Local farsightedness in network formation

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