Designing Weighted and Directed Networks Under Complementarities

47 Pages Posted: 8 Jan 2019 Last revised: 21 Aug 2019

See all articles by Xueheng Li

Xueheng Li

Economics Experimental Lab, Nanjing Audit University

Date Written: August 2019

Abstract

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

Suggested Citation

Li, Xueheng, Designing Weighted and Directed Networks Under Complementarities (August 2019). Available at SSRN: https://ssrn.com/abstract=3299331 or http://dx.doi.org/10.2139/ssrn.3299331

Xueheng Li (Contact Author)

Economics Experimental Lab, Nanjing Audit University ( email )

86 Yushan W Rd
Pukou, Jiangsu 210017
China

Register to save articles to
your library

Register

Paper statistics

Downloads
48
Abstract Views
489
PlumX Metrics