Communication and Coordination in Social Networks

Abstract

I model people in a coordination game who use a communication network to tell each other their willingness to participate. The minimal sufficient networks for coordination can be interpreted as placing people into a hierarchy of social roles or stages: initial adopters, then followers, and so on down to late adopters. A communication network helps coordination in exactly two ways: by informing each stage about earlier stages, and by creating common knowledge within each stage. We then consider two examples: first we show that dimensional networks can be better for coordination even though they have far fewer links than dimensional networks; second we show that wide dispersion of insurgents, people predisposed toward participation, can be good for coordination but too much dispersion can be bad. Although collective action depends on both social structure and individual incentives, these integral aspects have been formalized separately, in the fields of social network theory and game theory. By considering them together, this paper engages the classic question of which structures are conducive to coordination and shows that structure and strategy are related in a mutually interesting way. Here we consider a coordination game in which each person wants to participate only if others participate. Social structure is thought of as a communication network by which people tell each other their willingness to participate. Each person knows whether her neighbours in the network are willing, but does not know about anyone else. Our model is thus a game of incomplete information in which each person, given his local knowledge, decides whether to participate. The main result is a characterization of the minimal sufficient networks for coordination in terms of a hierarchy of social roles or stages: initial adopters, then followers, and so on down to late adopters, for example. A communication network helps coordination in exactly two ways: by informing each stage about earlier stages, and by creating common knowledge within each stage. We also consider two simple examples: first, we show that low dimension or strong link networks can be better for coordination even though they have far fewer links than high dimension or weak link networks; second, we show that wide dispersion of insurgents, people predisposed toward participation, can be good for coordination but too much dispersion can be bad. This paper is built on the assumption that the most basic and common mechanism for coordination is the I'll if you go mechanism: individuals first communicate with each other about their preferences, and then each individual chooses whether to participate or not. Hence a person's participation depends on what he knows about his neighbours; it does not depend solely on their participation itself, either through learning, adaptation, or social influence. The physical analogies of contagion or diffusion are not