The Reality Game

22 Pages Posted: 3 Feb 2009 Last revised: 9 Feb 2009

See all articles by Dmitriy Cherkashin

Dmitriy Cherkashin

Goldman Sachs Group, Inc. - Equity Derivatives Research

J. Doyne Farmer

University of Oxford - Institute for New Economic Thinking at the Oxford Martin School; Santa Fe Institute

Seth Lloyd

affiliation not provided to SSRN

Date Written: February 3, 2009

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

JEL Classification: G12, D44, D61, C62

Suggested Citation

Cherkashin, Dmitriy and Farmer, J. Doyne and Lloyd, Seth, The Reality Game (February 3, 2009). Available at SSRN: https://ssrn.com/abstract=1336822 or http://dx.doi.org/10.2139/ssrn.1336822

Dmitriy Cherkashin

Goldman Sachs Group, Inc. - Equity Derivatives Research ( email )

One New York Plaza, 42nd Floor
New York, NY 10004
United States

J. Doyne Farmer (Contact Author)

University of Oxford - Institute for New Economic Thinking at the Oxford Martin School ( email )

Eagle House
Walton Well Road
Oxford, OX2 6ED
United Kingdom

HOME PAGE: http://www.inet.ox.ac.uk/people/view/4

Santa Fe Institute ( email )

1399 Hyde Park Road
Santa Fe, NM 87501
United States
505-984-8800 (Phone)
505-982-0565 (Fax)

HOME PAGE: http://www.santafe.edu/~jdf/

Seth Lloyd

affiliation not provided to SSRN ( email )

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