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The Reality Game

Author

Listed:
  • Dmitriy Cherkashin
  • J. Doyne Farmer
  • Seth Lloyd
Abstract
We introduce an evolutionary game with feedback between perception and reality, which we call the reality game. It is a game of chance in which the probabilities for different objective outcomes (e.g., heads or tails in a coin toss) depend on the amount wagered on those outcomes. By varying the `reality map', which relates the amount wagered to the probability of the outcome, it is possible to move continuously from a purely objective game in which probabilities have no dependence on wagers to a purely subjective game in which probabilities equal the amount wagered. We study self-reinforcing games, in which betting more on an outcome increases its odds, and self-defeating games, in which the opposite is true. This is investigated in and out of equilibrium, with and without rational players, and both numerically and analytically. We introduce a method of measuring the inefficiency of the game, similar to measuring the magnitude of the arbitrage opportunities in a financial market. We prove that convergence to equilibrium is is a power law with an extremely slow rate of convergence: The more subjective the game, the slower the convergence.

Suggested Citation

  • Dmitriy Cherkashin & J. Doyne Farmer & Seth Lloyd, 2009. "The Reality Game," Papers 0902.0100, arXiv.org, revised Feb 2009.
    • Handle: RePEc:arx:papers:0902.0100
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    References listed on IDEAS

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    1. Hommes, Cars H., 1991. "Adaptive learning and roads to chaos : The case of the cobweb," Economics Letters, Elsevier, vol. 36(2), pages 127-132, June.
    2. Blume, Lawrence E. & Easley, David, 2002. "Optimality and Natural Selection in Markets," Journal of Economic Theory, Elsevier, vol. 107(1), pages 95-135, November.
    3. Hens, Thorsten & Schenk-Hoppe, Klaus Reiner, 2005. "Evolutionary finance: introduction to the special issue," Journal of Mathematical Economics, Elsevier, vol. 41(1-2), pages 1-5, February.
    4. Hens, Thorsten & Schenk-Hoppe, Klaus Reiner, 2005. "Evolutionary stability of portfolio rules in incomplete markets," Journal of Mathematical Economics, Elsevier, vol. 41(1-2), pages 43-66, February.
    5. Arthur, W Brian, 1994. "Inductive Reasoning and Bounded Rationality," American Economic Review, American Economic Association, vol. 84(2), pages 406-411, May.
    6. Alvaro Sandroni, 2000. "Do Markets Favor Agents Able to Make Accurate Predicitions?," Econometrica, Econometric Society, vol. 68(6), pages 1303-1342, November.
    7. Yuzuru Sato & Eizo Akiyama & J. Doyne Farmer, 2001. "Chaos in Learning a Simple Two Person Game," Working Papers 01-09-049, Santa Fe Institute.
    8. Alos-Ferrer, Carlos & Ania, Ana B., 2005. "The asset market game," Journal of Mathematical Economics, Elsevier, vol. 41(1-2), pages 67-90, February.
    9. Dosi, Giovanni & Ermoliev, Yuri & Kaniovski, Yuri, 1994. "Generalized urn schemes and technological dynamics," Journal of Mathematical Economics, Elsevier, vol. 23(1), pages 1-19, January.
    10. Hommes, Cars H., 1994. "Dynamics of the cobweb model with adaptive expectations and nonlinear supply and demand," Journal of Economic Behavior & Organization, Elsevier, vol. 24(3), pages 315-335, August.
    11. Anufriev, Mikhail & Bottazzi, Giulio & Pancotto, Francesca, 2006. "Equilibria, stability and asymptotic dominance in a speculative market with heterogeneous traders," Journal of Economic Dynamics and Control, Elsevier, vol. 30(9-10), pages 1787-1835.
    12. G. Dosi & Y. Kaniovski, 2000. "On "Badly Behaved" Dynamics: Some Applications of Generalized urn Schemes to Technological and Economic Change," Chapters, in: Innovation, Organization and Economic Dynamics, chapter 13, pages 379-409, Edward Elgar Publishing.
    13. Challet, D. & Zhang, Y.-C., 1997. "Emergence of cooperation and organization in an evolutionary game," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 246(3), pages 407-418.
    14. Blume, Lawrence & Easley, David, 1992. "Evolution and market behavior," Journal of Economic Theory, Elsevier, vol. 58(1), pages 9-40, October.
    15. Blume, Lawrence E. & Easley, David, 1993. "Economic natural selection," Economics Letters, Elsevier, vol. 42(2-3), pages 281-289.
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    Cited by:

    1. Martin Hilbert, 2017. "Complementary Variety: When Can Cooperation in Uncertain Environments Outperform Competitive Selection?," Complexity, Hindawi, vol. 2017, pages 1-15, September.
    2. Hilbert, Martin, 2016. "Formal definitions of information and knowledge and their role in growth through structural change," Structural Change and Economic Dynamics, Elsevier, vol. 38(C), pages 69-82.

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