Modelling investment in artificial stock markets: Analytical and Numerical Results

Silvio Renato Dahmen Instituto de F́ısica, Universidade Federal do Rio Grande do Sul, Av. Bento Gonçalves, 9500, CEP 91501-970, Porto Alegre, RS, Brazil‡ 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 σi = 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. keywords: Game Theory; statistical mechanics; transfer matrix methods.