Using the minority game as a model for competition dynamics, we investigate the effects of interagent communications across a network on the global evolution of the game. Agent communication across this network leads to the formation of an influence network, which is dynamically coupled to the evolution of the game, and it is responsible for the information flow driving the agents' actions. We show that the influence network spontaneously develops hubs with a broad distribution of in-degrees, defining a scale-free robust leadership structure. Furthermore, in realistic parameter ranges, facilitated by information exchange on the network, agents can generate a high degree of cooperation making the collective almost maximally efficient.