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Effective history length of the minority game

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  • Hung, Chia-Hsiang
  • Liaw, Sy-Sang

Abstract

It is known that the memory is relevant in the symmetric phase of the minority game. In our previous work we have successfully explained the quasi-periodic behavior of the game in the symmetric phase with the help of the probability theory. Based on this explanation, we are able to determine how the history length affects the variance of the system in this paper. By using some particular types of fake history such as periodic type and random type, we determine how efficient the history length has been used in the standard game. Furthermore, the analysis on the effective history length strongly supports the result we proposed previously that there are three distinct phases in the minority game.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:phsmap:v:382:y:2007:i:1:p:129-137
    DOI: 10.1016/j.physa.2007.02.048
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    References listed on IDEAS

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    1. A C C Coolen & J A F Heimel, 2001. "Dynamical Solution of the On-Line Minority Game," Papers cond-mat/0107600, arXiv.org.
    2. Liaw, Sy-Sang & Liu, Ching, 2005. "The quasi-periodic time sequence of the population in minority game," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 351(2), pages 571-579.
    3. Zheng, Dafang & Wang, Bing-Hong, 2001. "Statistical properties of the attendance time series in the minority game," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 301(1), pages 560-566.
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    5. Challet, Damien & Zhang, Yi-Cheng, 1998. "On the minority game: Analytical and numerical studies," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 256(3), pages 514-532.
    6. Manuca, Radu & Li, Yi & Riolo, Rick & Savit, Robert, 2000. "The structure of adaptive competition in minority games," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 282(3), pages 559-608.
    7. Liaw, Sy-Sang & Hung, Chia-Hsiang & Liu, Ching, 2007. "Three phases of the minority game," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 374(1), pages 359-368.
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