Stable Outcomes for Two-Sided Contract Choice Problems

In this paper we study the cooperative theory of stable outcomes for the roommates problem modeled as a contract choice problem. We show, that a simple generalization of the Deferred Acceptance Procedure with firms proposing due to Gale and Shapley (1962), yields outcomes for a two-sided contract choice problem, which necessarily belong to the core and are Weakly Pareto Optimal for firms. Under additional assumptions : (a) given any two distinct workers, the set of yields achievable by a firm with the first worker is disjoint from the set of yields achievable by it with the second, and (b) the contract choice problem is pair-wise efficient, we prove that there is no stable outcome at which a firm can get more than what it gets at the unique outcome of our procedure.