The reality game
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 the inefficiency converges to equilibrium as a power law with an extremely slow rate of convergence: the more subjective the game, the slower the convergence.
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- 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.
- Blume, Lawrence E. & Easley, David, 2002.
"Optimality and Natural Selection in Markets,"
Journal of Economic Theory,
Elsevier, vol. 107(1), pages 95-135, November.
- Lawrence E. Blume & David Easley, 1997. "Optimality and Natural Selection in Markets," GE, Growth, Math methods 9712003, EconWPA, revised 09 Jul 1998.
- Lawrence E. Blume & David Easley, 1998. "Optimality and Natural Selection in Markets," Working Papers 98-09-082, Santa Fe Institute.
- 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.
- 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.
- Alos-Ferrer, Carlos & Ania, Ana B., 2005. "The asset market game," Journal of Mathematical Economics, Elsevier, vol. 41(1-2), pages 67-90, February.
- Carlos Alós-Ferrer & Ana B. Ania, 2003. "The Asset Market Game," Vienna Economics Papers 0320, University of Vienna, Department of Economics.
- 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.
- 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.
- Arthur, W Brian, 1994. "Inductive Reasoning and Bounded Rationality," American Economic Review, American Economic Association, vol. 84(2), pages 406-411, May.
- Alvaro Sandroni, 2000. "Do Markets Favor Agents Able to Make Accurate Predicitions?," Econometrica, Econometric Society, vol. 68(6), pages 1303-1342, November.
- 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.
- Yuzuru Sato & Eizo Akiyama & J. Doyne Farmer, 2001. "Chaos in Learning a Simple Two Person Game," Working Papers 01-09-049, Santa Fe Institute.
- Blume, Lawrence & Easley, David, 1992. "Evolution and market behavior," Journal of Economic Theory, Elsevier, vol. 58(1), pages 9-40, October.
- Blume, Lawrence E. & Easley, David, 1993. "Economic natural selection," Economics Letters, Elsevier, vol. 42(2-3), pages 281-289.
- 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.
- 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. Full references (including those not matched with items on IDEAS)
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