We derive asymptotic approximations for models of strategic network formation, where limits are taken as the number of nodes (agents) increases to infinity. Our framework assumes a random utility model where agents have heterogeneous tastes over links, and payoffs allow for anonymous and non-anonymous interaction effects, and the observed network is assumed to be pairwise stable. Our main results concern convergence of the link intensity from finite pairwise stable networks to the (many-player) limiting distribution. The set of possible limiting distributions is shown to have a fairly simple form and is characterized through aggregate equilibrium conditions, which may permit multiple solutions. We illustrate how these formal results can be used to analyze identification of link preferences and estimate or bound preference parameters. We also derive an analytical expression for agents’ welfare (expected surplus) from the structure of the network.
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