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”Illusion of control” in Time-Horizon Minority and Parrondo Games

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  • J. B. Satinover
  • D. Sornette

Abstract

Human beings like to believe they are in control of their destiny. This ubiquitous trait seems to increase motivation and persistence, and is probably evolutionarily adaptive [J.D. Taylor, S.E. Brown, Psych. Bull. 103, 193 (1988); A. Bandura, Self-efficacy: the exercise of control (WH Freeman, New York, 1997)]. But how good really is our ability to control? How successful is our track record in these areas? There is little understanding of when and under what circumstances we may over-estimate [E. Langer, J. Pers. Soc. Psych. 7, 185 (1975)] or even lose our ability to control and optimize outcomes, especially when they are the result of aggregations of individual optimization processes. Here, we demonstrate analytically using the theory of Markov Chains and by numerical simulations in two classes of games, the Time-Horizon Minority Game [M.L. Hart, P. Jefferies, N.F. Johnson, Phys. A 311, 275 (2002)] and the Parrondo Game [J.M.R. Parrondo, G.P. Harmer, D. Abbott, Phys. Rev. Lett. 85, 5226 (2000); J.M.R. Parrondo, How to cheat a bad mathematician (ISI, Italy, 1996)], that agents who optimize their strategy based on past information may actually perform worse than non-optimizing agents. In other words, low-entropy (more informative) strategies under-perform high-entropy (or random) strategies. This provides a precise definition of the “illusion of control” in certain set-ups a priori defined to emphasize the importance of optimization. Copyright EDP Sciences/Società Italiana di Fisica/Springer-Verlag 2007

Suggested Citation

  • J. B. Satinover & D. Sornette, 2007. "”Illusion of control” in Time-Horizon Minority and Parrondo Games," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 60(3), pages 369-384, December.
    • Handle: RePEc:spr:eurphb:v:60:y:2007:i:3:p:369-384
    DOI: 10.1140/epjb/e2007-00353-6
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    References listed on IDEAS

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    1. Huber, Jurgen & Kirchler, Michael & Sutter, Matthias, 2008. "Is more information always better: Experimental financial markets with cumulative information," Journal of Economic Behavior & Organization, Elsevier, vol. 65(1), pages 86-104, January.
    2. Robert J. Shiller, 1992. "Market Volatility," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262691515, December.
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    Cited by:

    1. Wei-Xing Zhou & Guo-Hua Mu & Si-Wei Chen & Didier Sornette, "undated". "Strategies used as Spectroscopy of Financial Markets Reveal New Stylized Facts," Working Papers ETH-RC-11-005, ETH Zurich, Chair of Systems Design.
    2. Piekunko-Mantiuk Iwona, 2019. "Parameterized Trade on the Futures Market on the WIG20," Folia Oeconomica Stetinensia, Sciendo, vol. 19(1), pages 114-125, June.
    3. Stefan Kerbl, 2010. "Regulatory Medicine Against Financial Market Instability: What Helps And What Hurts?," Papers 1011.6284, arXiv.org, revised Nov 2010.
    4. Anirban Chakraborti & Ioane Muni Toke & Marco Patriarca & Frédéric Abergel, 2011. "Econophysics review: II. Agent-based models," Post-Print hal-00621059, HAL.
    5. Alessio Emanuele Biondo & Alessandro Pluchino & Andrea Rapisarda, 2012. "The beneficial role of random strategies in social and financial systems," Papers 1209.5881, arXiv.org, revised Jan 2013.
    6. Satinover, J.B. & Sornette, D., 2007. "Illusion of control in a Brownian game," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 386(1), pages 339-344.
    7. Didier SORNETTE, 2014. "Physics and Financial Economics (1776-2014): Puzzles, Ising and Agent-Based Models," Swiss Finance Institute Research Paper Series 14-25, Swiss Finance Institute.
    8. Hardik Rajpal & Deepak Dhar, 2018. "Achieving Perfect Coordination amongst Agents in the Co-Action Minority Game," Games, MDPI, vol. 9(2), pages 1-13, May.

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