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The Full Strategy Minority Game

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  • Acosta, Gabriel
  • Caridi, Inés
  • Guala, Sebastián
  • Marenco, Javier

Abstract

The Full Strategy Minority Game (FSMG) is an instance of the Minority Game (MG) which includes a single copy of every potential agent. In this work, we explicitly solve the FSMG thanks to certain symmetries of this game. Furthermore, by considering the MG as a statistical sample of the FSMG, we compute approximated values of the key variable σ2/N in the symmetric phase for different versions of the MG. As another application we prove that our results can be easily modified in order to handle certain kinds of initial biased strategy scores, in particular when the bias is introduced at the agents’ level. We also show that the FSMG verifies a strict period two dynamics (i.e., period two dynamics satisfied with probability 1) giving, to the best of our knowledge, the first example of an instance of the MG for which this feature can be analytically proved. Thanks to this property, it is possible to compute in a simple way the probability that a general instance of the MG breaks the period two dynamics for the first time in a given simulation.

Suggested Citation

  • Acosta, Gabriel & Caridi, Inés & Guala, Sebastián & Marenco, Javier, 2012. "The Full Strategy Minority Game," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(1), pages 217-230.
    • Handle: RePEc:eee:phsmap:v:391:y:2012:i:1:p:217-230
    DOI: 10.1016/j.physa.2011.07.049
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    References listed on IDEAS

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    1. 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.
    2. 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.
    3. Caridi, Inés & Ceva, Horacio, 2003. "Minority game: a mean-field-like approach," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 317(1), pages 247-258.
    4. Challet, D. & Zhang, Y.-C., 1997. "Emergence of cooperation and organization in an evolutionary game," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 246(3), pages 407-418.
    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.
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    1. Acosta, Gabriel & Caridi, Inés & Guala, Sebastián & Marenco, Javier, 2013. "The quasi-periodicity of the minority game revisited," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(19), pages 4450-4465.

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