We introduce and develop a framework for the study of competition between firms who have budgets to “seed” the initial adoption of their products by consumers located in a social network. The payoffs to the firms are the eventual number of adoptions of their product through a competitive stochastic diffusion process in the network. This framework yields a very rich class of competitive strategies, which depend in subtle ways on the stochastic dynamics of adoption, the relative budgets of the players, and the underlying structure of the social network.

We identify a general property of the adoption dynamics –  namely, decreasing re- turns to local adoption – for which the inefficiency of resource use at equilibrium (the Price of Anarchy ) is uniformly bounded above, across all equilibria and networks. We also show that if this property is even slightly violated, the Price of Anarchy can be unbounded, thus yielding sharp threshold behavior for a broad class of dynamics.

We also introduce a new notion, the Price of Budgets , that measures the extent that imbalances in player budgets can be amplified at equilibrium. We again identify a general property of the adoption dynamics –  namely, proportional local adoption between competitors – for which the (pure) Price of Budgets is uniformly bounded above, across all equilibria and all networks. We show that even a slight departure from this property can lead to unbounded Price of Budgets, again yielding sharp threshold behavior for a broad class of dynamics.

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