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Stability and Segregation in Group Formation

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Author Info
Igal Milchtaich ()
Eyal Winter ()

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Abstract

This paper presents a model of group formation based on the assumption that individuals prefer to associate with people similar to them. It is shown that, in general, if the number of groups that can be formed is bounded, then a stable partition of the society into groups may not exist. A partition is defined as stable if none of the individuals would prefer be in a different group than the one he is in. However, if individuals’ characteristics are one-dimensional, then a stable partition always exists. We give sufficient conditions for stable partitions to be segregating (in the sense that, for example, low-characteristic individuals are in one group and high-characteristic ones are in another) and Pareto efficient. In addition, we propose a dynamic model of individual myopic behavior describing the evolution of group formation to an eventual stable, segregating, and Pareto efficient partition.

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Publisher Info
Paper provided by Center for Rationality and Interactive Decision Theory, Hebrew University, Jerusalem in its series Discussion Paper Series with number dp263.

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Length: 37 pages
Date of creation: Apr 2000
Date of revision:
Publication status: Published in Games and Economic Behavior, 2002, vol. 38, pp. 318-346.
Handle: RePEc:huj:dispap:dp263

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Related research
Keywords: group formation; coalition structure; local public goods; segregation; myopic optimization; weak acyclicity;

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Find related papers by JEL classification:
C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
H41 - Public Economics - - Publicly Provided Goods - - - Public Goods

References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:

  1. Westhoff, Frank, 1977. "Existence of equilibria in economies with a local public good," Journal of Economic Theory, Elsevier, vol. 14(1), pages 84-112, February. [Downloadable!] (restricted)
  2. 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. [Downloadable!]
    Other versions:
  3. Mamoru Kaneko & Myrna Holtz Wooders, 1982. "Cores of Partitioning Games," Cowles Foundation Discussion Papers 620, Cowles Foundation, Yale University. [Downloadable!]
    Other versions:
  4. Kaneko, Mamoru & Kimura, Toshiyuki, 1992. "Conventions, social prejudices and discrimination: A festival game with merrymakers," Games and Economic Behavior, Elsevier, vol. 4(4), pages 511-527, October. [Downloadable!] (restricted)
  5. Bryan Ellickson & Birgit Grodal & Suzanne Scotchmer & William R. Zame, 1999. "Clubs and the Market," Econometrica, Econometric Society, vol. 67(5), pages 1185-1218, September.
    Other versions:
  6. Bewley, Truman F, 1981. "A Critique of Tiebout's Theory of Local Public Expenditures," Econometrica, Econometric Society, vol. 49(3), pages 713-40, May. [Downloadable!] (restricted)
  7. Konishi, Hideo & Le Breton, Michel & Weber, Shlomo, 1998. "Equilibrium in a Finite Local Public Goods Economy," Journal of Economic Theory, Elsevier, vol. 79(2), pages 224-244, April. [Downloadable!] (restricted)
  8. Karni, Edi & Schmeidler, David, 1990. "Fixed Preferences and Changing Tastes," American Economic Review, American Economic Association, vol. 80(2), pages 262-67, May. [Downloadable!] (restricted)
  9. Igal Milchtaich, 1998. "Crowding games are sequentially solvable," International Journal of Game Theory, Springer, vol. 27(4), pages 501-509. [Downloadable!] (restricted)
  10. Wooders, Myrna, 1980. "The Tiebout Hypothesis: Near Optimality in Local Public Good Economies," Econometrica, Econometric Society, vol. 48(6), pages 1467-85, September. [Downloadable!] (restricted)
  11. Greenberg Joseph & Weber Shlomo, 1993. "Stable Coalition Structures with a Unidimensional Set of Alternatives," Journal of Economic Theory, Elsevier, vol. 60(1), pages 62-82, June. [Downloadable!] (restricted)
  12. Young, H Peyton, 1993. "The Evolution of Conventions," Econometrica, Econometric Society, vol. 61(1), pages 57-84, January. [Downloadable!] (restricted)
  13. Bernheim, B. Douglas & Peleg, Bezalel & Whinston, Michael D., 1987. "Coalition-Proof Nash Equilibria I. Concepts," Journal of Economic Theory, Elsevier, vol. 42(1), pages 1-12, June. [Downloadable!] (restricted)
  14. Greenberg, J. & Weber, S., 1991. "Stable Coalition Structures with Unidimensional Set of Alternatives," Papers 9133, Tilburg - Center for Economic Research.
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  15. Monderer, Dov & Shapley, Lloyd S., 1996. "Potential Games," Games and Economic Behavior, Elsevier, vol. 14(1), pages 124-143, May. [Downloadable!] (restricted)
  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. [Downloadable!] (restricted)
Full references

