Competitive Contagion in Networks

TL;DR

This paper introduces a game-theoretic framework to analyze how competing firms seed product adoption in social networks, revealing conditions under which resource inefficiencies and budget imbalances are bounded or unbounded.

Contribution

It develops a novel framework for competitive diffusion in networks, identifying properties that bound inefficiency and budget imbalance at equilibrium.

Findings

Bounded Price of Anarchy under decreasing returns to local adoption.

Unbounded Price of Anarchy when decreasing returns property is violated.

Bounded Budget Multiplier under proportional local adoption dynamics.

Abstract

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. 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 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 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 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 Budget Multiplier, 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 strategy) Budget Multiplier is uniformly bounded above, across all networks. We show that a violation of this property can lead to unbounded Budget Multiplier, again yielding sharp threshold behavior for a broad class of dynamics.