Abstract:

We bring the notion of “satisficing” to matching theory and develop a weaker notion of stability. Satisficing behavior is an alternative to maximizing behavior, where instead of always going for the best, satisficers settle on something that is “good enough”. We say that a matching is satisficing if every agent is matched to an achievable partner. (An agent is achievable to another if they are matched in some stable matching.)

We show that satisficing matchings have the following properties: (i) They are Pareto efficient; (ii) All women (men) weakly prefer the woman-optimal (man-optimal) stable matching to any satisficing matching; (iii) For any two satisficing matchings, there exist two couples, each formed under one of the two matchings, such that the agents in each couple have opposite preferences over the two matchings (weak decomposition); (iv) If agents are asked to vote between a stable matching and a satisficing matching, the two matchings tie; (v) Using as operator an extension, via the join, of the least upper bound of the common order of one gender, the set of satisficing matchings forms an abelian semigroup whose ideal is the set of stable matching; (vi) Truthtelling is a rationalizable strategy for satisficing mechanisms.

We also extend the results to the college admission model.

Joint with Tina Danting Zhang and Ester Camiña.

Paper available here.