Approximate Variational Estimation for a Model of Network Formation
AbstractWe study an equilibrium model of sequential network formation with heterogeneous
players. The payoffs depend on the number and composition of direct connections, but
also the number of indirect links. We show that the network formation process is a potential
game and in the long run the model converges to an exponential random graph (ERGM).
Since standard simulation-based inference methods for ERGMs could have exponentially
slow convergence, we propose an alternative deterministic method, based on a variational
approximation of the likelihood. We compute bounds for the approximation error for a given
network size and we prove that our variational method is asymptotically exact, extending
results from the large deviations and graph limits literature to allow for covariates in the
ERGM. A simple Monte Carlo shows that our deterministic method provides more robust
estimates than standard simulation based inference.