Equilibrium Computation in Discrete Network Games

79 Pages Posted: 11 Jul 2019 Last revised: 19 Jun 2020

See all articles by Michael P. Leung

Michael P. Leung

University of Southern California - Department of Economics

Date Written: July 11, 2019

Abstract

Counterfactual policy evaluation often requires computation of game-theoretic equilibria. We provide new algorithms for computing pure-strategy Nash equilibria of games on networks with finite action spaces. The algorithms exploit the fact that many agents may be endowed with types such that a particular action is a dominant strategy. These agents can be used to partition the network into smaller subgames whose equilibrium sets may be more feasible to compute. We provide bounds on the complexity of our algorithms for models obeying certain restrictions on the strength of strategic interactions. These restrictions are 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. For these models, our algorithms 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. We also provide algorithms for computing pairwise stable and directed Nash stable networks in network formation games.

Keywords: multiple equilibria, graphical games, network formation, empirical games

JEL Classification: C31, C57, C63, C73

Suggested Citation

Leung, Michael, Equilibrium Computation in Discrete Network Games (July 11, 2019). Available at SSRN: https://ssrn.com/abstract=3418017 or http://dx.doi.org/10.2139/ssrn.3418017

Michael Leung (Contact Author)

University of Southern California - Department of Economics ( email )

3620 South Vermont Ave.
Kaprielian (KAP) Hall, 310A
Los Angeles, CA 90089
United States

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