Stable Matchings for A Generalized Marriage Problem

We show, that a simple generalization of the Deferred Acceptance Procedure with men proposing due to Gale and Shapley (1962), yields outcomes for a generalized marriage problem, which are necessarily stable. We also show, that any outcome of this procedure is Weakly Pareto Optimal for Men, i.e. there is no other outcome which all men prefer to an outcome of this procedure. In a final concluding section of this paper, we consider the problem of choosing a set of multi-party contracts, where each coalition of agents has a non-empty finite set of feasible contracts to choose from. We call such problems, generalized contract choice problems. The model we propose is a generalization of the model due to Shapley and Scarf (1974) called the housing market. We are able to show with the help of a three agent example, that there exists a generalized contract choice problem, which does not admit any stable outcome.