Symmetrically multilateral-bargained allocations in multi-sided assignment markets
We extend Rochfords (1983) notion of symmetrically pairwise-bargained equilibrium to assignment games with more than two sides. A symmetrically multilateral-bargained (SMB) allocation is a core allocation such that any agent is in equilibrium with respect to a negotiation process among all agents based on what every agent could receive -and use as a threat- in her preferred alternative matching to the optimal matching that is formed. We prove that, for balanced multi-sided assignment games, the set of SMB is always nonempty and that, unlike the two-sided case, it does not coincide in general with the kernel (Davis and Maschler, 1965). We also give an answer to an open question formulated by Rochford (1983) by introducing a kernel-based set that, together with the core, characterizes the set of SMB.
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- Theo S. H. Driessen, 1998. "A note on the inclusion of the kernel in the core of the bilateral assignment game," International Journal of Game Theory, Springer, vol. 27(2), pages 301-303.
- Kaneko, Mamoru & Wooders, Myrna Holtz, 1982.
"Cores of partitioning games,"
Mathematical Social Sciences,
Elsevier, vol. 3(4), pages 313-327, December.
- Quint, Thomas, 1991. "The core of an m-sided assignment game," Games and Economic Behavior, Elsevier, vol. 3(4), pages 487-503, November.
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