Efficiency and Voluntary Implementation in Markets with Repeated Pairwise Bargaining

We examine a simple bargaining setting where heterogeneous buyers and sellers are repeatedly matched with each other. We begin by characterizing efficiency in such a dynamic setting, and discuss how it differs from efficiency in a centralized static setting. We then study the allocations which can result in equilibrium when the matched buyers and sellers bargain through some extensive game form. We take an implementation approach, characterizing the possible allocation rules which result as the extensive game form is varied. We are particularly concerned with the impact of making trade voluntary: imposing individual rationality on and off the equilibrium path. No buyer or seller consummates an agreement which leaves them worse off than the discounted expected value of their future rematching in the market. Finally, we compare and contrast the efficient allocations with those that could ever arise as the equilibria of some voluntary negotiation procedure.