Abstract: This paper develops estimation methods for network formation using observed data from a single large network. We characterize network formation as a simultaneous-move game with incomplete information, where we allow for utility externalities from indirect friends such as friends in common, so the expected utility from direct friends can be nonlinear. Nonlinearity poses a challenge in estimation because each individual faces an interdependent multinomial discrete choice problem with 2ⁿ⁻¹ alternatives, which is difficult to solve. We propose a novel method to linearize the expected utility using Legendre transform and derive a closed-form expression for the conditional choice probability (CCP). Using the closed-form expression, we show that the CCP in n-player games converge to the CCP in a limit game as n approaches infinity. We propose a two-step estimation procedure that requires few assumptions on equilibrium selection, is simple to compute, and provides asymptotically valid estimators for the parameters. Monte Carlo results show that the estimation procedure can provide accurate estimates if networks are large.
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