Abstract
This paper develops strategic foundations for an important statistical model of random networks with heterogeneous expected degrees. Based on this, we show how social networking services that subtly alter the costs and indirect benefits of relationships can cause large changes in behavior and welfare. In the model, agents who value friends and friends of friends choose how much to socialize, which increases the probabilities of links but is costly. There is a sharp transition from fragmented, sparse equilibrium networks to connected, dense ones when the value of friends of friends crosses a cost-dependent threshold. This transition mitigates an extreme inefficiency.
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