Let N be a set of agents in a two-sided matching market. Apply a version of the deferred acceptance alghoritm and suppose it produces the allocation in which agent i is matched with itself. Suppose now that we delete agent i from the set of agents and from the preferences of each of the other agents.

(a) is stable also in the new model?

(b) If we apply the same version of deferred acceptance in the new model, will the outcome will be necessarily the same as before (that is the allocation )?