Designing weighted and directed networks under complementarities

Abstract

Strategic complementarities influence various social and economic activities. This study introduces a model to design a weighted and directed complementarity network to achieve a planner's objectives. The network represents the direction and intensity of complementarities between agents, influencing their best-responses to one another and determining equilibrium efforts. The planner's objective function can be convex, as commonly assumed in prior research, or arbitrarily concave to represent scenarios with diminishing marginal returns to each agent's effort. In all scenarios, optimal networks are generalized nested split graphs (GNSGs) which exhibit a link-dominance hierarchy among agents. These optimal networks are often strictly hierarchical, leading to inequality between ex ante identical agents. Additional analysis of a non-cooperative network formation game reveals that all decentralized equilibrium networks are inefficient GNSGs.