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Herding as a consensus problem

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Abstract

In this paper, we show that herding phenomena in financial markets can be interpreted using the theoretical tools of pinning control. This is accomplished by viewing herding as a diffusion of a certain opinion in a network of financial agents, whose trading strategies dynamically depend on that of their neighbors according to a nonlinear state-dependent law. The interaction among the agents is modeled through a directed weighted graph, and following the logic of pinning control, we model the generic exogenous information triggering herding behavior as a control signal fed by an external entity to a subset of agents that, by virtue of the received information, can play the correct trading action. The topological conditions of partial pinning control theory enable us to predict the number of agents reaching consensus, i.e., the diffusion of information through the network, and thus the magnitude of the herding phenomenon triggered by the informed/pinned nodes. By testing our model of opinion dynamics in an artificial agent-based financial market, we prove that it is capable of replicating herding phenomena of different and predictable intensities.

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References

  1. Avery, C., Zemsky, P.: Multidimensional uncertainty and herd behavior in financial markets. Am. Econ. Rev. 88, 724–748 (1998)

    Google Scholar 

  2. Banerjee, A.V.: A simple model of herd behavior. Q. J. Econ. 107, 797–817 (1992)

    Article  Google Scholar 

  3. Bargigli, L., Tedeschi, G.: Interaction in agent-based economics: a survey on the network approach. Phys. A Stat. Mech. Appl. 399, 1–15 (2014)

    Article  MathSciNet  Google Scholar 

  4. Barmish, B.R., Primbs, J.A.: On market-neutral stock trading arbitrage via linear feedback. In: 2012 American Control Conference (ACC), pp. 3693–3698. IEEE (2012)

  5. Bikhchandani, S., Hirshleifer, D., Welch, I.: A theory of fads, fashion, custom, and cultural change as informational cascades. J. Political Econ. 100, 992–1026 (1992)

    Article  Google Scholar 

  6. DeGroot, M.H.: Reaching a consensus. J. Am. Stat. Assoc. 69(345), 118–121 (1974)

    Article  MATH  Google Scholar 

  7. DeLellis, P., di Bernardo, M., Russo, G.: On quad, lipschitz, and contracting vector fields for consensus and synchronization of networks. IEEE Trans. Circuits Syst. I Regul. Papers 58(3), 576–583 (2011)

    Article  MathSciNet  Google Scholar 

  8. DeLellis, P., Garofalo, F., Iudice, F.L.: Partial pinning control of complex networks. In: 2016 IEEE 55th Conference on Decision and Control (CDC), pp. 7398–7403. IEEE (2016)

  9. DeLellis, P., Garofalo, F., Iudice, F.L., Napoletano, E.: Wealth distribution across communities of adaptive financial agents. New J. Phys. 17(8), 083003 (2015)

    Article  Google Scholar 

  10. DeLellis, P., Garofalo, F., Lo Iudice, F.: The partial pinning control strategy for large complex networks. Automatica 89, 111–116 (2018)

    Article  MathSciNet  Google Scholar 

  11. DeLellis, P., Meglio Anna Di, F., Iudice, F.L.: Overconfident agents and evolving financial networks. Nonlinear Dyn. 1–8 (2017)

  12. Devenow, A., Welch, I.: Rational herding in financial economics. Eur. Econ. Rev. 40(3), 603–615 (1996)

    Article  Google Scholar 

  13. Estrada, E., Vargas-Estrada, E., Ando, H.: Communicability angles reveal critical edges for network consensus dynamics. Phys. Rev. E 92(5), 052809 (2015)

    Article  MathSciNet  Google Scholar 

  14. Farmer, J.D., Foley, D.: The economy needs agent-based modelling. Nature 460(7256), 685–686 (2009)

    Article  Google Scholar 

  15. Friedkin, N.E., Johnsen, E.: Social influence networks and opinion change. Adv. Group Process. 16, 1–29 (1999)

    Google Scholar 

  16. Friedkin, N.E., Proskurnikov, A.V., Tempo, R., Parsegov, S.E.: Network science on belief system dynamics under logic constraints. Science 354(6310), 321–326 (2016)

    Article  MathSciNet  MATH  Google Scholar 

  17. Gleason, K.C., Lee, C.I., Mathur, I.: Herding behavior in european futures markets. Finance Lett. 1(1), 5–8 (2003)

    Google Scholar 

  18. Hegselmann, R., Krause, U., et al.: Opinion dynamics and bounded confidence models, analysis, and simulation. J. Artif. Soc. Soc. Simul. 5(3), 1–33 (2002)

    Google Scholar 

  19. Hirshleifer, D., Hong Teoh, S.: Herd behaviour and cascading in capital markets: a review and synthesis. Eur. Financ. Manag. 9(1), 25–66 (2003)

    Article  Google Scholar 

  20. Holt, C.A., Laury, S.K., et al.: Risk aversion and incentive effects. Am. Econ. Rev. 92(5), 1644–1655 (2002)

    Article  Google Scholar 

  21. Huang, M., Manton, J.H.: Coordination and consensus of networked agents with noisy measurements: stochastic algorithms and asymptotic behavior. SIAM J. Control Optim. 48(1), 134–161 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  22. Ingersoll, J.E.: Theory of Financial Decision Making, vol. 3. Rowman & Littlefield, Lanham, Maryland, USA (1987)

