Equilibrium Computation in Discrete Network Games
71 Pages Posted: 11 Jul 2019 Last revised: 12 Jul 2019
Date Written: July 11, 2019
Computing game-theoretic equilibria is important in many applications, including counterfactual policy evaluation and model estimation. This paper is concerned with the computation of pure-strategy Nash equilibria in graphical games and pairwise stable and directed Nash stable networks in network formation games. We study a class of models obeying a restriction on the strength of strategic interactions, analogous to the assumption in the widely used linear-in-means model of social interactions that the magnitude of the endogenous peer effect is bounded below one. This is an empirically useful class to study because it has been shown that a sampling theory is possible under large-network asymptotics. We provide new algorithms for computing the equilibrium set and prove they have complexity O_p(n^c), where the randomness is with respect to the data-generating process, n is the number of agents, and c depends on the strength of strategic interactions.
Keywords: multiple equilibria, graphical games, network formation, empirical games
JEL Classification: C31, C57, C63, C73
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