Modelling investment in artificial stock markets: Analytical and Numerical Results

da Silva, Roberto; Baraviera, Alexandre Tavares; Dahmen, Silvio R.

Modelling investment in artificial stock markets: Analytical and Numerical Results

Authors

da Silva, Roberto

Baraviera, Alexandre Tavares

Dahmen, Silvio R.

Description

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.
19 pages 10 figures