Local farsightedness in network formation

We propose the concept of local‐k farsighted consistent network for analyzing network formation games where players only consider a limited number of feasible networks. A network g is said to be local‐k farsightedly consistent if, for any network g′ within the distance‐k neighborhood of g, either g is not defeated by g′, or g defeats g′. We show that if the utility function is (componentwise) egalitarian or satisfies reversibility or excludes externalities across components, then local‐k farsightedness is more likely to be a good proxy for what would happen when players have full knowledge of all feasible networks.