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Network Interventions: Targeting Agents or Targeting Links?

Krishna Dasaratha, Anant Shah

Abstract

Consider a network game with linear best responses and spillovers between players, and let agents endogenously choose their links. A planner considers interventions to subsidize actions and/or links between players, aiming to maximize a welfare function depending on equilibrium actions. The structure of the optimal intervention depends on whether links provide non-negative intrinsic value to agents. When they do, it is optimal to focus only on subsidizing actions. When the intrinsic value of links is negative, we give conditions for including link subsidies to be optimal. This reverses the basic structure of the optimal intervention in settings with exogenous links.

Network Interventions: Targeting Agents or Targeting Links?

Abstract

Consider a network game with linear best responses and spillovers between players, and let agents endogenously choose their links. A planner considers interventions to subsidize actions and/or links between players, aiming to maximize a welfare function depending on equilibrium actions. The structure of the optimal intervention depends on whether links provide non-negative intrinsic value to agents. When they do, it is optimal to focus only on subsidizing actions. When the intrinsic value of links is negative, we give conditions for including link subsidies to be optimal. This reverses the basic structure of the optimal intervention in settings with exogenous links.
Paper Structure (14 sections, 5 theorems, 94 equations, 1 figure)

This paper contains 14 sections, 5 theorems, 94 equations, 1 figure.

Table of Contents

  1. Introduction
  2. Related Literature
  3. Model
  4. Remarks on the model
  5. Equilibrium and Spillover Dynamics
  6. Optimal Interventions With Endogenous Spillovers
  7. Characterization of optimal subsidies
  8. Discussion of Applications
  9. Peer Effects in Education
  10. R&D Collaboration Networks
  11. Optimal Interventions In A Benchmark Model
  12. Optimal subsidy in general environments
  13. Conclusion
  14. Omitted Proofs

Key Result

Proposition 1

Consider an intervention $(\bm{\beta},\bm{\sigma})$ and a pure strategy Nash equilibrium $(\mathbf{a}^*,\mathbf{g}^*)$ under this intervention. Let $\mathcal{S} \subseteq \mathcal{N}$ be the set of agents for whom the equilibrium first-order condition for actions binds. Then actions satisfy Furthermore, any link intensity $g_{ij}^*$ for which the equilibrium first-order condition binds satisfies

Figures (1)

  • Figure 1: Ratio of welfare of the optimal subsidy to the welfare of the optimal subsidy which only subsidizes links as a function of the number of agents.

Theorems & Definitions (12)

  • Proposition 1
  • Lemma 1
  • Theorem 1
  • Example 1
  • Theorem 2
  • Definition
  • Definition
  • Theorem 3
  • proof : Proof of \ref{['p:welfarederivativeendogenous']}
  • proof : Proof of \ref{['t:endogenousmodel']}
  • ...and 2 more