  We construct a model of strategic imitation in an arbitrary network of
players who interact through an additive game. Assuming a discrete time update,
we show a condition under which the resulting difference equations converge to
consensus. Two conjectures on general convergence are also discussed. We then
consider the case where players not only may choose their strategies, but also
affect their local topology. We show that for prisoner's dilemma, the graph
structure converges to a set of disconnected cliques and strategic consensus
occurs in each clique. Several examples from various matrix games are provided.
A variation of the model is then used to create a simple model for the
spreading of trends, or information cascades in (e.g., social) networks. We
provide theoretical and empirical results on the trend-spreading model.
