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Mathematical models of stable jurisdiction partitions: A survey of results and new directions

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  • Musatov, D.

    (Moscow Institute of Physics and Technology, Dolgoprudny, Russia
    Russian Presidential Academy of National Economy and Public Administration, Moscow, Russia
    Caucasus Mathematical Center at Adyghe State University, Maykop, Russia)

  • Savvateev, A.

    (Moscow Institute of Physics and Technology, Dolgoprudny, Russia
    Caucasus Mathematical Center at Adyghe State University, Maykop, Russia
    Central Economics and Mathematics Institute, RAS, Moscow, Russia)

Abstract

The human society consists of many large and small groups. Why do these groups emerge? How does their structure form? What does their dynamics look like? Is there always a stable configuration that does not change anymore? In the models described in this survey it is assumed that agents live in some geographical or virtual space and groups are formed to produce some club good located in the same space and available only inside a group. There are two opposite forces that influence the size of the groups. On the one hand, in larger groups the agents enjoy economy of scale, so the good costs less. On the other hand, in smaller and homogeneous groups the good may be located close to all members. Do these forces always balance each other in some stable configuration and what does this configuration look like? The answer depends on the model details and on the notion of equilibrium. In this survey we present different frameworks and main known results about (non-)existence of equilibria and their properties, as well as some new directions of research.

