Strategic Random Networks

34 Pages Posted: 20 Oct 2010

See all articles by Benjamin Golub

Benjamin Golub

Stanford Graduate School of Business

Yair Livne


Date Written: September 30, 2010


To study how economic fundamentals affect the formation of social networks, a model is needed that (i) has agents responding rationally to incentives (ii) can be taken to the data. This paper combines game-theoretic and statistical approaches to network formation in order to develop such a model. Agents spend costly resources to socialize. Their effort levels determine the probabilities of relationships, which are valuable for their direct benefits and also because they lead to other relationships in a second stage of “meeting friends of friends.” The model predicts random graphs with tunable degree distributions and clustering, and characterizes how those statistics depend on the economic fundamentals. When the value of friends of friends is low, equilibrium networks can be either sparse or thick. But as soon as this value crosses a key threshold, the sparse equilibrium disappears completely and only densely connected networks are possible. This transition mitigates an extreme inefficiency.

Keywords: Network Formation, Random Graphs, Random Networks, Phase Transition

JEL Classification: D85

Suggested Citation

Golub, Benjamin and Livne, Yair, Strategic Random Networks (September 30, 2010). NET Institute Working Paper No. 10-21, Available at SSRN: or

Benjamin Golub

Stanford Graduate School of Business ( email )

655 Knight Way
Stanford, CA 94305-5015
United States

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