PHENOMENOLOGY OF MINORITY GAMES IN EFFICIENT REGIME

Karol Wawrzyniak () and Wojciech Wislicki ()
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Karol Wawrzyniak: Interdisciplinary Centre for Mathematical and Computational Modelling, University of Warsaw, Pawińskiego 5A, PL-02-106 Warszawa, Poland
Wojciech Wislicki: A. Sołtan Institute for Nuclear Studies, Hoża 69, PL-00-681 Warszawa, Poland

Advances in Complex Systems (ACS), 2009, vol. 12, issue 06, 619-639

Abstract: 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 functiong(x) =sgn(x), we explicitly represent the game as the Markov process and prove the finiteness 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 preferred 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 analyzing the game in terms of de Bruijn graphs, we can also explain distinct peaks of demand and their frequencies.

Keywords: Minority game; adaptive system; Markov process; de Bruijn graph (search for similar items in EconPapers)
Date: 2009
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Citations: View citations in EconPapers (1)

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Persistent link: https://EconPapers.repec.org/RePEc:wsi:acsxxx:v:12:y:2009:i:06:n:s0219525909002398

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DOI: 10.1142/S0219525909002398

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