  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 &#963;_{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 &#946;) 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.
