Mitigating cascades in sandpile models: an immunization strategy for systemic risk?


We use a simple model of distress propagation (the sandpile model) to show how financial systems are naturally subject to the risk of systemic failures. Taking into account possible network structures among financial institutions, we investigate if simple policies can limit financial distress propagation to avoid system-wide crises, i.e. to dampen systemic risk. We therefore compare different immunization policies (i.e. targeted helps to financial institutions) and find that the information coming from the network topology allows to mitigate systemic cascades by targeting just few institutions.

This is a preview of subscription content, log in to check access.


  1. 1.

    J. Lorenz, S. Battiston, F. Schweitzer, Eur. Phys. J. B 71, 441 (2009)

    ADS  MathSciNet  Article  Google Scholar 

  2. 2.

    S. Battiston, M. Puliga, R. Kaushik, P. Tasca, G. Caldarelli, Sci. Rep. 2, 541 (2012)

    ADS  Article  Google Scholar 

  3. 3.

    M. Bardoscia, S. Battiston, F. Caccioli, G. Caldarelli, PLoS ONE 10, e0130406 (2015)

    Article  Google Scholar 

  4. 4.

    N. Musmeci, S. Battiston, G. Caldarelli, M. Puliga, A. Gabrielli, J. Stat. Phys. 151, (2013)

  5. 5.

    P. Bak, C. Tang, K. Wiesenfeld, Phys. Rev. Lett. 59, 381 (1987)

    ADS  MathSciNet  Article  Google Scholar 

  6. 6.

    G. D’Agostino, A. Scala, V. Zlatic, G. Caldarelli, EPL 97, 68006 (2012)

    ADS  Article  Google Scholar 

  7. 7.

    D. Dhar, R. Ramaswamy, Phys. Rev. Lett. 63, 1659 (1989)

    ADS  MathSciNet  Article  Google Scholar 

  8. 8.

    C. Tang, P. Bak, Phys. Rev. Lett. 60, 2347 (1988)

    ADS  Article  Google Scholar 

  9. 9.

    D. Dhar, Phys. Rev. Lett. 64 1613 (1990)

    ADS  MathSciNet  Article  Google Scholar 

  10. 10.

    T.E. Harris. The theory of branching processes. Die Grundlehren der Mathematischen Wissenschaften, Bd. 119 (Springer-Verlag, Berlin, 1963)

  11. 11.

    K.-I. Goh, D.-S. Lee, B. Kahng, D. Kim, Phys. Rev. Lett. 91, 148701 (2003)

    ADS  Article  Google Scholar 

  12. 12.

    J.P. da Cruz, P. G. Lind, Phys. Stat. Mech. Appl. 391, 1445 (2012)

    Article  Google Scholar 

  13. 13.

    P. Bak, K. Chen, J. Scheinkman, M. Woodford, Ricerche Economiche 47, 3 (1993)

    Article  Google Scholar 

  14. 14.

    J. Scheinkman, M. Woodford, Am. Econ. Rev. 84, 417 (1994)

    Google Scholar 

  15. 15.

    N. Xi, P. Ormerod, Y. Wang, Self-organized criticality in market economies, 17th International Conference on Computing in Economics and Finance (CEF 2011), Society for Computational Economics Sponsored by the Federal Reserve Bank of San Francisco June 29 through July 1, 2011 Session : B5: Intermarket Dynamics Self-Organized Criticality in Market Economies By N. Xi; University of Shanghai for Science and Technology paul ormerod; Volterra Consulting Yougui Wang; Beijing Normal University Presented by: Yougui Wang, Beijing Normal University

  16. 16.

    S. Gualdi, M. Medo, Y.-C. Zhang, Eur. Phys. J. B 79, 91 (2011)

    ADS  Article  Google Scholar 

  17. 17.

    P. Gai, S. Kapadia, Proc. R. Soc. London Math. Phys. Eng. Sci. 466, 2401 (2010)

    ADS  MathSciNet  Article  Google Scholar 

  18. 18.

    L. Eisenberg, T.H. Noe, Management Science, INFORMS 47, 236 (2001)

    Google Scholar 

  19. 19.

    K. Christensen, Z. Olami, Phys. Rev. E 48, 3361 (1993)

    ADS  Article  Google Scholar 

  20. 20.

    J.D. Noh, H. Rieger, Phys. Rev. Lett. 92, 118701 (2004)

    ADS  Article  Google Scholar 

  21. 21.

    Y. Shilo, O. Biham, Phys. Rev. E 67, 066102, (2003)

    ADS  Article  Google Scholar 

  22. 22.

    X. Huang, I. Vodenska, S. Havlin, H.E. Stanley, Sci. Rep. 3, 1219 (2013)

    ADS  Google Scholar 

  23. 23.

    G. D’Agostino, A. Scala (eds.) Networks of Networks: The Last Frontier of Complexity. Understanding Complex Systems (Springer International Publishing, 2014)

  24. 24.

    C.D. Brummitt, T. Kobayashi, Phys. Rev. E 91, 062813 (2015)

    ADS  Article  Google Scholar 

  25. 25.

    A. Scala, P.G. De Sanctis Lucentini, G. Caldarelli, G. DAgostino, Physica D 323324, 35 (2016)

    ADS  Article  Google Scholar 

Download references

Author information



Corresponding author

Correspondence to Antonio Scala.

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Scala, A., Zlatić, V., Caldarelli, G. et al. Mitigating cascades in sandpile models: an immunization strategy for systemic risk?. Eur. Phys. J. Spec. Top. 225, 2017–2023 (2016).

Download citation