We show that a simple generalisation of the Deferred Acceptance Procedure with men proposing due to Gale and Shapley (1962) yields outcomes for a generalised 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, generalised contract choice problems. The model we propose is a generalisation 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 generalised contract choice problem, which does not admit any stable outcome.
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Paper provided by Fondazione Eni Enrico Mattei in its series Working Papers with number
2003.117.
Find related papers by JEL classification: C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games C78 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Bargaining Theory; Matching Theory