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Stable Many-to-Many Matchings with Contracts

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Working paper
Author/s: 
Bettina Klaus, Markus Walzl
Issue number: 
RM/06/041
Publisher: 
Maastricht University
Year: 
2006
We propose a new concept, the pairwise farsightedly stable set, in order to predict which networks may be formed among farsighted players. A set of networks G is pair- wise farsightedly stable (i) if all possible pairwise deviations from any network g ∈ G to a network outside G are deterred by the threat of ending worse off or equally well off, (ii) if there exists a farsightedly improving path from any network outside the set leading to some network in the set, and (iii) if there is no proper subset of G satisfying (i) and (ii). We show that a non-empty pairwise farsightedly stable set always exists and we provide a full characterization of unique pairwise farsightedly stable sets of networks. Contrary to other pairwise concepts, pairwise farsighted stability yields a Pareto dominating network, if it exists, as the unique outcome. Finally, we study the relationship between pairwise farsighted stability and other concepts such as the largest consistent set.
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