that guarantee that each agent will capture the change in the aggregate social surplus that results from any investment change he makes. We further show that for any given problem, there exists a bargaining rule by which pairs split their surplus that will support efficient investment choices in equilibrium. We also show, however, that overinvest­ ment or underinvestment can occur for natural bargaining rules. *This paper draws heavily from two earlier papers of ours, "Bargaining and Investment in a Two-Sided Matching Model" and "Efficient Non-Contractible Investments." We thank Daron Acemoglu, Jere Behrman, John Moore, Mark Rosenzweig, Randall Wright, and seminar audi­ ences at numerous universities for helpful discussion and comments. The views expressed herein are those of the authors and not necessarily those of the Federal Reserve Bank of Minneapolis or the Federal Reserve System. tMailath and Postlewaite gratefully acknowledge financial support from the NSF. Efficient Non-contractible Investments in a Finite Economy by Harold L. Cole, George J. Mailath, and Andrew Postlewaite