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Dynamical Solution of the On-Line Minority Game

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  • A C C Coolen
  • J A F Heimel

Abstract

We solve the dynamics of the on-line minority game, with general types of decision noise, using generating functional techniques a la De Dominicis and the temporal regularization procedure of Bedeaux et al. The result is a macroscopic dynamical theory in the form of closed equations for correlation- and response functions defined via an effective continuous-time single-trader process, which are exact in both the ergodic and in the non-ergodic regime of the minority game. Our solution also explains why, although one cannot formally truncate the Kramers-Moyal expansion of the process after the Fokker-Planck term, upon doing so one still finds the correct solution, that the previously proposed diffusion matrices for the Fokker-Planck term are incomplete, and how previously proposed approximations of the market volatility can be traced back to ergodicity assumptions.

Suggested Citation

  • A C C Coolen & J A F Heimel, 2001. "Dynamical Solution of the On-Line Minority Game," Papers cond-mat/0107600, arXiv.org.
    • Handle: RePEc:arx:papers:cond-mat/0107600
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    Cited by:

    1. Damien Challet & Tobias Galla, 2005. "Price return autocorrelation and predictability in agent-based models of financial markets," Quantitative Finance, Taylor & Francis Journals, vol. 5(6), pages 569-576.
    2. Hung, Chia-Hsiang & Liaw, Sy-Sang, 2007. "Effective history length of the minority game," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 382(1), pages 129-137.
    3. Matteo Ortisi & Valerio Zuccolo, 2012. "From Minority Game to Black & Scholes pricing," Papers 1205.2521, arXiv.org, revised May 2013.

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