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Stochastic analysis of an agent-based model

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  • Veglio, A.
  • Marsili, M.

Abstract

We analyze the dynamics of a forecasting game that exhibits the phenomenon of information cascades. Each agent aims at correctly predicting a binary variable and he/she can either look for independent information or herd on the choice of others. We show that dynamics can be analytically described in terms of a Langevin equation and its collective behavior is described by the solution of a Kramers’ problem. This provides very accurate results in the region where the vast majority of agents herd, that corresponds to the most interesting one from a game theoretic point of view.

Suggested Citation

  • Veglio, A. & Marsili, M., 2007. "Stochastic analysis of an agent-based model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 385(2), pages 631-636.
    • Handle: RePEc:eee:phsmap:v:385:y:2007:i:2:p:631-636
    DOI: 10.1016/j.physa.2007.07.027
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    References listed on IDEAS

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    1. Olivier Guedj & Jean-Philippe Bouchaud, 2004. "Experts' earning forecasts: bias, herding and gossamer information," Papers cond-mat/0410079, arXiv.org.
    2. Anders Johansen & Olivier Ledoit & Didier Sornette, 2000. "Crashes As Critical Points," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 3(02), pages 219-255.
    3. Bikhchandani, Sushil & Hirshleifer, David & Welch, Ivo, 1992. "A Theory of Fads, Fashion, Custom, and Cultural Change in Informational Cascades," Journal of Political Economy, University of Chicago Press, vol. 100(5), pages 992-1026, October.
    4. Olivier Guedj & Jean-Philippe Bouchaud, 2004. "Experts' earning forecasts: bias, herding and gossamer information," Science & Finance (CFM) working paper archive 500062, Science & Finance, Capital Fund Management.
    5. Philippe Curty & Matteo Marsili, 2005. "Phase coexistence in a forecasting game," Papers physics/0506151, arXiv.org, revised Feb 2006.
    6. Kaizoji, Taisei & Bornholdt, Stefan & Fujiwara, Yoshi, 2002. "Dynamics of price and trading volume in a spin model of stock markets with heterogeneous agents," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 316(1), pages 441-452.
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