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Deterministic dynamics in the minority game.

P Jefferies1, M L Hart, N F Johnson

  • 1Physics Department, Clarendon Laboratory, Oxford University, Oxford OX1 3PU, United Kingdom.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|January 22, 2002
PubMed
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The minority game (MG) is a stochastically disturbed deterministic system. Averaging reveals deterministic dynamics, showing how antipersistence arises from quenched disorder and market impact.

Area of Science:

  • Complex systems
  • Game theory
  • Statistical mechanics

Background:

  • The minority game (MG) exhibits dynamics influenced by stochasticity from tie-breaking mechanisms.
  • Understanding the deterministic core of such systems is crucial for modeling collective behavior.

Purpose of the Study:

  • To analyze the deterministic dynamics of the minority game by averaging over stochasticity.
  • To derive analytical expressions for strategy scores and global information.
  • To investigate the emergence of antipersistence and system responses to perturbations.

Main Methods:

  • Stochastic averaging to derive mapping equations for system dynamics.
  • Analytical derivation of expressions for strategy score and global information maps.
  • Analysis of system behavior on a de Bruijn graph representation.

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Main Results:

  • The strategy-score map includes restoring-force and bias terms dependent on quenched disorder.
  • Approximate analytical expressions for these terms were obtained.
  • Antipersistence was analytically demonstrated to arise from quenched disorder, particularly for small disorder levels where a Eulerian trail acts as a stable attractor.

Conclusions:

  • The minority game's complex behavior can be understood through its underlying deterministic dynamics.
  • Quenched disorder plays a significant role in shaping system properties like antipersistence.
  • The de Bruijn graph framework provides insights into the system's trajectory and stability.