On the transition to efficiency in Minority Games

TL;DR

This paper investigates how the presence of a subset of optimally learning agents influences the phase transition to efficiency in various types of Minority Games, showing that even a small fraction of optimal agents guarantees an efficient regime.

Contribution

It demonstrates that a non-zero fraction of agents with optimal learning rules ensures the existence of an efficient phase in mixed population Minority Games.

Findings

Any non-zero fraction of optimal agents guarantees efficiency.

The critical point depends on the fraction of optimal agents.

Analysis covers MGs with market impact correction, grand-canonical MGs, and heterogeneous comfort levels.

Abstract

The existence of a phase transition with diverging susceptibility in batch Minority Games (MGs) is the mark of informationally efficient regimes and is linked to the specifics of the agents' learning rules. Here we study how the standard scenario is affected in a mixed population game in which agents with the `optimal' learning rule (i.e. the one leading to efficiency) coexist with ones whose adaptive dynamics is sub-optimal. Our generic finding is that any non-vanishing intensive fraction of optimal agents guarantees the existence of an efficient phase. Specifically, we calculate the dependence of the critical point on the fraction $q$ of `optimal' agents focusing our analysis on three cases: MGs with market impact correction, grand-canonical MGs and MGs with heterogeneous comfort levels.