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Strategic Interaction in Interacting Particle Systems

  • Paolo Dai PraEmail author
  • Elena Sartori
  • Marco Tolotti
Chapter
Part of the Emergence, Complexity and Computation book series (ECC, volume 27)

Abstract

In the last decades, models inspired by statistical mechanics have been vastly used in the context of social sciences to model the behavior of interacting economic actors. In particular, parallel updating models such as Probabilistic Cellular Automata have been proved to be very useful to represent rational agents aiming at maximize their utility in the presence of social externalities. What PCA do not account for is strategic interaction, i.e., the fact that, when deciding, agents forecast the action of other agents. In this contribution, we compare models that differ in the presence of strategic interaction and memory of past actions. We will show that the emergent equilibria can be very different: Fixed points, cycles of period 2, and chaotic behavior may appear and, possibly, coexist for some values of the parameters, of the model.

Notes

Acknowledgements

We thank Marco LiCalzi and Paolo Pellizzari for inspiring discussions.

References

  1. 1.
    Bouchaud, J.P.: Crises and collective socio-economic phenomena: simple models and challenges. J. Stat. Phys. 151, 567–606 (2013)MathSciNetCrossRefzbMATHGoogle Scholar
  2. 2.
    Brock, W.A., Durlauf, S.N.: Discrete choice with social interactions. Rev. Econ. Stud. 68, 235–260 (2001)MathSciNetCrossRefzbMATHGoogle Scholar
  3. 3.
    Dai Pra, P., Sartori, E., Tolotti, M.: Strategic interaction in trend-driven dynamics. J. Stat. Phys. 152, 724–741 (2013)MathSciNetCrossRefzbMATHGoogle Scholar
  4. 4.
    Dai Pra, P., Scoppola, B., Scoppola, E.: Sampling from a Gibbs measure with pair interaction by means of PCA. J. Stat. Phys. 149, 722–737 (2012)MathSciNetCrossRefzbMATHGoogle Scholar
  5. 5.
    Fudenberg, D.: The Theory of Learning in Games, vol. 2. MIT Press, Cambridge (1998)zbMATHGoogle Scholar
  6. 6.
    Landman, K.A., Binder, B.J., Newgreen, D.F.: Modeling development and disease in our “Second” brain. Cellular Automata, pp. 405–414. Springer, Berlin (2012)CrossRefGoogle Scholar
  7. 7.
    Lämmer, S., Helbing, D.: Self-control of traffic lights and vehicle flows in urban road networks. J. Stat. Mech. Theory Exp. 2008, P04019 (2012)Google Scholar
  8. 8.
    Myerson, R.B.: Game Theory. Harvard University Press, Cambridge (2013)zbMATHGoogle Scholar
  9. 9.
    Piccoli, B., Tosin, A.: Time-evolving measures and macroscopic modeling of pedestrian flow. Arch. Ration. Mech. Anal. 199, 707–738 (2011)MathSciNetCrossRefzbMATHGoogle Scholar

Copyright information

© Springer International Publishing AG 2018

Authors and Affiliations

  1. 1.Dipartimento di MatematicaUniversità di PadovaPadovaItaly
  2. 2.Dipartimento di ManagementUniversità Ca’ FoscariVeneziaItaly

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