Deterministic Dynamics in the Minority Game
arXiv:cond-mat/0103259 · doi:10.1103/PhysRevE.65.016105
Abstract
The Minority Game (MG) behaves as a stochastically perturbed deterministic system due to the coin-toss invoked to resolve tied strategies. Averaging over this stochasticity yields a description of the MG's deterministic dynamics via mapping equations for the strategy score and global information. The strategy-score map contains both restoring-force and bias terms, whose magnitudes depend on the game's quenched disorder. Approximate analytical expressions are obtained and the effect of `market impact' discussed. The global-information map represents a trajectory on a De Bruijn graph. For small quenched disorder, an Eulerian trail represents a stable attractor. It is shown analytically how anti-persistence arises. The response to perturbations and different initial conditions are also discussed.
16 pages, 5 figures
Cited by in corpus (12)
- Theory of Networked Minority Games based on Strategy Pattern Dynamics
- Theory of enhanced performance emerging in a sparsely-connected competitive population
- Dynamics of the Time Horizon Minority Game
- Statistical Mechanics of Competitive Resource Allocation using Agent-based Models
- Multi-Agent Complex Systems and Many-Body Physics
- Anatomy of extreme events in a complex adaptive system
- An Investigation of Crash Avoidance in a Complex System
- Phenomenology of minority games in efficient regime
- Self-organized global control of carbon emissions
- Influence of external information in the minority game
- Physics and Financial Economics (1776-2014): Puzzles, Ising and Agent-Based models
- Mesoscopic approach to minority games in herd regime