Spreading Information via Social Networks: An Irrelevance Result

TL;DR

The paper studies how information about a beneficial technology spreads through acyclic social networks (trees) under network externalities and asks whether network structure or seeding affects coordinated adoption. Using a model with imperfect transmission probability $\varepsilon$ and a planner that seeds forests, it introduces the notion of common $p$-beliefs and shows that the extent of approximate common knowledge $C^{p}_{\mathcal{T}}(G)$ is invariant to the forest’s shape and seeding strategy, depending only on the number of agents $I$, prior $\rho$, and $\varepsilon$. The main result ties equilibrium adoption outcomes to these beliefs, proving that the maximum probability of coordinated adoption is independent of the tree structure, with implications that extend to technology adoption games and certain potential games. The paper also identifies limitations: cycles, multiple seeds, and random seeding can alter results, highlighting a trade-off between diffusion speed and higher-order knowledge, and offering guidance for designing seeding strategies to achieve robust coordination.

Abstract

An informed planner wishes to spread information among a group of agents in order to induce efficient coordination -- say the adoption of a new technology with positive externalities. The agents are connected via a social network. The planner informs a seed and then the information spreads via the network. While the structure of the network affects the rate of diffusion, we show that the rate of adoption is the same for all acyclic networks.

Figures (6)

• Figure 1: Star and Line Networks
• Figure 2: Seeding the Line Network
• Figure 3: Broadcast
• Figure 4: Undirected Forest to Directed Tree by Seeding
• Figure 5: Cycle Network

Theorems & Definitions (20)

• Theorem 1
• Proposition 3.1
• Proposition 3.2
• Proposition 3.3
• Proposition 3.4
• Proposition 4.1
• Corollary 4.1
• Proposition 4.2
• Claim 5.1
• Claim 5.2