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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.

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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    Cited by:

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    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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