2009/02/01 by Dmitriy Cherkashin, J. Doyne Farmer, Cherkashin, Dmitriy +3
Economics, Econometrics and Finance · #FOS: Economics and business #General Finance (q-fin.GN) #q-fin.GN
paper · pdf · doi:10.48550/arxiv.0902.0100
21 pages, 5 figures
arxiv created 2009/02/09 · arxiv updated 2009/12/01
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.