  Static and dynamic equilibria in noisy binary choice games on graphs are
considered. Equations defining static quantal response equilibria (QRE) for
binary choice games on graphs with arbitrary topology and noise distribution
are written. It is shown that in the special cases of complete graph and
arbitrary noise distribution, and circular and star topology and logistic noise
distribution the resulting equations can be cast in the form coinciding with
that derived in the earlier literature. Explicit equations QRE for non-directed
graphs in the annealed approximation are derived. It is shown that the
resulting effect on the phase transition is the same as found in the literature
on phase transition in the Ising model on graphs in the same
approximation.Evolutionary noisy binary choice game having the earlier
described QRE as its stationary equilibria in the mean field approximation is
constructed using the formalism of master equation.
