Credible group stability in many-to-many matching problems.

*(English)*Zbl 1132.91579Summary: It is known that in two-sided many-to-many matching problems, pairwise-stable matchings may not be immune to group deviations, unlike in many-to-one matching problems [C. Blair, Math. Oper. Res. 13, No. 4, 619–628 (1988; Zbl 0664.90075)]. In this paper, we show that pairwise stability is equivalent to credible group stability when one side has responsive preferences and the other side has categorywise-responsive preferences. A credibly group-stable matching is immune to any “executable” group deviations with an appropriate definition of executability. Under the same preference restriction, we also show the equivalence between the set of pairwise-stable matchings and the set of matchings generated by coalition-proof Nash equilibria of an appropriately defined strategic-form game.

##### MSC:

91B68 | Matching models |

##### Keywords:

many-to-many matching; pairwise stability; group stability; credible deviation; coalition-proof Nash equilibrium
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\textit{H. Konishi} and \textit{M. U. Ünver}, J. Econ. Theory 129, No. 1, 57--80 (2006; Zbl 1132.91579)

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