The Reality Game
| dc.creator | Cherkashin, Dmitriy | |
| dc.creator | Farmer, J. Doyne | |
| dc.creator | Lloyd, Seth | |
| dc.date | 2009-02-01 | |
| dc.date | 2009-02-09 | |
| dc.date.accessioned | 2026-07-07T12:38:51Z | |
| dc.date.available | 2026-07-07T12:38:51Z | |
| dc.description | 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. | |
| dc.description | 21 pages, 5 figures | |
| dc.identifier | https://arxiv.org/abs/0902.0100 | |
| dc.identifier | http://arxiv.org/abs/0902.0100 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/218906 | |
| dc.subject | General Finance | |
| dc.title | The Reality Game | |
| dc.type | text |