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Spatial Competition and Price Formation


  • Kai Nagel
  • Martin Shubik
  • Maya Paczuski
  • Per Bak


We look at price formation in a retail setting, that is, companies set prices, and consumers either accept prices or go someplace else. In contrast to most other models in this context, we use a two-dimensional spatial structure for information transmission, that is, consumers can only learn from nearest neighbors. Many aspects of this can be understood in terms of generalized evolutionary dynamics. In consequence, we first look at spatial competition and cluster formation without price. This leads to establishment size distributions, which we compare to reality. After some theoretical considerations, which at least heuristically explain our simulation results, we finally return to price formation, where we demonstrate that our simple model with nearly no organized planning or rationality on the part of any of the agents indeed leads to an economically plausible price.

Suggested Citation

  • Kai Nagel & Martin Shubik & Maya Paczuski & Per Bak, 2000. "Spatial Competition and Price Formation," Working Papers 00-05-029, Santa Fe Institute.
  • Handle: RePEc:wop:safiwp:00-05-029

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    References listed on IDEAS

    1. Kiyotaki, Nobuhiro & Wright, Randall, 1989. "On Money as a Medium of Exchange," Journal of Political Economy, University of Chicago Press, vol. 97(4), pages 927-954, August.
    2. Hehenkamp, Burkhard, 2002. "Sluggish Consumers: An Evolutionary Solution to the Bertrand Paradox," Games and Economic Behavior, Elsevier, vol. 40(1), pages 44-76, July.
    3. Per Bak & Simon F. Norrelykke & Martin Shubik, 1998. "The Dynamics of Money," Research in Economics 98-11-102e, Santa Fe Institute.
    4. Stanley, Michael H. R. & Buldyrev, Sergey V. & Havlin, Shlomo & Mantegna, Rosario N. & Salinger, Michael A. & Eugene Stanley, H., 1995. "Zipf plots and the size distribution of firms," Economics Letters, Elsevier, vol. 49(4), pages 453-457, October.
    5. Burkhard Hehenkamp & Wolfgang Leininger, 1999. "A note on evolutionary stability of Bertrand equilibrium," Journal of Evolutionary Economics, Springer, vol. 9(3), pages 367-371.
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    Cited by:

    1. Tomoya Mori & Koji Nishikimi & Tony E. Smith, 2008. "The Number-Average Size Rule: A New Empirical Relationship Between Industrial Location And City Size," Journal of Regional Science, Wiley Blackwell, vol. 48(1), pages 165-211.
    2. Tomoya Mori & Koji Nishikimi & Tony E. Smith, 2002. "Some Empirical Regularities of Spatial Economies: A Relationship between Industrial Location and City Size," KIER Working Papers 551, Kyoto University, Institute of Economic Research.
    3. Tomoya Mori & Tony E. Smith, 2009. "A Reconsideration of the NAS Rule from an Industrial Agglomeration Perspective," KIER Working Papers 669, Kyoto University, Institute of Economic Research.
    4. D'Hulst, R. & Rodgers, G.J., 2001. "Business size distributions," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 299(1), pages 328-333.

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