Modelling investment in artificial stock markets: Analytical and Numerical Results

TL;DR

This paper models the behavior of economic agents in artificial stock markets using a modified Potts Model, analyzing investment dynamics through analytical and numerical methods to understand how investments vary with a control parameter.

Contribution

It introduces a novel application of the Potts Model to simulate agent interactions in stock markets, providing analytical and numerical insights into investment behaviors.

Findings

Analytical results for q=2 and 3 cases showing investment dependence on control parameter

Numerical evaluation of eigenvalues for q>3 cases

High-precision derivatives to analyze investment behavior

Abstract

In this article we study the behavior of a group of economic agents in the context of cooperative game theory, interacting according to rules based on the Potts Model with suitable modifications. Each agent can be thought of as belonging to a chain, where agents can only interact with their nearest neighbors (periodic boundary conditions are imposed). Each agent can invest an amount σ_{i}=0,...,q-1. Using the transfer matrix method we study analytically, among other things, the behavior of the investment as a function of a control parameter (denoted β) for the cases q=2 and 3. For q>3 numerical evaluation of eigenvalues and high precision numerical derivatives are used in order to assess this information.