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Unique Stability in Simple Coalition Formation Games

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  • Szilvia Papai

    (Universidade Nova de Lisboa)

Abstract

In this paper we study the existence and uniqueness of stable coalition structures, when the value of a coalition to a member depends solely on the other members of the coalition. We search for collections of admissible coalitions that induce uniquely stable coalition structures, that is, ensure that there is a unique stable coalition structure at every preference profile when only admissible coalitions may form. A collection of coalitions satisfies the single-lapping property if (a) no two coalitions have more than one member in common, and (b) in a cycle formed by coalitions with a non-empty intersection all the coalitions have the same member in common. We prove that a collection of coalitions induces a unique stable coalition structure if and only if it satisfies the single-lapping property. We also provide a graph representation of collections of coalitions that satisfy the single-lapping property. This alternative representation is used to explore implications of our characterization result for matching problems such as the marriage and roommate problems. We also discuss the implications for the existence of strategyproof rules of coalition formation.

Suggested Citation

  • Szilvia Papai, 2000. "Unique Stability in Simple Coalition Formation Games," Econometric Society World Congress 2000 Contributed Papers 1537, Econometric Society.
    • Handle: RePEc:ecm:wc2000:1537
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    1. Chung, Kim-Sau, 2000. "On the Existence of Stable Roommate Matchings," Games and Economic Behavior, Elsevier, vol. 33(2), pages 206-230, November.
    2. Abeledo, Hernan & Isaak, Garth, 1991. "A characterization of graphs that ensure the existence of stable matchings," Mathematical Social Sciences, Elsevier, vol. 22(1), pages 93-96, August.
    3. Alkan, Ahmet, 1988. "Nonexistence of stable threesome matchings," Mathematical Social Sciences, Elsevier, vol. 16(2), pages 207-209, October.
    4. Roger B. Myerson, 1977. "Graphs and Cooperation in Games," Mathematics of Operations Research, INFORMS, vol. 2(3), pages 225-229, August.
    5. Tayfun Sönmez & Suryapratim Banerjee & Hideo Konishi, 2001. "Core in a simple coalition formation game," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 18(1), pages 135-153.
    6. Dutta, Bhaskar & Masso, Jordi, 1997. "Stability of Matchings When Individuals Have Preferences over Colleagues," Journal of Economic Theory, Elsevier, vol. 75(2), pages 464-475, August.
    7. Barbera, Salvador & Gerber, Anke, 2003. "Corrigendum to "On coalition formation: durable coalition structures": [Mathematical Social Sciences 45 (2003) 185-203]," Mathematical Social Sciences, Elsevier, vol. 46(3), pages 355-356, December.
    8. Martinez, Ruth & Masso, Jordi & Neme, Alejandro & Oviedo, Jorge, 2004. "An algorithm to compute the full set of many-to-many stable matchings," Mathematical Social Sciences, Elsevier, vol. 47(2), pages 187-210, March.
    9. Demange, Gabrielle, 1994. "Intermediate preferences and stable coalition structures," Journal of Mathematical Economics, Elsevier, vol. 23(1), pages 45-58, January.
    10. Alcalde, Jose & Revilla, Pablo, 2004. "Researching with whom? Stability and manipulation," Journal of Mathematical Economics, Elsevier, vol. 40(8), pages 869-887, December.
    11. Antonio Romero-Medina & Katari´na Cechlárová, 2001. "Stability in coalition formation games," International Journal of Game Theory, Springer;Game Theory Society, vol. 29(4), pages 487-494.
    12. Burani, Nadia & Zwicker, William S., 2003. "Coalition formation games with separable preferences," Mathematical Social Sciences, Elsevier, vol. 45(1), pages 27-52, February.
    13. Sotomayor, Marilda, 1996. "A Non-constructive Elementary Proof of the Existence of Stable Marriages," Games and Economic Behavior, Elsevier, vol. 13(1), pages 135-137, March.
    14. Shapley, Lloyd & Scarf, Herbert, 1974. "On cores and indivisibility," Journal of Mathematical Economics, Elsevier, vol. 1(1), pages 23-37, March.
    15. José Alcalde & Antonio Romero-Medina, 2006. "Coalition Formation and Stability," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 27(2), pages 365-375, October.
    16. Roth, Alvin E., 1982. "Incentive compatibility in a market with indivisible goods," Economics Letters, Elsevier, vol. 9(2), pages 127-132.
    17. José Alcalde, 1994. "Exchange-proofness or divorce-proofness? Stability in one-sided matching markets," Review of Economic Design, Springer;Society for Economic Design, vol. 1(1), pages 275-287, December.
    18. Roth, Alvin E. & Postlewaite, Andrew, 1977. "Weak versus strong domination in a market with indivisible goods," Journal of Mathematical Economics, Elsevier, vol. 4(2), pages 131-137, August.
    19. Alcalde, Jose & Barbera, Salvador, 1994. "Top Dominance and the Possibility of Strategy-Proof Stable Solutions to Matching Problems," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 4(3), pages 417-435, May.
    20. Bogomolnaia, Anna & Jackson, Matthew O., 2002. "The Stability of Hedonic Coalition Structures," Games and Economic Behavior, Elsevier, vol. 38(2), pages 201-230, February.
    21. Kalai, Ehud & Postlewaite, Andrew & Roberts, John, 1979. "A group incentive compatible mechanism yielding core allocations," Journal of Economic Theory, Elsevier, vol. 20(1), pages 13-22, February.
    22. Tayfun Sonmez, 1999. "Strategy-Proofness and Essentially Single-Valued Cores," Econometrica, Econometric Society, vol. 67(3), pages 677-690, May.
    23. Dreze, J H & Greenberg, J, 1980. "Hedonic Coalitions: Optimality and Stability," Econometrica, Econometric Society, vol. 48(4), pages 987-1003, May.
    24. Ledyard, John O, 1977. "Incentive Compatible Behavior in Core-Selecting Organizations," Econometrica, Econometric Society, vol. 45(7), pages 1607-1621, October.
    25. Guillaume Haeringer, 2000. "Stable Coalition Structures with Common Decision Scheme," Econometric Society World Congress 2000 Contributed Papers 1077, Econometric Society.
    26. Sotomayor, Marilda, 1999. "Three remarks on the many-to-many stable matching problem," Mathematical Social Sciences, Elsevier, vol. 38(1), pages 55-70, July.
    27. Greenberg, Joseph & Weber, Shlomo, 1986. "Strong tiebout equilibrium under restricted preferences domain," Journal of Economic Theory, Elsevier, vol. 38(1), pages 101-117, February.
    28. Ma, Jinpeng, 1994. "Strategy-Proofness and the Strict Core in a Market with Indivisibilities," International Journal of Game Theory, Springer;Game Theory Society, vol. 23(1), pages 75-83.
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