Relevance of memory in minority games

Area of Science:

• Agent-based modeling
• Complex systems dynamics
• Statistical physics

Background:

• The minority game models adaptive agent competition.
• Agent strategies evolve based on past outcomes.
• Understanding history dynamics is key to game behavior.

Purpose of the Study:

• To analyze the dynamics of histories in the minority game.
• To investigate the impact of biased transition probabilities on history visitation frequencies.
• To develop a self-consistent theory for real histories.

Main Methods:

• Utilizing diffusion on De Bruijn graphs to model temporal evolution of M-bit strings (histories).
• Analyzing visit frequencies of histories under biased transition probabilities.
• Developing and validating a theoretical framework for real histories.

Main Results:

• History visit frequencies deviate from uniform distribution (1/2^M) for large M with biased probabilities.
• Model quantities significantly depend on whether histories are real or randomly sampled.
• A self-consistent theory for real histories shows strong agreement with simulations.

Conclusions:

• Biased probabilities in the minority game lead to non-uniform history exploration.
• The distinction between real and randomly sampled histories is crucial for accurate modeling.
• The developed theory accurately captures the behavior of real histories in the minority game.