    Google Scholar 

  23. Kaltwasser, P.R.: Uncertainty about fundamentals and herding behavior in the FOREX market. Phys. A Stat. Mech. Appl. 389(6), 1215–1222 (2010)

    Article  Google Scholar 

  24. Klamser, P.P., Wiedermann, M., Donges, J.F., Donner, R.V.: Zealotry effects on opinion dynamics in the adaptive voter model (2016). Preprint. arXiv:1612.06644

  25. Kononovicius, A., Gontis, V.: Three-state herding model of the financial markets. EPL (Europhys. Lett.) 101(2), 28001 (2013)

    Article  Google Scholar 

  26. Kremer, S., Nautz, D.: Causes and consequences of short-term institutional herding. J. Bank. Finance 37(5), 1676–1686 (2013)

    Article  Google Scholar 

  27. Lakonishok, J., Shleifer, A., Vishny, R.W.: The impact of institutional trading on stock prices. J. Financ. Econ. 32(1), 23–43 (1992)

    Article  Google Scholar 

  28. Li, K., Sun, W., Small, M., Fu, X.: Practical synchronization on complex dynamical networks via optimal pinning control. Phys. Rev. E 92(1), 010903 (2015)

    Article  MathSciNet  Google Scholar 

  29. Lillo, F., Moro, E., Vaglica, G., Mantegna, R.N.: Specialization and herding behavior of trading firms in a financial market. New J. Phys. 10(4), 043019 (2008)

    Article  MathSciNet  Google Scholar 

  30. Lotero, L., Hurtado, R.G., Floría, L.M., Gómez-Gardeñes, J.: Rich do not rise early: spatio-temporal patterns in the mobility networks of different socio-economic classes. R. Soc. Open Sci. 3(10), 150654 (2016)

    Article  MathSciNet  Google Scholar 

  31. Mai, V.S., Abed, E.H.: Opinion dynamics with persistent leaders. In: 2014 IEEE 53rd Annual Conference on Decision and Control (CDC), pp. 2907–2913. IEEE (2014)

  32. Mirtabatabaei, A., Jia, P., Friedkin, N.E., Bullo, F.: On the reflected appraisals dynamics of influence networks with stubborn agents. In: American Control Conference (ACC), pp. 3978–3983. IEEE (2014)

  33. Parker, W.D., Prechter, R.R.: Herding: an interdisciplinary integrative review from a socioeconomic perspective. Available at SSRN 2009898 (2005)

  34. Parsegov, S.E., Proskurnikov, A.V., Tempo, R., Friedkin, N.E.: Novel multidimensional models of opinion dynamics in social networks. IEEE Trans. Autom. Control 62, 2270 (2016)

    Article  MathSciNet  MATH  Google Scholar 

  35. Proskurnikov, A.V., Tempo, R.: A tutorial on modeling and analysis of dynamic social networks. Part I. Ann. Rev. Control 43, 65 (2017)

    Article  Google Scholar 

  36. Shapira, Y., Berman, Y., Ben-Jacob, E.: Modelling the short term herding behaviour of stock markets. New J. Phys. 16(5), 053040 (2014)

    Article  Google Scholar 

  37. Sorrentino, F., di Bernardo, M., Garofalo, F., Chen, G.: Controllability of complex networks via pinning. Phys. Rev. E 75(4), 046103 (2007)

  38. Tian, Y., Wang, L.: Opinion consensus in social networks with stubborn agents: an issue-based perspective (2016). Preprint. arXiv:1609.03465

  39. Von Neumann, J., Morgenstern, O.: Theory of Games and Economic Behavior. Princeton University Press, Princeton (2007)

    MATH  Google Scholar 

  40. Welch, I.: Herding among security analysts. J. Financ. Econ. 58(3), 369–396 (2000)

    Article  Google Scholar 

  41. Yang, C., Hu, S., Xia, B.: The endogenous dynamics of financial markets: interaction and information dissemination. Physica A 391(12), 3513–3525 (2012)

    Article  Google Scholar 

  42. Zhang, J.: Strategic delay and the onset of investment cascades. RAND J. Econ. 28, 188–205 (1997)

    Article  Google Scholar 

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Authors and Affiliations

  1. Department of Electrical Engineering and Information Technology, University of Naples Federico II, Via Claudio 21, Naples, Italy

    Franco Garofalo, Francesco Lo Iudice & Elena Napoletano

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  1. Franco Garofalo
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  2. Francesco Lo Iudice
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  3. Elena Napoletano
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Correspondence to Elena Napoletano.

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Garofalo, F., Lo Iudice, F. & Napoletano, E. Herding as a consensus problem. Nonlinear Dyn 92, 25–32 (2018). https://doi.org/10.1007/s11071-018-4094-4

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  • DOI: https://doi.org/10.1007/s11071-018-4094-4

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