  We consider social systems in which agents are not only characterized by
their states but also have the freedom to choose their interaction partners to
maximize their utility. We map such systems onto an Ising model in which spins
are dynamically coupled by links in a dynamical network. In this model there
are two dynamical quantities which arrange towards a minimum energy state in
the canonical framework: the spins, s_i, and the adjacency matrix elements,
c_{ij}. The model is exactly solvable because microcanonical partition
functions reduce to products of binomial factors as a direct consequence of the
c_{ij} minimizing energy. We solve the system for finite sizes and for the two
possible thermodynamic limits and discuss the phase diagrams.
