Structure-preserving desynchronization of minority games

TL;DR

This paper introduces a method to convert synchronized multi-agent models into asynchronous ones without losing their core structure, revealing how different levels of stochasticity affect system behavior.

Contribution

It presents a general framework for desynchronizing adaptive agent models while maintaining their global properties, with a detailed study on the Minority Game.

Findings

The phase and fluctuation structure of the Minority Game persists under maximal determinism.

Adding stochasticity to interactions destroys the original structure.

Heterogeneous communication speeds create a new information ecology.

Abstract

Perfect synchronicity in $N$-player games is a useful theoretical dream, but communication delays are inevitable and may result in asynchronous interactions. Some systems such as financial markets are asynchronous by design, and yet most theoretical models assume perfectly synchronized actions. We propose a general method to transform standard models of adaptive agents into asynchronous systems while preserving their global structure under some conditions. Using the Minority Game as an example, we find that the phase and fluctuations structure of the standard game subsists even in maximally asynchronous deterministic case, but that it disappears if too much stochasticity is added to the temporal structure of interaction. Allowing for heterogeneous communication speeds and activity patterns gives rise to a new information ecology that we study in details.