Repeated Interactions and the Social Network Multiplier Markus Mobius Adam Szeidl FIRST DRAFT, 2010 Abstract We build a model of social capital in networks based on repeated interactions. The strength of a relationship in part derives from the value of transactions it enables in the future. We show that shocks can be amplified through a network multiplier, because trust withdrawal that constrains exchange locally can lead to further trust withdrawals that ripple through the network. New technologies that limit social interaction, such as the television, can substantially reduce trust and social capital through this mechanism. We consider a finitely repeated borrowing game in an economic or social network. The key novelty is that the strength of a link is endogenously determined as a function of future loan activity in the network. This approach makes our setup suitable for modeling business connections, where agents transact with each other repeatedly through a web of economic relationships, and also allows us to think about agents’ incentives for forming links, because endogenous link strength depends on the identity and network position of partners. 1. Model setup Consider an exogenous network, and assume that every link of an agent pays a value of 1 dollar at the end of the final period. This is the “direct value” of the link, and can represent either economic or social benefits of being connected. Link capacities in periods before the final date reflect both this direct value and the indirect value of future loan activity. In each period, agents play a borrowing game identical to our basic model. In particular, contracts are enforced by punishment at the level of a link: failure to keep a promise results in the loss of the link for all subsequent periods. One might worry that due to repeated interaction, more complex punishment schemes may enforce higher levels of borrowing. For example, agents who fail to repay a loan may be excluded from future borrowing by the entire community. However, such complex punishments can be ruled out by requiring that the dynamic equilibrium be robust to coalitional deviations (side-deal proof) in every period. Exclusion from future borrowing is not side-deal proof, because when an excluded agent needs to borrow an asset, he can propose a profitable side-deal to the lender and all intermediate agents. 2. Endogenous capacities We now outline the implications of the dynamic model for indirect link values using two example networks. 1