Theory of Phase Transition in the Evolutionary Minority Game

TL;DR

This paper analyzes the phase transition mechanism in the evolutionary minority game, revealing how market impact and inefficiency influence agent behavior and population distribution.

Contribution

It introduces a statistical mechanics analysis of a simplified EMG, identifying key factors driving the transition between self-segregation and clustering.

Findings

Market impact favors fixed-strategy players.

Market inefficiency promotes cautious behavior.

Transition depends on number of agents, reward ratio, and wealth threshold.

Abstract

We discover the mechanism for the transition from self-segregation (into opposing groups) to clustering (towards cautious behaviors) in the evolutionary minority game (EMG). The mechanism is illustrated with a statistical mechanics analysis of a simplified EMG involving three groups of agents: two groups of opposing agents and one group of cautious agents. Two key factors affect the population distribution of the agents. One is the market impact (the self-interaction), which has been identified previously. The other is the market inefficiency due to the short-time imbalance in the number of agents using opposite strategies. Large market impact favors "extreme" players who choose fixed strategies, while large market inefficiency favors cautious players. The phase transition depends on the number of agents ($N$), the reward-to-fine ratio ($R$), as well as the wealth reduction threshold ($d$) for switching strategy. When the rate for switching strategy is large, there is strong clustering of cautious agents. On the other hand, when $N$ is small, the market impact becomes large, and the extreme behavior is favored.