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Spatial Equilibrium in a Multidimensional Space: An Immigration-Consistent Division into Countries Centered at Barycenter

  • Valeriy MarakulinEmail author
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11548)

Abstract

It studies the problem of immigration proof partition for communities (countries) in a multidimensional space. This is an existence problem of Tiebout type equilibrium, where migration stability suggests that every inhabitant has no incentives to change current jurisdiction. In particular, an inhabitant at every frontier point has equal costs for all available jurisdictions. It is required that the inter-country border is represented by a continuous curve.

The paper presents the solution for the case of the costs described as the sum of the two values: the ratio of total costs on the total weight of the population plus transportation costs to the center presented as a barycenter of the state. In the literature, this setting is considered as a case of especial theoretical interest and difficulty. The existence of equilibrium division is stated via an approximation reducing the problem to the earlier studied case, in which centers of the states never can coincide: to do this an earlier proved a generalization of conic Krasnosel’skii fixed point theorem is applied.

Keywords

Migration stable partitions Barycenter Tiebout equilibrium Generalized fixed point theorems 

References

  1. 1.
    Alesina, A., Spolaore, E.: On the number and size of nations. Q. J. Econ. 113, 1027–56 (1997)CrossRefGoogle Scholar
  2. 2.
    Krasnosel’skii, M.A.: Fixed points of cone-compressing or cone-extending operators. Proc. USSR Acad. Sci. 135(3), 527–530 (1960). (in Russian)MathSciNetGoogle Scholar
  3. 3.
    Kwong, M.K.: On Krasnoselskii’s cone fixed point theorem. J. Fixed Point Theory Appl. 2008, 18 (2008).  https://doi.org/10.1155/2008/164537MathSciNetCrossRefzbMATHGoogle Scholar
  4. 4.
    Le Breton, M., Musatov, M., Savvateev, A., Weber, S.: Rethinking Alesina and Spolaore’s "uni-dimensional world": existence of migration proof country structures for arbitrary distributed populations. In: Proceedings of XI International Academic Conference on Economic and Social Development 2010, Moscow, 6–8 April 2010: University-Higher School of Economics (2010)Google Scholar
  5. 5.
    Marakulin, V.M.: On the existence of immigration proof partition into countries in multidimensional space. In: Kochetov, Y., Khachay, M., Beresnev, V., Nurminski, E., Pardalos, P. (eds.) DOOR 2016. LNCS, vol. 9869, pp. 494–508. Springer, Cham (2016).  https://doi.org/10.1007/978-3-319-44914-2_39CrossRefGoogle Scholar
  6. 6.
    Marakulin, V., M.: Spatial equilibrium on the plane and an arbitrary population distribution. In: Evtushenko, Yu. G. et al. (eds.) Proceedings of the OPTIMA-2017 Conference, Petrovac, Montenegro, 02–06 October 2017, CEUR Workshop Proceedings, vol 1987, pp. 378–385 (1987)Google Scholar
  7. 7.
    Marakulin, V.M.: Spatial equilibrium: the existence of immigration proof partition into countries for one-dimensional space. Siberian J. Pure Appl. Math. 17(4), 64–78 (2017). (in Russian)MathSciNetGoogle Scholar
  8. 8.
    Marakulin, V.M.: General spatial equilibrium and generalized Brouwer fixed point theorem. Mimeo, 20 p. (2017)Google Scholar
  9. 9.
    Marakulin, V.M.: On the existence of spatial equilibrium and generalized fixed point theorems. J. New Economic Assoc. (42) (2019, forthcoming). (in Russian)Google Scholar
  10. 10.
    Musatov, M., Savvateev, A., Weber, S.: Gale-Nikaido-Debreu and Milgrom-Shannon: communal interactions with endogenous community structures. J. Econ. Theory 166, 282–303 (2016)MathSciNetCrossRefGoogle Scholar
  11. 11.
    Savvateev, A., Sorokin, C., Weber, S.: Multidimensional free-mobility equilibrium: Tiebout revisited. Mimeo, 25 p. (2018)Google Scholar
  12. 12.
    Tiebout, C.M.: A pure theory of local expenditures. J. Polit. Econ. 64, 416–424 (1956)CrossRefGoogle Scholar

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Sobolev Institute of Mathematics, Russian Academy of SciencesNovosibirskRussia
  2. 2.Novosibirsk State UniversityNovosibirskRussia

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