A Strategic Theory of Network Status

This paper studies environments where individuals allocate resources across relationships with others, creating a weighted, directed network. Value is achieved both through an exogenous factor and maintaining close connections to high-value individuals. We consider two cases corresponding to the direction benefits flow along links. In Model A (for “asking”) agents receive benefits through the links they create, whereas in Model G (for “giving”) the reverse is true: agents pass value along their links. Equilibrium and socially efficient networks are characterized. In Model G equilibrium networks do not necessarily maximize group welfare, but in Model A efficient networks constitute equilibria despite extensive network externalities. This work has benefited from discussions with Meghana Bhatt, Kim Border, Christopher Chambers, Jernej Copic, Federico Echenique, Andrea Galeotti, Jacob Goeree, P.J. Healy, Matthew Jackson, Thomas Palfrey, Betsy Sinclair, Simon Wilkie, and participants at the 2005 SISL workshop, and was supported in part by a fellowship from SISL/IST. email: [email protected], website: http://www.hss.caltech.edu/∼rogers. Division of Humanities and Social Sciences, California Institute of Technology, Mail code 228-77, Pasadena, CA 91125, USA.