Suggested Citation

  • Musatov, D. & Savvateev, A., 2022. "Mathematical models of stable jurisdiction partitions: A survey of results and new directions," Journal of the New Economic Association, New Economic Association, vol. 54(2), pages 12-38.
  • Handle: RePEc:nea:journl:y:2022:i:54:p:12-38
    DOI: 10.31737/2221-2264-2022-54-2-1
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    as
    1. Bollobas, Bela & Stern, Nicholas, 1972. "The optimal structure of market areas," Journal of Economic Theory, Elsevier, vol. 4(2), pages 174-179, April.
    2. Alberto Alesina & Enrico Spolaore, 1997. "On the Number and Size of Nations," The Quarterly Journal of Economics, Oxford University Press, vol. 112(4), pages 1027-1056.
    3. Enrico Spolaore & Alberto Alesina & Romain Wacziarg, 2000. "Economic Integration and Political Disintegration," American Economic Review, American Economic Association, vol. 90(5), pages 1276-1296, December.
    4. Esteban, Joan & Flamand, Sabine & Morelli, Massimo & Rohner, Dominic, 2017. "The Survival and Demise of the State: A Dynamic Theory of Secessions," CEPR Discussion Papers 12398, C.E.P.R. Discussion Papers.
    5. Starrett, David, 1978. "Market allocations of location choice in a model with free mobility," Journal of Economic Theory, Elsevier, vol. 17(1), pages 21-37, February.
    6. Goyal, Sanjeev & Staal, Klaas, 2004. "The political economy of regionalism," European Economic Review, Elsevier, vol. 48(3), pages 563-593, June.
    7. Bewley, Truman F, 1981. "A Critique of Tiebout's Theory of Local Public Expenditures," Econometrica, Econometric Society, vol. 49(3), pages 713-740, May.
    8. Drèze, Jacques & Le Breton, Michel & Savvateev, Alexei & Weber, Shlomo, 2008. ""Almost" subsidy-free spatial pricing in a multi-dimensional setting," Journal of Economic Theory, Elsevier, vol. 143(1), pages 275-291, November.
    9. Anna Bogomolnaia & Michel Breton & Alexei Savvateev & Shlomo Weber, 2007. "Stability under unanimous consent, free mobility and core," International Journal of Game Theory, Springer;Game Theory Society, vol. 35(2), pages 185-204, January.
    10. Thisse, Jacques-Francois & Wildasin, David E., 1992. "Public facility location and urban spatial structure : Equilibrium and welfare analysis," Journal of Public Economics, Elsevier, vol. 48(1), pages 83-118, June.
    11. Michel Le Breton & Shlomo Weber, 2003. "The Art of Making Everybody Happy: How to Prevent a Secession," IMF Staff Papers, Palgrave Macmillan, vol. 50(3), pages 1-4.
    12. Krugman, Paul, 1991. "Increasing Returns and Economic Geography," Journal of Political Economy, University of Chicago Press, vol. 99(3), pages 483-499, June.
    13. Anna Bogomolnaia & Michel Breton & Alexei Savvateev & Shlomo Weber, 2008. "Stability of jurisdiction structures under the equal share and median rules," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 34(3), pages 525-543, March.
    14. Patrick Bolton & Gérard Roland, 1997. "The Breakup of Nations: A Political Economy Analysis," The Quarterly Journal of Economics, Oxford University Press, vol. 112(4), pages 1057-1090.
    15. Enrico Spolaore, 2008. "Civil conflict and secessions," Economics of Governance, Springer, vol. 9(1), pages 45-63, January.
    16. AUMANN, Robert J. & DREZE, Jacques H., 1974. "Cooperative games with coalition structures," LIDAM Reprints CORE 217, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    17. Philippe Jehiel & Suzanne Scotchmer, 2001. "Constitutional Rules of Exclusion in Jurisdiction Formation," Review of Economic Studies, Oxford University Press, vol. 68(2), pages 393-413.
    18. Charles M. Tiebout, 1956. "A Pure Theory of Local Expenditures," Journal of Political Economy, University of Chicago Press, vol. 64, pages 416-416.
    19. Haimanko, Ori & Le Breton, Michel & Weber, Shlomo, 2004. "Voluntary formation of communities for the provision of public projects," Journal of Economic Theory, Elsevier, vol. 115(1), pages 1-34, March.
    20. repec:ebl:ecbull:v:8:y:2005:i:11:p:1-5 is not listed on IDEAS
    21. Pablo D. Fajgelbaum & Edouard Schaal, 2020. "Optimal Transport Networks in Spatial Equilibrium," Econometrica, Econometric Society, vol. 88(4), pages 1411-1452, July.
    22. Michel Le Breton & Juan Moreno-Ternero & Alexei Savvateev & Shlomo Weber, 2013. "Stability and fairness in models with a multiple membership," International Journal of Game Theory, Springer;Game Theory Society, vol. 42(3), pages 673-694, August.
    23. Savvateev, A., 2013. "Coalitional Stability of a "Bipolar World"," Journal of the New Economic Association, New Economic Association, vol. 17(1), pages 10-43.
    24. Remy Oddou, 2016. "The Effect of Spillovers and Congestion on the Endogenous Formation of Jurisdictions," Journal of Public Economic Theory, Association for Public Economic Theory, vol. 18(1), pages 67-83, February.
    25. Fujita, Masahisa, 1986. "Optimal location of public facilities : Area dominance approach," Regional Science and Urban Economics, Elsevier, vol. 16(2), pages 241-268, May.
    26. Jo Thori Lind, 2017. "Group Structure and Public Goods Provision in Heterogeneous Societies," Journal of Public Economic Theory, Association for Public Economic Theory, vol. 19(2), pages 377-408, April.
    27. Kolen, Antoon, 1983. "Solving covering problems and the uncapacitated plant location problem on trees," European Journal of Operational Research, Elsevier, vol. 12(3), pages 266-278, March.
    28. Brakman,Steven & Garretsen,Harry & van Marrewijk,Charles, 2009. "The New Introduction to Geographical Economics," Cambridge Books, Cambridge University Press, number 9780521875325, December.
    29. Stern, Nicholas, 1972. "The optimal size of market areas," Journal of Economic Theory, Elsevier, vol. 4(2), pages 154-173, April.
    30. Shlomo Wever & Alexei Savvateev & Michel Le Breton & Anna Bogomolnaia, 2005. "The Egalitarian sharing rule in provision of public goods," Economics Bulletin, AccessEcon, vol. 8(11), pages 1-5.
    31. Johansson, Borje & Leonardi, Giorgio, 1987. "Public facility location: A multiregional and multi-authority decision context," Handbook of Regional and Urban Economics, in: P. Nijkamp (ed.), Handbook of Regional and Urban Economics, edition 1, volume 1, chapter 4, pages 133-170, Elsevier.
    32. Wooders, Myrna, 1980. "The Tiebout Hypothesis: Near Optimality in Local Public Good Economies," Econometrica, Econometric Society, vol. 48(6), pages 1467-1485, September.
    33. 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.
    34. 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.
    35. Bordignon, Massimo & Brusco, Sandro, 2001. "Optimal secession rules," European Economic Review, Elsevier, vol. 45(10), pages 1811-1834, December.
    36. Bloch, Francis & Zenginobuz, E. Unal, 2006. "Tiebout equilibria in local public good economies with spillovers," Journal of Public Economics, Elsevier, vol. 90(8-9), pages 1745-1763, September.
    37. Gordon Mulligan & Mark Partridge & John Carruthers, 2012. "Central place theory and its reemergence in regional science," The Annals of Regional Science, Springer;Western Regional Science Association, vol. 48(2), pages 405-431, April.
    38. Musatov, Daniil & Savvateev, Alexei & Weber, Shlomo, 2016. "Gale–Nikaido–Debreu and Milgrom–Shannon: Communal interactions with endogenous community structures," Journal of Economic Theory, Elsevier, vol. 166(C), pages 282-303.
    39. THISSE, Jacques-François & WILDASIN, David, 1992. "Public facility location and urban spatial structure," LIDAM Reprints CORE 1011, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    40. Savvateev Alexey, 2004. "Achieving stability in heterogeneous societies: multi-jurisdictional structures, and redistribution policies," EERC Working Paper Series 04-13e, EERC Research Network, Russia and CIS.
    41. Greenberg, Joseph & Weber, Shlomo, 1986. "Strong tiebout equilibrium under restricted preferences domain," Journal of Economic Theory, Elsevier, vol. 38(1), pages 101-117, February.
    42. Marakulin, V., 2019. "On the Existence of Spatial Equilibrium and Generalized Fixed Point Theorems," Journal of the New Economic Association, New Economic Association, vol. 42(2), pages 12-34.
    43. Panov, P., 2017. "Nash Equilibria in the Facility Location Problem with Externalities," Journal of the New Economic Association, New Economic Association, vol. 33(1), pages 28-42.
    44. Andreu Mas-Colell, 1980. "Efficiency and Decentralization in the Pure Theory of Public Goods," The Quarterly Journal of Economics, Oxford University Press, vol. 94(4), pages 625-641.
    45. Gabriel Loumeau, 2021. "Locating Public Facilities: Theory and Micro Evidence from Paris," CESifo Working Paper Series 8908, CESifo.
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    More about this item

    Keywords

    club goods; horizontal differentiation of tastes; coalition partition; median principle; egalitarian principle; migrational stability; coalitional stability; fixed-points theorems;
    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
    • D63 - Microeconomics - - Welfare Economics - - - Equity, Justice, Inequality, and Other Normative Criteria and Measurement
    • H41 - Public Economics - - Publicly Provided Goods - - - Public Goods
    • R12 - Urban, Rural, Regional, Real Estate, and Transportation Economics - - General Regional Economics - - - Size and Spatial Distributions of Regional Economic Activity; Interregional Trade (economic geography)

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