Strategic diffusion in networks through contagion

This paper studies the diffusion of products and behaviour with coordination effects through social networks when agents are myopic best responders. We develop a new network measure, the contagion threshold, that determines when a p-dominant action—an action that is a best response when adopted by at least proportion p of an agent’s opponents—spreads to the whole population starting from a group of players whose size is smaller than half and independent of the population size. We show that a p-dominant action spreads to the whole network whenever the contagion threshold of that network is greater or equal to p. We then show that in settings where agents regularly or occasionally experiment and choose non-optimal actions, there exists a threshold level of experimentation below which a p-dominant action is chosen with the highest probability in the long run. This result implies that targeted contagion, a network-wide diffusion of actions initiated by targeting agents, is justified even in settings where agents’ decisions are noisy.