We consider several notions of setwise stability for many-to-many matching markets with contracts and provide an analysis of the relations between the resulting sets of stable allocations for general, substitutable, and strongly substitutable preferences. Apart from obtaining "set inclusion...

For the classical marriage model (introduced in Gale and Shapley, 1962) efficiency and envy-freeness are not always compatible, i.e., fair matchings do not always exist. However, for many allocation of indivisible goods models (see Velez, 2008, and references therein), fairness can be restored...

We consider two-sided matching markets with couples. First, we extend a result by Klaus and Klijn (2005, Theorem 3.3) and show that for any weakly responsive couples market there always exists a "double stable" matching, i.e., a matching that is stable for the couples market and for any...

Using a bi-choice graph technique (Klaus and Klijn, 2009), we show that a matching for a roommate market indirectly dominates another matching if and only if no blocking pair of the former is matched in the latter (Proposition 1). Using this characterization of indirect dominance, we investigate...

In this note we study von Neumann-Morgenstern farsightedly stable sets for Shapley and Scarf (1974) housing markets. Kawasaki (2008) shows that the set of competitive allocations coincides with the unique von Neumann-Morgenstern stable set based on a farsighted version of antisymmetric weak...

One-sided assignment problems combine important features of two well-known matching models. First, as in roommate problems, any two agents can be matched and second, as in two-sided assignment problems, the payoffs of a matching can be divided between the agents. We take a similar approach to...

Ehlers and Klaus (2003) study so-called house allocation problems and claim to characterize all rules satisfying efficiency, independence of irrelevant objects, and resource-monotonicity on two preference domains (Ehlers and Klaus, 2003, Theorem 1). They explicitly prove Theorem 1 for preference...

We consider estate division problems, a generalization of bankruptcy problems. We show that in a direct revelation claim game, if the underlying division rule satisfies efficiency, equal treatment of equals, and weak order preservation, then all (pure strategy) Nash equilibria induce equal...

We consider one-to-one matching markets in which agents can either be matched as pairs or remain single. In these so-called roommate markets agents are consumers and resources at the same time. We investigate two new properties that capture the effect a newcomer has on incumbent agents....

We consider one-to-one, one-sided matching (roommate) problems in which agents can either be matched as pairs or remain single. We introduce a so-called bi-choice graph for each pair of stable matchings and characterize its structure. Exploiting this structure we obtain as a corollary the "lone...