Competitive contagion in networks

We develop a game-theoretic 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. We identify a general property of the adoption dynamics — namely, decreasing returns to local adoption — for which the inefficiency of resource use at equilibrium (the Price of Anarchy) is uniformly bounded above, across all networks. We also show that if this property is violated, even the Price of Stability can be unbounded, thus yielding sharp threshold behavior for a broad class of dynamics. We provide similar results for a new notion, the Budget Multiplier, that measures the extent to which the imbalances in player budgets can be amplified at equilibrium.