The European Physical Journal B

, Volume 60, Issue 3, pp 369–384 | Cite as

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

  • J. B. Satinover
  • D. SornetteEmail author
Interdisciplinary Physics


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.


89.75.-k Complex systems 89.65.Gh Economics; econophysics, financial markets, business and management 02.50.Le Decision theory and game theory 


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Copyright information

© EDP Sciences/Società Italiana di Fisica/Springer-Verlag 2007

Authors and Affiliations

  1. 1.Laboratoire de Physique de la Matière Condensée, CNRS UMR6622 and Université des SciencesNice Cedex 2France
  2. 2.Department of ManagementZurichSwitzerland

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