Statistical mechanics of the mixed majority-minority game with random external information

TL;DR

This paper analyzes a mixed majority-minority game with random external information, revealing how the proportion of trend-followers affects market efficiency and fluctuations, using replica and dynamical methods validated by numerical results.

Contribution

It introduces a model combining majority and minority behaviors, showing how trend-followers impact market efficiency and fluctuations, and solves it with replica and dynamical techniques.

Findings

Efficiency decreases as trend-followers increase beyond 50%

Global fluctuations sharply rise when trend-followers exceed 50%

Model solutions match numerical simulations

Abstract

We study the asymptotic macroscopic properties of the mixed majority-minority game, modeling a population in which two types of heterogeneous adaptive agents, namely ``fundamentalists'' driven by differentiation and ``trend-followers'' driven by imitation, interact. The presence of a fraction f of trend-followers is shown to induce (a) a significant loss of informational efficiency with respect to a pure minority game (in particular, an efficient, unpredictable phase exists only for f<1/2), and (b) a catastrophic increase of global fluctuations for f>1/2. We solve the model by means of an approximate static (replica) theory and by a direct dynamical (generating functional) technique. The two approaches coincide and match numerical results convincingly.