  We investigate the implementation of reduced-form allocation probabilities in
a two-person bargaining problem without side payments, where the agents have to
select one alternative from a finite set of social alternatives. We provide a
necessary and sufficient condition for the implementability. We find that the
implementability condition in bargaining has some new feature compared to
Border's theorem. Our results have applications in compromise problems and
package exchange problems where the agents barter indivisible objects and the
agents value the objects as complements.
