IDEAS home Printed from https://ideas.repec.org/
MyIDEAS: Login to save this paper or follow this series

On Stable Equilibria in Discrete-Space Social Interaction Models

  • Akamatsu, Takashi
  • Fujishima, Shota
  • Takayama, Yuki

We investigate the differences and connections between discrete-space and continuous-space social interaction models. Although our class of continuous-space model has a unique equilibrium, we find that discretized models can have multiple equilibria for any degree of discretization, which necessitates a stability analysis of equilibria. We present a general framework for characterizations of equilibria and their stability under a broad class of evolutionary dynamics by using the properties of a potential game. Although the equilibrium population distribution in the continuous space is uniquely given by a symmetric unimodal distribution, we find that such a distribution is not always stable in a discrete space. On the other hand, we also show that any sequence of a discrete-space model's equilibria converges with the continuous-space model's unique equilibrium as the discretization is refined.

If you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.

File URL: http://mpra.ub.uni-muenchen.de/55938/1/MPRA_paper_55938.pdf
File Function: original version
Download Restriction: no

File URL: http://mpra.ub.uni-muenchen.de/61184/8/MPRA_paper_61184.pdf
File Function: revised version
Download Restriction: no

Paper provided by University Library of Munich, Germany in its series MPRA Paper with number 55938.

as
in new window

Length:
Date of creation: 08 May 2014
Date of revision:
Handle: RePEc:pra:mprapa:55938
Contact details of provider: Postal: Schackstr. 4, D-80539 Munich, Germany
Phone: +49-(0)89-2180-2219
Fax: +49-(0)89-2180-3900
Web page: http://mpra.ub.uni-muenchen.de

More information through EDIRC

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.:

as in new window
  1. Oyama, Daisuke, 2009. "History versus expectations in economic geography reconsidered," Journal of Economic Dynamics and Control, Elsevier, vol. 33(2), pages 394-408, February.
  2. J. Swinkels, 2010. "Adjustment Dynamics and Rational Play in Games," Levine's Working Paper Archive 456, David K. Levine.
  3. Geoffrey Caruso & Dominique Peeters & Jean Cavailh�s & Mark Rounsevell, 2009. "Space – time patterns of urban sprawl, a 1D cellular automata and microeconomic approach," Environment and Planning B: Planning and Design, Pion Ltd, London, vol. 36(6), pages 968-988, November.
  4. Fujishima, Shota, 2013. "Evolutionary implementation of optimal city size distributions," Regional Science and Urban Economics, Elsevier, vol. 43(2), pages 404-410.
  5. Sandholm, William H., 2005. "Excess payoff dynamics and other well-behaved evolutionary dynamics," Journal of Economic Theory, Elsevier, vol. 124(2), pages 149-170, October.
  6. Kiminori Matsuyama, 2013. "Endogenous Ranking and Equilibrium Lorenz Curve Across (ex ante) Identical Countries," Econometrica, Econometric Society, vol. 81(5), pages 2009-2031, 09.
  7. Monderer, Dov & Shapley, Lloyd S., 1996. "Potential Games," Games and Economic Behavior, Elsevier, vol. 14(1), pages 124-143, May.
  8. Mossay, P. & Picard, P.M., 2011. "On spatial equilibria in a social interaction model," Journal of Economic Theory, Elsevier, vol. 146(6), pages 2455-2477.
  9. Caruso, Geoffrey & Peeters, Dominique & Cavailhes, Jean & Rounsevell, Mark, 2007. "Spatial configurations in a periurban city. A cellular automata-based microeconomic model," Regional Science and Urban Economics, Elsevier, vol. 37(5), pages 542-567, September.
  10. Oyama, Daisuke, 2006. "Agglomeration under Forward-Looking Expectations: Potentials and Global Stability," MPRA Paper 15239, University Library of Munich, Germany.
  11. repec:cup:cbooks:9781107001411 is not listed on IDEAS
  12. repec:cup:cbooks:9780521171960 is not listed on IDEAS
  13. T Tabuchi, 1982. "Optimal distribution of city sizes in a region," Environment and Planning A, Pion Ltd, London, vol. 14(1), pages 21-32, January.
  14. Anas, Alex & Xu, Rong, 1999. "Congestion, Land Use, and Job Dispersion: A General Equilibrium Model," Journal of Urban Economics, Elsevier, vol. 45(3), pages 451-473, May.
  15. Josef Hofbauer & William H. Sandholm, 2002. "On the Global Convergence of Stochastic Fictitious Play," Econometrica, Econometric Society, vol. 70(6), pages 2265-2294, November.
  16. Sandholm, William H., 2007. "Pigouvian pricing and stochastic evolutionary implementation," Journal of Economic Theory, Elsevier, vol. 132(1), pages 367-382, January.
  17. O'Hara, Donald J, 1977. "Location of Firms within a Square Central Business District," Journal of Political Economy, University of Chicago Press, vol. 85(6), pages 1189-1207, December.
  18. E Borukhov & O Hochman, 1977. "Optimum and market equilibrium in a model of a city without a predetemined center," Environment and Planning A, Pion Ltd, London, vol. 9(8), pages 849-856, August.
  19. Turner, Matthew A., 2005. "Landscape preferences and patterns of residential development," Journal of Urban Economics, Elsevier, vol. 57(1), pages 19-54, January.
  20. I. Gilboa & A. Matsui, 2010. "Social Stability and Equilibrium," Levine's Working Paper Archive 534, David K. Levine.
  21. Sandholm, William H., 2001. "Potential Games with Continuous Player Sets," Journal of Economic Theory, Elsevier, vol. 97(1), pages 81-108, March.
  22. Braid, Ralph M., 1988. "Heterogeneous preferences and non-central agglomeration of firms," Regional Science and Urban Economics, Elsevier, vol. 18(1), pages 57-68, February.
  23. Tabuchi, Takatoshi, 1986. "Urban agglomeration economies in a Linear City," Regional Science and Urban Economics, Elsevier, vol. 16(3), pages 421-436, August.
Full references (including those not matched with items on IDEAS)

This item is not listed on Wikipedia, on a reading list or among the top items on IDEAS.

When requesting a correction, please mention this item's handle: RePEc:pra:mprapa:55938. See general information about how to correct material in RePEc.

For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Ekkehart Schlicht)

If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

If references are entirely missing, you can add them using this form.

If the full references list an item that is present in RePEc, but the system did not link to it, you can help with this form.

If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your profile, as there may be some citations waiting for confirmation.

Please note that corrections may take a couple of weeks to filter through the various RePEc services.

This information is provided to you by IDEAS at the Research Division of the Federal Reserve Bank of St. Louis using RePEc data.