Sustaining Cooperation with Multiple Relations: a Theory of Multiplexity
Abstract: People are embedded in multiple social relations. These relationships are not isolated from each other. This paper provides a framework to analyze the multiplex of networks. We present a model in which each pair of agents may form more than one relationship. Each relationship is captured by an infinitely repeated prisoner’s dilemma with variable stakes of cooperation. We show that multiplexity, i.e. having more than one relationship on a link, boosters incentives as different relationships serve as social collateral for each other. We then endogenize the network formation and ask: when an agent has a new link to add, will she multiplex with a current neighbor or link with a stranger? 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 the current neighbor(s), even if it is more compatible to cooperate with a stranger. (2) Individuals tend to multiplex when the current network (a) has a low degree dispersion (i.e., all individuals have similar numbers of friends), or (b) is positively assortative. We also find that when relationships differ in their importance, agents tend to multiplex when the new relationship is less important and link with a stranger when it’s more important. Lastly, we find empirical evidence that supports our theoretical findings.
