Minority game with arbitrary cutoffs

TL;DR

This paper explores a variant of the minority game with arbitrary attendance cutoffs, revealing how the population's attendance behavior splits into distinct groups due to feedback mechanisms, unlike random history scenarios.

Contribution

It introduces a generalized minority game model with arbitrary cutoffs and analyzes how feedback influences attendance grouping, extending prior models.

Findings

Attendance groups form based on cutoff levels.

Feedback mechanisms cause the grouping effect.

Standard deviations differ significantly between groups.

Abstract

We study a model of a competing population of N adaptive agents, with similar capabilities, repeatedly deciding whether to attend a bar with an arbitrary cutoff L. Decisions are based upon past outcomes. The agents are only told whether the actual attendance is above or below L. For L-> N/2, the game reproduces the main features of Challet and Zhang's minority game. As L is lowered, however, the mean attendances in different runs tend to divide into two groups. The corresponding standard deviations for these two groups are very different. This grouping effect results from the dynamical feedback governing the game's time-evolution, and is not reproduced if the agents are fed a random history.