Effect of detailed information in Minority Game: Optimality of 2-day memory and enhanced efficiency due to random exogenous data

TL;DR

This paper investigates how different types of information and memory lengths affect agent coordination and efficiency in the Minority Game, revealing that a 2-day memory is optimal and that random exogenous data can enhance coordination.

Contribution

It demonstrates that in the Minority Game, a fixed 2-day memory is optimal for large systems and that random exogenous information can improve agent coordination, contrasting with traditional models.

Findings

Optimal memory length is always two for large systems.

System efficiency decreases with memory length greater than two.

Random exogenous information enhances coordination compared to endogenous data.

Abstract

In the Minority Game (MG), an odd number of heterogeneous and adaptive agents choose between two alternatives and those who end up on the minority side win. When the information available to the agents to make their choice is the identity of the minority side for the past $m$ days, it is well-known that emergent coordination among the agents is maximum when $m \sim \log_2(N)$. The optimal memory-length thus increases with the system size. In this work, we show that, in MG when the information available to the agents to make their choice is the strength of the minority side for the past $m$ days, the optimal memory length for the agents is always two ($m=2$) for large enough system sizes. The system is inefficient for $m=1$ and converge to random choice behaviour for $m > 2$ for large $N$. Surprisingly, providing the agents with uniformly and randomly sampled $m=1$ exogenous information results in an increase in coordination between them compared to the case of endogenous information with any value of $m$. This is in stark contrast to the conventional MG, where agent's coordination is invariant or gets worse with respect to such random exogenous information.