Working Papers

Optimizing Katz-Bonacich Centrality in a Network

Network Comparative Statics (Oct 2020) link

Abstract: This paper develops a framework for analyzing the effect of arbitrary changes to network structure in linear-quadratic games on networks. Changes to network structure which increase total activity and total utility are studied for the case of strategic complements and strategic substitutes. Changes which are welfare increasing are found to depend on a new measure of centrality which counts the total length of walks from a node.

Two optimal network design problems are then considered. Total activity is found to be a convex function of the edge weights of the network, which allows for convex optimization techniques to be applied to minimize total activity as in the traditional `key player' problem. Welfare maximizing network structures are also studied and previous results which associate optimal networks with nested split graphs are generalized.

Older Papers

Minimum Effort Games on Networks (Sept 2016) link - earlier version (Jan 2013) - link