Designing Weighted and Directed Networks Under Complementarities
47 Pages Posted: 8 Jan 2019 Last revised: 21 Aug 2019
Date Written: August 2019
A planner designs a network with weighted and directed links on which a group of agents play a game with complementarities. A network is optimal if it maximizes an increasing objective function in each agent's effort subject to the planner's available budget. We show that all optimal networks are generalized nested split graphs (GNSGs) in which agents are ordered by “link-dominance”. If link cost is linear, every connected optimal network exhibits a leader-follower division of labor such that a small number of agents, the leaders, influence all the rest to work hard. If link cost is strictly convex, there can be a strict link-dominance ordering between ex ante identical agents. Additionally, we study a non-cooperative network formation game and show that equilibrium networks are inefficient GNSGs.
Keywords: weighted and directed networks, network games, complementarity, optimal network, nested split graph, network formation
JEL Classification: D85, C72
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