The reality game

Dmitriy Cherkashin, J. Doyne Farmer and Seth Lloyd

Journal of Economic Dynamics and Control, 2009, vol. 33, issue 5, pages 1091-1105

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 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.

Keywords: Financial; markets; Evolutionary; games; Information; theory; Arbitrage; Market; efficiency; Beauty; contests; Noise; trader; models; Market; reflexivity (search for similar items in EconPapers)
Date: 2009

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Persistent link: http://EconPapers.repec.org/RePEc:eee:dyncon:v:33:y:2009:i:5:p:1091-1105

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