A Theory of Multiplexity: Sustaining Cooperation with Multiple Relations

People are embedded in multiple social relations. We examine when different networks overlap with each other, and especially, what network features affect the overlapping pattern. We start with 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 to link with a stranger? The key tradeoff that we emphasize is the one between multiplexity (having multiple relations with the same person) and community enforcement. Multiplexity enhances cooperation because various relations serve as social collateral for each other, while linking to a stranger might better 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 “multiplexity trap” can occur; that is, agents may keep adding relations with friends, even when it is more efficient to link with a stranger; (2) Agents tend to multiplex when the existing networks either (a) have low degree dispersions (i.e., all agents have similar numbers of friends) or (b) exhibit positive assortativity (agents are linked with those who have a similar number of friends). We also find that agents tend to multiplex more when the new relationship is more important. Using the Indian Village Survey data, we also find supportive evidence for our theoretical predictions.
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