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Stable Partitions in a Model with Group-Dependent Feasible Sets

Author

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  • Michel Le Breton

    (Université de Toulouse I)

  • Shlomo Weber

    (Department of Economics, Southern Methodist University)

Abstract

In this paper we consider a model of group formation where group of individuals may have different feasible sets. We focus on two polar cases, increasing returns, when the set of feasible alternatives increases if a new member joins thegroup, and decreasing returns, when a new member has an opposite effect and reduces the number of alternatives available for the enlarged group. We consider two notions, stability and strong stability of group structures, that correspond to Nash and Strong Nash equilibrium of the associated non-cooperative game. We prove existence results for various classes of environments and also investigate the link between the dimensionality of the set of alternatives and the existence of stable structures.

Suggested Citation

  • Michel Le Breton & Shlomo Weber, "undated". "Stable Partitions in a Model with Group-Dependent Feasible Sets," Discussion Papers 03-24, University of Copenhagen. Department of Economics, revised May 2003.
    • Handle: RePEc:kud:kuiedp:0324
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    File URL: http://www.econ.ku.dk/english/research/publications/wp/2003/0324.pdf/
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    References listed on IDEAS

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    1. Maurice Salles, 2016. "Social choice," Chapters, in: Gilbert Faccarello & Heinz D. Kurz (ed.), Handbook on the History of Economic Analysis Volume III, chapter 36, pages 518-537, Edward Elgar Publishing.
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    3. Breton, M. le & Weber, S., 1992. "Stability of Coalition Structures and the Principle of Optimal Partitioning," Papers 93-6, York (Canada) - Department of Economics.
    4. Barnett,William A. & Moulin,Hervé & Salles,Maurice & Schofield,Norman J. (ed.), 1995. "Social Choice, Welfare, and Ethics," Cambridge Books, Cambridge University Press, number 9780521443401.
    5. Dreze, J H & Greenberg, J, 1980. "Hedonic Coalitions: Optimality and Stability," Econometrica, Econometric Society, vol. 48(4), pages 987-1003, May.
    6. Moulin, Herve, 1994. "Social choice," Handbook of Game Theory with Economic Applications, in: R.J. Aumann & S. Hart (ed.), Handbook of Game Theory with Economic Applications, edition 1, volume 2, chapter 31, pages 1091-1125, Elsevier.
    7. Le Breton, M, 1989. "A Note on Balancedness and Nonemptiness of the Core in Voting Games," International Journal of Game Theory, Springer;Game Theory Society, vol. 18(1), pages 111-117.
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    Cited by:

    1. Ulrich Faigle & Michel Grabisch, 2012. "Values for Markovian coalition processes," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 51(3), pages 505-538, November.
    2. repec:hal:pseose:halshs-00749950 is not listed on IDEAS
    3. Jean-Marc Bourgeon & Marie-Laure Breuillé, 2023. "Citizen preferences and the architecture of government," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 61(3), pages 537-585, October.
    4. Clempner, Julio B. & Poznyak, Alexander S., 2015. "Computing the strong Nash equilibrium for Markov chains games," Applied Mathematics and Computation, Elsevier, vol. 265(C), pages 911-927.
    5. Braouezec, Yann, 2012. "Customer-class pricing, parallel trade and the optimal number of market segments," International Journal of Industrial Organization, Elsevier, vol. 30(6), pages 605-614.

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    More about this item

    Keywords

    feasible sets; stable partitions; positive externality; increasing and decreasing returns;
    All these keywords.

    JEL classification:

    • C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games
    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • D62 - Microeconomics - - Welfare Economics - - - Externalities
    • D71 - Microeconomics - - Analysis of Collective Decision-Making - - - Social Choice; Clubs; Committees; Associations

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