We consider a dynamic game over a network with information externalities. Agents' payoffs depend on an unknown true state of the world and actions of everyone else in the network; therefore, the interactions between agents are strategic. Each agent has a private initial piece of information about the underlying state and repeatedly observes actions of her neighbors. We consider strictly concave and supermodular utility functions that exhibit a quadratic form. We analyze the asymptotic behavior of agents' expected utilities in a connected network when it is common knowledge that the agents are myopic and rational. When utility functions are symmetric and adhere to the diagonal dominance criterion, each agent believes that the limit strategies of her neighbors yield the same payoff as her own limit strategy. Given a connected network, this yields a consensus in the actions of agents in the limit. We demonstrate our results using examples from technological and social settings.