Equilibrium computation in discrete network games

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.