Economic Theory

, Volume 30, Issue 2, pp 223–241 | Cite as

Type interaction models and the rule of six

Research Article

Abstract

In this paper, I describe and analyze a class of type interaction models. In these models, an infinite population of agents with discrete types interact in groups of fixed size and possibly change their types as a function of those interactions. I then derive conditions for these models to produce multiple equilibria. These conditions demonstrate a trade off between the number of types and the size of the interacting groups. For deterministic interaction rules, I derive the rule of six: the number of agent types plus the group size must be at least six in order to support multiple equilibria given a spanning assumption.

Keywords

Interactions Multiple equilibria Dynamics 

JEL Classification Numbers

C00 

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References

  1. Alberts B., Bray D., Lewis J., Raff M., Roberts K., Watson J. (1994). Molecular biology of the cell NCBI. Garland Publishing, New YorkGoogle Scholar
  2. Arthur B. (1994). Increasing returns and path dependence in the economy. The University of Michigan Press, Ann ArborGoogle Scholar
  3. Axelrod R., Mitchell W., Thomas R., Bennett D.S., Bruderer E. (1995). Coalition formation in standard setting alliances. Manage Sci 41:1493–1508CrossRefGoogle Scholar
  4. Axelrod R. (1997). The dissemination of culture: a model with local convergence and global polarization. J Conflict Resolut 41:203–226Google Scholar
  5. Bikhchandani S., Hirshleifer D., Welch D. (1992). A theory of fads, fashions, custom, and cultural change as information cascades. J Polit Econ 100:992–1026CrossRefGoogle Scholar
  6. Bikhchandani S., Hirshleifer D., Welch I. (1998). Fads, and informational cascades. J Econ Perspect 12(3):151–170Google Scholar
  7. Banerjee A. (1992). A simple model of herd behavior. Q J Econ 107:797–817CrossRefGoogle Scholar
  8. Blume L. (1993). The statistical mechanics of strategic interaction. Games and Econ Behav 5:387–426CrossRefGoogle Scholar
  9. David P. (1985). Clio and the economics of QWERTY. Am Econ Rev 75(2):332–337Google Scholar
  10. Durlauf S. (1997). Statistical mechanics approaches to socioeconomic behavior. In: Arthur W.B., Durlauf S., Lane D (eds). The economy as an evolving complex system II. Addison-Wesley, Menlo Park, CAGoogle Scholar
  11. Foster D., Young H.P. (1990). Stochastic evolutionary game dynamics. Theor Popul Biol 38:219–232CrossRefGoogle Scholar
  12. Glaeser E., Sacerdotal B., Scheinkman J. (1996). Crime and social interactions. Q J Econ CXI:507–548CrossRefGoogle Scholar
  13. Holland J.H. (1975). Adaptation in natural and artificial systems. University of Michigan Press, Ann ArborGoogle Scholar
  14. Kandori M., Mailath G., Rob R. (1992). Learning, mutation, and long run equilibria in games. Econometrica 61:29–56CrossRefGoogle Scholar
  15. Manski C. (1993). Identification problems in the social sciences. Basil Blackwell, CambridgeGoogle Scholar
  16. Picker R. (1997). Simple rules in a complex world: A generative approach to the adoption of norms. Univ Chic Law Rev 64:1225CrossRefGoogle Scholar
  17. Watts D. (1999). Small worlds: The dynamics of networks between order and randomness. Princeton University Press, Princeton, NJGoogle Scholar
  18. Wolfram S. (1994). Cellular automata and complexity. Reading, Addison-WesleyGoogle Scholar
  19. Wolfram S. (2002). A new kind of science. Wolfram Media, Champaign, ILGoogle Scholar

Copyright information

© Springer 2005

Authors and Affiliations

  1. 1.Center for the Study of Complex Systems, Departments of Political Science and EconomicsThe University of MichiganAnn ArborUSA

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