×

zbMATH — the first resource for mathematics

On combining implementable social choice rules. (English) Zbl 1155.91344
Summary: We study if (and when) the intersections and unions of social choice rules that are implementable with respect to a certain equilibrium concept are themselves implementable with respect to that equilibrium concept. Our results for dominant strategy equilibrium are mostly of negative nature; similarly, the intersection of Nash implementable SCCs need not be Nash implementable. On the other hand, we find that the union of any set of Nash implementable social choice rules is Nash implementable (for societies of at least three constituents). This last observation allows us to formulate the notion of the largest Nash implementable subcorrespondence of a social choice rule.

MSC:
91B14 Social choice
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] Benoît, J.-P., Ok, E.A., 2004. Maskin’s theorem without no-veto power. Mimeo, NYU
[2] Benoît, J.-P.; Ok, E.A., Maskin’s theorem with limited veto power, Games econ. behav., 55, 331-339, (2006) · Zbl 1125.91010
[3] Jackson, M., A crash course in implementation theory, Soc. choice welfare, 18, 655-708, (2001) · Zbl 1069.91557
[4] Kara, T.; Sönmez, T., Implementation of college admission rules, Econ. theory, 9, 197-218, (1997) · Zbl 0872.90006
[5] Maskin, E., Nash equilibrium and welfare optimality, Rev. econ. stud., 66, 23-38, (1999) · Zbl 0956.91034
[6] Maskin, E.; Sjöström, T., Implementation theory, (), 237-288
[7] Sen, A., The implementation of social choice functions via social choice correspondences: A general formulation and limit result, Soc. choice welfare, 12, 277-292, (1995) · Zbl 0837.90009
[8] Serrano, R.; Vohra, R., Implementing the Mas-Colell bargaining set, Games econ. behav., 26, 285-298, (2002)
[9] Thomson, W., Monotonic extensions on economic domains, Rev. econ. design, 4, 13-33, (1999)
[10] Thomson, W., 2003. Private communication
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.