  This paper models games where the strategies are nodes of a graph G (we
denote them as G-games) and in presence of coalition structures. The cases of
one-shot and repeated games are presented. In the latter situation, coalitions
are assumed to move from a strategy to another one under the constraint that
they are adjacent in the graph. We introduce novel concepts of pure and mixed
equilibria which are comparable with classical Nash and Berge equilibria. A
Folk Theorem for G-games of repeated type is presented. Moreover, equilibria
are proven to be described through suitably defined Markov Chains, hence
leading to a constrained Monte Carlo Markov Chain procedure.
