Skip to main content
Log in

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

The European Physical Journal B Aims and scope Submit manuscript

An Erratum to this article was published on 19 March 2008

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.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  • J.D. Taylor, S.E. Brown, Psych. Bull. 103, 193 (1988)

    Article  Google Scholar 

  • A. Bandura, Self-efficacy: the exercise of control (WH Freeman, New York, 1997)

  • E. Langer, J. Pers. Soc. Psych. 7, 185 (1975)

    Google Scholar 

  • D. Challet, Y.C. Zhang, Phys. A 246, 407 (1997)

    Article  Google Scholar 

  • D. Challet, Y.C. Zhang, Phys. A 256, 514 (1998)

    Article  Google Scholar 

  • D. Challet, M. Marsili, Y.-C. Zhang, Phys. A 276, 284 (2000)

    Article  MathSciNet  Google Scholar 

  • J.S. Doran, C. Wright, What really matters when buying and selling stocks? Working paper of Florida State University, 2007) (http://ssrn.com/abstract=980291)

  • J.M.R. Parrondo, How to cheat a bad mathematician, in EEC HC&M Network on Complexity and Chaos (#ERBCHRX-CT940546) (ISI, Torino, Italy, 1996), Unpublished

  • G.P. Harmer, D. Abbott, Stat. Sci. 14, 206 (1999)

    Article  MATH  MathSciNet  Google Scholar 

  • W.B. Arthur, Out-of-Equilibrium Economics and Agent-Based Modeling, in the Handbook of Computational Economics, Vol. 2: Agent-Based Computational Economics, edited by K. Judd, L. Tesfatsion (Elsevier/North-Holland, 2005)

  • M. Hart, P. Jefferies, P.M. Hui, N.F. Johnson, Eur. Phys. J. B 20, 547 (2001)

    Article  ADS  MathSciNet  Google Scholar 

  • M.L. Hart, P. Jefferies, N.F. Johnson, Phys. A 311, 275 (2002)

    Article  MATH  Google Scholar 

  • (The mathematical derivation is given in Appendix A)

  • R. D'Hulst, G.J. Rodgers, Phys. A 270, 514 (1999)

    Article  MathSciNet  Google Scholar 

  • Y. Li, R. Riolo, R. Savit, Phys. A 276, 265 (2000)

    Article  ADS  MathSciNet  Google Scholar 

  • M. Andrecut, M.K. Ali, Phys. Rev. E 64, 67103 (2001)

    Article  ADS  MathSciNet  Google Scholar 

  • R.M. Araujo, L.C. Lamb, Proceedings of the 16th IEEE International Conference on Tools with Artificial Intelligence (ICTAI'04)-Volume 00, 727 (2004)

    Article  Google Scholar 

  • W.C. Man, H.F. Chau, Phys. Rev. E 73, 36106 (2006)

    Article  ADS  Google Scholar 

  • M. Sysi-Aho, A. Chakraborti, K. Kaski, Eur. Phys. J. B 34, 373 (2003)

    Article  ADS  Google Scholar 

  • M. Sysi-Aho, A. Chakraborti, K. Kaski, Phys. Rev. E 69, 36125 (2004)

    Article  ADS  Google Scholar 

  • W.S. Yang, B.H. Wang, Y.L. Wu, Y.B. Xie, Phys. A 339, 583 (2004)

    Article  Google Scholar 

  • J. Menche, J.R.L. de Almeida, It is worth thinking twice or Improving the performance of minority games, e-print arXiv:preprint cond-mat/0308181 (2003)

  • M. Marsili, D. Challet, Adv. Complex Systems. 3-I, 3 (2001)

  • D. Challet, M. Marsili, R. Zecchina, Phys. Rev. Lett. 84, 1824 (2000)

    Article  ADS  Google Scholar 

  • J. Duffy, E. Hopkins, Games Econ. Behav. 51, 31 (2005)