Cited by:
(explanations, Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.)

  1. Alison Watts, 2007. "Formation of segregated and integrated groups," International Journal of Game Theory, Springer, vol. 35(4), pages 505-519, April. [Downloadable!] (restricted)
  2. Alberto Alesina & Eliana La Ferrara, 2004. "Ethnic Diversity and Economic Performance," Development Working Papers 193, Centro Studi Luca d\'Agliano, University of Milano. [Downloadable!]
  3. Arnold, Tone & Wooders, Myrna, 2002. "Dynamic Club Formation With Coordination," The Warwick Economics Research Paper Series (TWERPS) 640, University of Warwick, Department of Economics. [Downloadable!]
    Other versions:
  4. Guillaume Haeringer, 2000. "Stable Coalition Structures with Common Decision Scheme," Econometric Society World Congress 2000 Contributed Papers 1077, Econometric Society. [Downloadable!]
  5. Le Breton, Michel & Weber, Shlomo, 2004. "Group Formation with Heterogeneous Sets," IDEI Working Papers 288, Institut d'Économie Industrielle (IDEI), Toulouse. [Downloadable!]
  6. Brams, S. J. & Jones, M. A. & Kilgour, M. D., 2001. "Single-Peakedness and Disconnected Coalitions," Working Papers 01-06, C.V. Starr Center for Applied Economics, New York University. [Downloadable!]
  7. Salvador Barber?Author-Name: Carmen Bevi?Author-Email: Carmen.Bevia@uab.es, . "Stable Condorcet Rules," UFAE and IAE Working Papers 539.02, Unitat de Fonaments de l'Anàlisi Econòmica (UAB) and Institut d'Anàlisi Econòmica (CSIC). [Downloadable!]
  8. Guillaume Haeringer, 2000. "Stable Coalition Structures with Fixed Decision Schme," UFAE and IAE Working Papers 471.00, Unitat de Fonaments de l'Anàlisi Econòmica (UAB) and Institut d'Anàlisi Econòmica (CSIC). [Downloadable!]
  9. Carmen Bevi? & Salvador Barber?, . "Self-Selection Consistent Functions," UFAE and IAE Working Papers 468.00, Unitat de Fonaments de l'Anàlisi Econòmica (UAB) and Institut d'Anàlisi Econòmica (CSIC). [Downloadable!]
    Other versions:
  10. Desmet, Klaus & Le Breton, Michel & Ortuno-Ortin, Ignacio, 2006. "Nation Formation and Genetic Diversity," IDEI Working Papers 133, Institut d'Économie Industrielle (IDEI), Toulouse. [Downloadable!]
    Other versions:
  11. Alison Watts, 2006. "Formation of Segregated and Integrated Groups," Working Papers 2006.127, Fondazione Eni Enrico Mattei. [Downloadable!]
  12. 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. [Downloadable!]
    Other versions:
  13. Michel Le Breton & Shlomo Weber, . "Stable Partitions in a Model with Group-Dependent Feasible Sets," Discussion Papers 03-24, University of Copenhagen. Department of Economics, revised May 2003. [Downloadable!]
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