Strategy-Proofness and Singleton Cores in Generalized Matching Problems

Abstract

We introduce and study the class of generalized matching problems. Two subclasses of this class are marriage problems (Gale and Shapley 1962) and the housing market (Shapley and Scarf 1974). We search for strategy-proof solutions to generalized matching problems. We show that if the core is a singleton and is stable for all problems then it is sstrategy-proof as a solution. We also show that on the class of problems with a non-empty core therre exists a Pareto efficient, individually rational, and sstrategy-proof solution only if the core is a singleton for all problems. Furthermore if such a solution exists, it is the core.