Non-Cooperative Implementation in an Assignment Model

This paper examines non-cooperative implementation of stable outcomes in an assignment model. We find that there are two critical features that ensure stability - that the responders can hold more than one offer at the same time and that the proposers cannot renege on their offer once some agent pair leaves the market. We show that in a model where both criteria are satisfied we obtain a stable outcome. In a model satisfying the first but not the second criteria stability is not obtained. In the dynamic version with an aspiration generation process, however, we obtain stability in the limit. If both criteria fail, we find that neither an aspiration generation process nor both sided bargaining can lead to stable outcomes.