Efficient Non-Contractible Investments in Finite Economies

Individuals making investments typically do not have incentives to invest efficiently when they cannot contract prior to their decisions. When they bargain over the surplus generated by their investments, they will usually not obtain the full fruits of the investment. Intuitively, this 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 overinvestment or underinvestment can occur for natural bargaining rules.