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Simple Priorities and Core Stability in Hedonic Games

  • Dinko Dimitrov

    (Center and Department of Econometrics and Operations Research, Tilburg University)

  • Peter Borm

    (Center and Department of Econometrics and Operations Research, Tilburg University)

  • Ruud Hendrickx

    (Center and Department of Econometrics and Operations Research, Tilburg University)

  • Shao Chin Sung

    (School of Information Science, Japan Advanced Institute of Science and Technology)

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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Paper provided by Fondazione Eni Enrico Mattei in its series Working Papers with number 2004.51.

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Date of creation: Mar 2004
Date of revision:
Handle: RePEc:fem:femwpa:2004.51
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  1. Ballester, Coralio, 2004. "NP-completeness in hedonic games," Games and Economic Behavior, Elsevier, vol. 49(1), pages 1-30, October.
  2. Dreze, J H & Greenberg, J, 1980. "Hedonic Coalitions: Optimality and Stability," Econometrica, Econometric Society, vol. 48(4), pages 987-1003, May.
  3. Ray, Debraj, 1989. "Credible Coalitions and the Core," International Journal of Game Theory, Springer, vol. 18(2), pages 185-87.
  4. Herbert E. Scarf, 1965. "The Core of an N Person Game," Cowles Foundation Discussion Papers 182R, Cowles Foundation for Research in Economics, Yale University.
  5. Suryapratim Banerjee & Hideo Konishi & Tayfun Sonmez, 1999. "Core in a Simple Coalition Formation Game," Boston College Working Papers in Economics 449, Boston College Department of Economics.
  6. Alcalde, Jose & Revilla, Pablo, 2004. "Researching with whom? Stability and manipulation," Journal of Mathematical Economics, Elsevier, vol. 40(8), pages 869-887, December.
  7. Dimitrov, D.A. & Borm, P.E.M. & Hendrickx, R.L.P. & Sung, S.C., 2004. "Simple Priorities and Core Stability in Hedonic Games," Discussion Paper 2004-5, Tilburg University, Center for Economic Research.
  8. Bogomolnaia, Anna & Jackson, Matthew O., 2002. "The Stability of Hedonic Coalition Structures," Games and Economic Behavior, Elsevier, vol. 38(2), pages 201-230, February.
  9. Antonio Romero-Medina & Katari´na Cechlárová, 2001. "Stability in coalition formation games," International Journal of Game Theory, Springer, vol. 29(4), pages 487-494.
  10. Burani, Nadia & Zwicker, William S., 2003. "Coalition formation games with separable preferences," Mathematical Social Sciences, Elsevier, vol. 45(1), pages 27-52, February.
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