Agents compete for the same resources and are only aware of their direct neighbors in a network. The natural outcome of repeated interactions in these settings is what we call peer-consistent equilibrium (PCE).  We decompose the network into communities and completely characterize peer-consistent equilibria by identifying which sets of agents can be active in equilibrium. An agent is active if she either belongs to a strong community or if few agents are aware of her existence. We show that there is a unique stable PCE, in which agents’ effort levels are proportional to their eigenvector centrality in the network.