Statistical Mechanics of Competitive Resource Allocation using Agent-based Models

TL;DR

This paper reviews multi-agent models of competition for limited resources, highlighting how statistical mechanics tools can analyze collective phenomena like phase transitions and long memory in large-scale adaptive systems.

Contribution

It introduces a unifying framework using statistical mechanics to understand diverse multi-agent models of resource competition and heterogeneity.

Findings

Statistical mechanics effectively explains phase transitions in agent-based models.

Heterogeneity in agents maps to physical disorder, influencing collective behavior.

The approach provides a unified perspective across multiple disciplines.

Abstract

Demand outstrips available resources in most situations, which gives rise to competition, interaction and learning. In this article, we review a broad spectrum of multi-agent models of competition (El Farol Bar problem, Minority Game, Kolkata Paise Restaurant problem, Stable marriage problem, Parking space problem and others) and the methods used to understand them analytically. We emphasize the power of concepts and tools from statistical mechanics to understand and explain fully collective phenomena such as phase transitions and long memory, and the mapping between agent heterogeneity and physical disorder. As these methods can be applied to any large-scale model of competitive resource allocation made up of heterogeneous adaptive agent with non-linear interaction, they provide a prospective unifying paradigm for many scientific disciplines.