The Reality Game

Journal article

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.

Authors: Cherkashin, D; Farmer, J; Lloyd, S

• Publication status: Published
• Journal: JOURNAL OF ECONOMIC DYNAMICS and CONTROL
• Volume: 33
• Issue: 5
• Pages: 1091-1105
• Publication date: 2009-02-01
• DOI: 10.1016/j.jedc.2009.02.002
• ISSN: 0165-1889
• Language: English
• Keywords: q-fin.GN