To complement the theory of incomplete markets under perfect competition and anonymity, this paper examines the theory of incomplete markets under strategic bargaining. Households bargain over bilateral nominal contracts that specify transfers for all states of uncertainty. The lone institutional feature is the limit on the number of contracts that a household can agree to. These contract limits for all households determine whether or not the equilibrium allocations are first-best. Specifically, if all households can be linked via a series of contracts to all other households, then the equilibrium allocations will be first-best; if not, then the allocations will generically not even be second-best.