A Theory of Multiplexity : Sustaining Cooperation with Multiple Relations

People are embedded in multiple social relations. These relations are not isolated from each other. Do different networks overlap and why? We focus on the following question: When an agent has a new relation to add, would they choose to multiplex, i.e., to link with a friend or a stranger? The key tradeoff that we emphasize is the one between multiplexity and community enforcement. Multiplexity enhances cooperation because various relations serve as social collateral for each other, while linking to a stranger can utilize community enforcement, whose power relies more on the rest of the network structure. We find the following: (1) There is a strong tendency to multiplex, and the “multiplexity trap” can occur; that is, agents may keep adding relationships with friends, even when it is more efficient to link with a stranger. (2) Agents tend to multiplex when the existing network (a) has a low degree dispersion (i.e., all agents have similar numbers of friends) or (b) is positively assortative (agents are linked with those with a similar number of friends). We also find that agents tend to multiplex when the new relationship is more important. Using the Indian Village Survey data, we provide supportive evidence for our theoretical predictions