    Article  MATH  MathSciNet  Google Scholar 

  • M. Smoluchowski, Z 13, 1069 (1912); R.P. Feynman, R.B. Leighton, M. Sands, The Feynman lectures on physics (Addison-Wesley Redwood City, Calif., 1963)

    Google Scholar 

  • A. Adjari, J. Prost, C. R. Acad. Sci. Paris II 315, 1635 (1992); M.O. Magnasco, Phys. Rev. Lett. 71, 1477 (1993)

    Google Scholar 

  • J. Prost, J.-F. Chawin, L. Peliti, A. Adjari, Phys. Rev. Lett. 72, 2652 (1994)

    Article  ADS  Google Scholar 

  • R. Pyke, On Random Walks and Diffusions Related to Parrondo's Games, e-print arXiv:math.PR/0206150 (2002)

  • D. Kinderlehrer, M. Kowalczyk, Arch. Rat. Mech. Anal. 161, 149 (2002)

    Article  MATH  MathSciNet  Google Scholar 

  • H. Moraal, J. Phys. A 33, L203 (2000)

  • G.P. Harmer, D. Abbott, P.G. Taylor, J.M. Parrondo, Chaos 11, 705 (2001)

    Article  MATH  ADS  Google Scholar 

  • S. Maslov, Y.C. Zhang, Int. J. Theor. Appl. Finan. 1, 377 (1998)

    Article  MATH  Google Scholar 

  • M. Boman, S.J. Johansson, D. Lyback, Parrondo strategies for artificial traders, in Proceedings of the 2nd International Conference on Intelligent Agent Technology (World Scientific, 2001)

  • W.S. Almberg, M. Boman, in Artificial Intelligence and Computer Science, edited by S. Shannon (Nova Science Publishers, 2005), p. 123

  • J.B. Satinover, D. Sornette, Phys. A 386, 339 (2007)

    Article  Google Scholar 

  • J.M.R. Parrondo, G.P. Harmer, D. Abbott, Phys. Rev. Lett. 85, 5226 (2000)

    Article  ADS  Google Scholar 

  • R.J. Kay, N.F. Johnson, Phys. Rev. E 67, 56128 (2003)

    Article  ADS  Google Scholar 

  • L. Dinis, Europhys. Lett. 63, 319 (2003)

    Article  ADS  Google Scholar 

  • J.M.R. Parrondo, L. Dinis, J. Buceta, K. Lindenberg, Paradoxical games, ratchets, and related phenomena, In Advances in Condensed Matter and Statistical Mechanics, edited by E. Korutcheva, R. Cuerno (Nova Science Publishers, 2003)

  • J. Huber, M. Kirchler, M. Sutter, Is more information always better? Experimental financial markets with cumulative information, Journal of Economic Behavior and Organization, forthcoming (2007)

  • C.W. Eurich, K. Pawelzik, in Artificial Neural Networks: Formal Models and Their Applications - ICANN 2005 (Springer, Berlin, 2005), p. 0302

  • S.P. Berczuk, B. Appleton, in Software Configuration Management Patterns: Effective Teamwork, Practical Integration (Addison-Wesley, 2002)

  • B.G. Malkiel, A Random Walk Down Wall Street:: the Time-tested Strategy for Successful Investing (WW Norton & Company, 2003)

  • R.J. Shiller, Market Volatility (MIT Press, 1992)

  • T. Grandin, C. Johnson, Animals in Translation: Using the Mysteries of Autism to Decode Animal Behavior (Scribner, 2005)

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to D. Sornette.

Additional information

An erratum to this article is available at http://dx.doi.org/10.1140/epjb/e2008-00112-3.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Satinover, J., Sornette, D. ”Illusion of control” in Time-Horizon Minority and Parrondo Games. Eur. Phys. J. B 60, 369–384 (2007). https://doi.org/10.1140/epjb/e2007-00353-6

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1140/epjb/e2007-00353-6

PACS.

Navigation