Deterministic Dynamics in the Minority Game

Details Deterministic Dynamics in the Minority Game Deterministic Dynamics in the Minority Game

2001-03-12

arxiv.org/abs/cond-mat/0103259v1

Physics

Condensed Matter

Disordered Systems and Neural Networks

16 pages, 5 figures

Scientific paper

10.1103/PhysRevE.65.016105

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.

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