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Strategy-Proof Coalition Formation

We analyze coalition formation problems in which a group of agents is partitioned into coalitions and agents' preferences only depend on the coalition they belong to. We study rules that associate to each profile of agents' preferences a partition of the society. We focus on strategy-proof rules on restricted domains of preferences, as the domains of additively representable or separable preferences. In such domains, the only strategy-proof and individually rational rules that satisfy either Pareto efficiency or non-bossiness and flexibility are single-lapping rules. Single-lapping rules are characterized by severe restrictions on the set of feasible coalitions that are consisitent with hierarchical organizations. These restrictions are necessary and sufficient for the existence of a unique core-stable partition. This fact implies that single-lapping rules always select the associated unique core-stable partition. Thus, our results highlight the relation between the non-cooperative concept of strategy-proofness and the cooperative concept of uniqueness of core-stable partitions.

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Paper provided by Centro de Estudios Andaluces in its series Economic Working Papers at Centro de Estudios Andaluces with number E2006/11.

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Length: 32 pages
Date of creation: 2006
Date of revision:
Handle: RePEc:cea:doctra:e2006_11
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  1. Dutta, B. & Masso, J., 1996. "Stability of Matchings when Individuals Have Preferences Over Colleagues," UFAE and IAE Working Papers 325.96, Unitat de Fonaments de l'Anàlisi Econòmica (UAB) and Institut d'Anàlisi Econòmica (CSIC).
  2. Gabrielle Demange, 2004. "On Group Stability in Hierarchies and Networks," Journal of Political Economy, University of Chicago Press, vol. 112(4), pages 754-778, August.
  3. Papai, Szilvia, 2004. "Unique stability in simple coalition formation games," Games and Economic Behavior, Elsevier, vol. 48(2), pages 337-354, August.
  4. Salvador Barberà & Anke Gerber, 2005. "A Note on the Impossibility of a Satisfactory Concept of Stability for Coalition Formation Games," UFAE and IAE Working Papers 656.05, Unitat de Fonaments de l'Anàlisi Econòmica (UAB) and Institut d'Anàlisi Econòmica (CSIC).
  5. Sonmez, T., 1995. "Strategy-Proofness in Many-To-One Matching Problems," Papers 95-01, Michigan - Center for Research on Economic & Social Theory.
  6. Antonio Romero-Medina & Katari´na Cechlárová, 2001. "Stability in coalition formation games," International Journal of Game Theory, Springer, vol. 29(4), pages 487-494.
  7. Barbera, Salvador & Gerber, Anke, 2003. "On coalition formation: durable coalition structures," Mathematical Social Sciences, Elsevier, vol. 45(2), pages 185-203, April.
  8. Dinko Dimitrov & Peter Borm & Ruud Hendrickx & Shao Sung, 2006. "Simple Priorities and Core Stability in Hedonic Games," Social Choice and Welfare, Springer, vol. 26(2), pages 421-433, April.
  9. Tayfun Sonmez, 1999. "Strategy-Proofness and Essentially Single-Valued Cores," Econometrica, Econometric Society, vol. 67(3), pages 677-690, May.
  10. Demange, Gabrielle, 2009. "The strategy structure of some coalition formation games," Games and Economic Behavior, Elsevier, vol. 65(1), pages 83-104, January.
  11. Satterthwaite, Mark Allen, 1975. "Strategy-proofness and Arrow's conditions: Existence and correspondence theorems for voting procedures and social welfare functions," Journal of Economic Theory, Elsevier, vol. 10(2), pages 187-217, April.
  12. Ledyard, John O, 1977. "Incentive Compatible Behavior in Core-Selecting Organizations," Econometrica, Econometric Society, vol. 45(7), pages 1607-21, October.
  13. Roth, Alvin E. & Sotomayor, Marilda, 1992. "Two-sided matching," Handbook of Game Theory with Economic Applications, in: R.J. Aumann & S. Hart (ed.), Handbook of Game Theory with Economic Applications, edition 1, volume 1, chapter 16, pages 485-541 Elsevier.
  14. José Alcalde & Pablo Revilla, 2003. "Researching with Whom? Stability and Manipulation," Economic Working Papers at Centro de Estudios Andaluces E2003/35, Centro de Estudios Andaluces.
  15. Dreze, J H & Greenberg, J, 1980. "Hedonic Coalitions: Optimality and Stability," Econometrica, Econometric Society, vol. 48(4), pages 987-1003, May.
  16. Bogomolnaia, Anna & Jackson, Matthew O., 2002. "The Stability of Hedonic Coalition Structures," Games and Economic Behavior, Elsevier, vol. 38(2), pages 201-230, February.
  17. Barbera, Salvador & Sonnenschein, Hugo & Zhou, Lin, 1991. "Voting by Committees," Econometrica, Econometric Society, vol. 59(3), pages 595-609, May.
  18. Koji Takamiya, 2003. "On strategy-proofness and essentially single-valued cores: A converse result," Social Choice and Welfare, Springer, vol. 20(1), pages 77-83.
  19. Tayfun Sönmez & Suryapratim Banerjee & Hideo Konishi, 2001. "Core in a simple coalition formation game," Social Choice and Welfare, Springer, vol. 18(1), pages 135-153.
  20. Gibbard, Allan, 1973. "Manipulation of Voting Schemes: A General Result," Econometrica, Econometric Society, vol. 41(4), pages 587-601, July.
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