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Phenomenology of minority games in efficient regime

  • Karol Wawrzyniak
  • Wojciech Wislicki
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    We present a comprehensive study of utility function of the minority game in its efficient regime. We develop an effective description of state of the game. For the payoff function $g(x)=\sgn (x)$ we explicitly represent the game as the Markov process and prove the finitness of number of states. We also demonstrate boundedness of the utility function. Using these facts we can explain all interesting observable features of the aggregated demand: appearance of strong fluctuations, their periodicity and existence of prefered levels. For another payoff, $g(x)=x$, the number of states is still finite and utility remains bounded but the number of states cannot be reduced and probabilities of states are not calculated. However, using properties of the utility and analysing the game in terms of de Bruijn graphs, we can also explain distinct peaks of demand and their frequencies.

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    File URL: http://arxiv.org/pdf/0907.3231
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    Paper provided by arXiv.org in its series Papers with number 0907.3231.

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    Date of creation: Jul 2009
    Date of revision: Mar 2011
    Publication status: Published in Advances in Complex Systems 6(2009)619
    Handle: RePEc:arx:papers:0907.3231
    Contact details of provider: Web page: http://arxiv.org/

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    1. Challet, Damien & Marsili, Matteo & Zhang, Yi-Cheng, 2004. "Minority Games: Interacting agents in financial markets," OUP Catalogue, Oxford University Press, number 9780198566403, March.
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