Mechanisms of Self-Organization and Finite Size Effects in a Minimal Agent Based Model

TL;DR

This paper investigates how finite size effects lead to self-organization in an agent-based market model, showing that agent entry and exit based on market stability and price movements produce realistic stylized facts.

Contribution

It introduces a mechanism where agents enter or leave based on market conditions, explaining the emergence of stylized facts in finite populations.

Findings

Self-organization occurs at finite agent numbers, not in the infinite limit.

Market stability discourages agent entry, while price movements attract traders.

The mechanism is robust across different entry/exit rules.

Abstract

We present a detailed analysis of the self-organization phenomenon in which the stylized facts originate from finite size effects with respect to the number of agents considered and disappear in the limit of an infinite population. By introducing the possibility that agents can enter or leave the market depending on the behavior of the price, it is possible to show that the system self-organizes in a regime with a finite number of agents which corresponds to the stylized facts. The mechanism to enter or leave the market is based on the idea that a too stable market is unappealing for traders while the presence of price movements attracts agents to enter and speculate on the market. We show that this mechanism is also compatible with the idea that agents are scared by a noisy and risky market at shorter time scales. We also show that the mechanism for self-organization is robust with respect to variations of the exit/entry rules and that the attempt to trigger the system to self-organize in a region without stylized facts leads to an unrealistic dynamics. We study the self-organization in a specific agent based model but we believe that the basic ideas should be of general validity.