Local Farsightedness in Network Formation

We propose the concept of local-k farsighted consistent network for analysing 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 neighbourhood 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.