Dynamics of multi-frequency minority games

TL;DR

This paper investigates the behavior of multi-frequency minority games using dynamical mean-field theory, analyzing how different trading frequencies and learning rates affect system dynamics, steady states, and efficiency.

Contribution

It introduces a comprehensive analysis of minority games with agents trading on various time scales and heterogeneous learning rates, providing new insights into their macroscopic properties and phase behavior.

Findings

Characterized steady states for different frequency and learning rate distributions.

Calculated phase diagrams illustrating system behavior under various conditions.

Discussed the impact of regular and occasional traders on global efficiency.

Abstract

The dynamics of minority games with agents trading on different time scales is studied via dynamical mean-field theory. We analyze the case where the agents' decision-making process is deterministic and its stochastic generalization with finite heterogeneous learning rates. In each case, we characterize the macroscopic properties of the steady states resulting from different frequency and learning rate distributions and calculate the corresponding phase diagrams. Finally, the different roles played by regular and occasional traders, as well as their impact on the system's global efficiency, are discussed.