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...

\Ve consider a generalised assignment model where the payoffs depend on the number of matchings that take place. We define several notions of stability, where these notions differ in the way the agents perceive their payoffs following a deviation. We show that if the agents are very pessimistic...