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The Reality Game

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  • 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.

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Bibliographic Info

Paper provided by arXiv.org in its series Papers with number 0902.0100.

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Date of creation: Jan 2009
Date of revision: Feb 2009
Handle: RePEc:arx:papers:0902.0100

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  1. Alvaro Sandroni, 2000. "Do Markets Favor Agents Able to Make Accurate Predicitions?," Econometrica, Econometric Society, vol. 68(6), pages 1303-1342, November.
  2. Dosi, G & Kaniovski, Y, 1994. "On "Badly Behaved" Dynamics: Some Applications of Generalized Urn Schemes to Technological and Economic Change," Journal of Evolutionary Economics, Springer, vol. 4(2), pages 93-123, June.
  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. Thorsten Hens & Klaus Reiner Schenk-Hoppé, 2003. "Evolutionary Stability of Portfolio Rules in Incomplete Markets," Discussion Papers 03-03, University of Copenhagen. Department of Economics.
  5. 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.
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  7. 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.
  8. 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.
  9. Arthur, W Brian, 1994. "Inductive Reasoning and Bounded Rationality," American Economic Review, American Economic Association, vol. 84(2), pages 406-11, May.
  10. Blume, Lawrence E. & Easley, David, 1993. "Economic natural selection," Economics Letters, Elsevier, vol. 42(2-3), pages 281-289.
  11. Lawrence E. Blume & David Easley, 1998. "Optimality and Natural Selection in Markets," Working Papers 98-09-082, Santa Fe Institute.
  12. 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.
  13. Yuzuru Sato & Eizo Akiyama & J. Doyne Farmer, 2001. "Chaos in Learning a Simple Two Person Game," Working Papers 01-09-049, Santa Fe Institute.
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