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Simple Priorities and Core Stability in Hedonic Games

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  • Dinko Dimitrov
  • Peter Borm

Abstract

In this paper we study hedonic games where each player views every other player either as a friend or as an enemy. Two simple priority criteria for comparison of coalitions are suggested, and the corresponding preference restrictions based on appreciation of friends and aversion to enemies are considered. It turns out that the first domain restriction guarantees non-emptiness of the strong core and the second domain restriction ensures non-emptiness of the weak core of the corresponding hedonic games. Moreover, an element of the strong core under friends appreciation can be found in polynomial time, while finding an element of the weak core under enemies aversion is NP-hard. We examine also the relationship between our domain restrictions and some sufficient conditions for non-emptiness of the core already known in the literature.

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Bibliographic Info

Paper provided by Econometric Society in its series Econometric Society 2004 North American Summer Meetings with number 135.

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Date of creation: 11 Aug 2004
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Handle: RePEc:ecm:nasm04:135

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Keywords: coalition formation; core stability; hedonic games; priority;

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  1. Tayfun Sönmez & Suryapratim Banerjee & Hideo Konishi, 2001. "Core in a simple coalition formation game," Social Choice and Welfare, Springer, Springer, vol. 18(1), pages 135-153.
  2. Burani, Nadia & Zwicker, William S., 2003. "Coalition formation games with separable preferences," Mathematical Social Sciences, Elsevier, Elsevier, vol. 45(1), pages 27-52, February.
  3. 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.
  4. Dreze, J H & Greenberg, J, 1980. "Hedonic Coalitions: Optimality and Stability," Econometrica, Econometric Society, Econometric Society, vol. 48(4), pages 987-1003, May.
  5. Herbert E. Scarf, 1965. "The Core of an N Person Game," Cowles Foundation Discussion Papers, Cowles Foundation for Research in Economics, Yale University 182R, Cowles Foundation for Research in Economics, Yale University.
  6. Bogomolnaia, Anna & Jackson, Matthew O., 2002. "The Stability of Hedonic Coalition Structures," Games and Economic Behavior, Elsevier, Elsevier, vol. 38(2), pages 201-230, February.
  7. Antonio Romero-Medina & Katari´na Cechlárová, 2001. "Stability in coalition formation games," International Journal of Game Theory, Springer, Springer, vol. 29(4), pages 487-494.
  8. Ballester, Coralio, 2004. "NP-completeness in hedonic games," Games and Economic Behavior, Elsevier, Elsevier, vol. 49(1), pages 1-30, October.
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Cited by:
  1. Vincent Iehlé, 2005. "The core-partition of hedonic games," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-00197528, HAL.
  2. Shao Chin Sung & Dinko Dimitrov, 2005. "A taxonomy of myopic stability concepts for hedonic games," Working Papers 373, Bielefeld University, Center for Mathematical Economics.
  3. Carmelo Rodríguez-Álvarez, 2009. "Strategy-proof coalition formation," International Journal of Game Theory, Springer, Springer, vol. 38(3), pages 431-452, November.
  4. Alison Watts, 2006. "Formation of Segregated and Integrated Groups," Working Papers, Fondazione Eni Enrico Mattei 2006.127, Fondazione Eni Enrico Mattei.
  5. Alison Watts, 2007. "Formation of segregated and integrated groups," International Journal of Game Theory, Springer, Springer, vol. 35(4), pages 505-519, April.
  6. Sung, Shao-Chin & Dimitrov, Dinko, 2010. "Computational complexity in additive hedonic games," European Journal of Operational Research, Elsevier, Elsevier, vol. 203(3), pages 635-639, June.
  7. Karakaya, Mehmet, 2011. "Hedonic coalition formation games: A new stability notion," Mathematical Social Sciences, Elsevier, Elsevier, vol. 61(3), pages 157-165, May.
  8. Shao Sung & Dinko Dimitrov, 2007. "On Myopic Stability Concepts for Hedonic Games," Theory and Decision, Springer, Springer, vol. 62(1), pages 31-45, February.
  9. Kleinberg, Jon & Ligett, Katrina, 2013. "Information-sharing in social networks," Games and Economic Behavior, Elsevier, Elsevier, vol. 82(C), pages 702-716.
  10. Woeginger, Gerhard J., 2013. "A hardness result for core stability in additive hedonic games," Mathematical Social Sciences, Elsevier, Elsevier, vol. 65(2), pages 101-104.
  11. Dimitrov, D.A. & Sung, S.C., 2004. "Enemies and Friends in Hedonic Games: Individual Deviations, Stability and Manipulation," Discussion Paper, Tilburg University, Center for Economic Research 2004-111, Tilburg University, Center for Economic Research.
  12. repec:lmu:muenec:6431 is not listed on IDEAS
  13. Dinko Dimitrov & Shao Chin Sung, 2011. "Size Monotonicity and Stability of the Core in Hedonic Games," Working Papers, Fondazione Eni Enrico Mattei 2011.52, Fondazione Eni Enrico Mattei.
  14. José Alcantud & Ritxar Arlegi, 2012. "An axiomatic analysis of ranking sets under simple categorization," SERIEs, Spanish Economic Association, Spanish Economic Association, vol. 3(1), pages 227-245, March.
  15. Iehle, Vincent, 2007. "The core-partition of a hedonic game," Mathematical Social Sciences, Elsevier, Elsevier, vol. 54(2), pages 176-185, September.

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