Von Neumann–Morgenstern solutions in the assignment market
The existence of von Neumann–Morgenstern solutions (stable sets) for assignment games has been an unsolved question since Shapley and Shubik (1972) . For each optimal matching between buyers and sellers, Shubik (1984)  proposed considering the union of the core of the game and the core of the subgames that are compatible with this matching. We prove in the present paper that this set is the unique stable set for the assignment game that excludes third-party payments with respect to a fixed optimal matching. Moreover, the stable sets that we characterize, as well as any other stable set of the assignment game, have a lattice structure with respect to the same partial order usually defined on the core.
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- EHLERS, Lars, 2005.
"Von Neumann-Morgenstern Stable Sets in Matching Problems,"
Cahiers de recherche
2005-11, Universite de Montreal, Departement de sciences economiques.
- Ehlers, Lars, 2007. "Von Neumann-Morgenstern stable sets in matching problems," Journal of Economic Theory, Elsevier, vol. 134(1), pages 537-547, May.
- EHLERS, Lars, 2005. "Von Neumann-Morgenstern Stable Sets in Matching Problems," Cahiers de recherche 12-2005, Centre interuniversitaire de recherche en économie quantitative, CIREQ.
- Quint, Thomas, 1991. "The core of an m-sided assignment game," Games and Economic Behavior, Elsevier, vol. 3(4), pages 487-503, November.
- T. E. S. Raghavan & Tamás Solymosi, 2001. "Assignment games with stable core," International Journal of Game Theory, Springer, vol. 30(2), pages 177-185.
- Núñez, Marina & Rafels, Carles, 2009. "A glove-market partitioned matrix related to the assignment game," Games and Economic Behavior, Elsevier, vol. 67(2), pages 598-610, November.
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