A necessary and sufficient condition for stable matching rules to be strategy-proof

Incompatibility between stability and strategy-proofness is well-known in the two-sided matching theory and this has been problems especially in designing matching rules. One possible resolution to such an impossibility result is to focus on the restricted preference domain. This paper analyzes the scope for the situation where the sets of admissible preferences for one side of the market are restricted. We advocate a new condition, called the no detour condition, and show that there exists a stable strategy-proof matching rule if and only if the sets of admissible preferences for the restricted side of the market satisfy this condition. This result is a generalization of Alcalde and Barberà (1994). Also, our characterization is without the assumptions of richness and anonymity for one side of the market that Alcalde and Barberà (1994) requires, which is economically meaningful.