title: Deterministic dynamics in the minority game.
abstract: The minority game (MG) behaves as a stochastically disturbed 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" is discussed. The global-information map represents a trajectory on a de Bruijn graph. For small quenched disorder, a Eulerian trail represents a stable attractor. It is shown analytically how antipersistence arises. The response to perturbations and different initial conditions is also discussed.
authors.affiliation: Physics Department, Clarendon Laboratory, Oxford University, Oxford OX1 3PU, United Kingdom.
authors.forename: P
authors.initials: P
authors.lastname: Jefferies
authors.forename: M L
authors.initials: ML
authors.lastname: Hart
authors.forename: N F
authors.initials: NF
authors.lastname: Johnson