The Impact of Connectivity on the Production and Diffusion of Knowledge

Abstract

We study a social bandit problem featuring production and diffusion of knowledge. While higher connectivity enhances knowledge diffusion, it may reduce knowledge production as agents shy away from experimentation with new ideas and free ride on the observation of other agents. As a result, under some conditions, greater connectivity can lead to homogeneity and lower social welfare.

Figures (10)

• Figure 1: Timeline of the two-period bandit
• Figure 2: Comparative statics of thresholds
• Figure 3: Equilibrium and optimum thresholds on the unit interval; $\underline{\pi}$ is the equilibrium exploitation cutoff; $\bar{\pi}$ is the equilibrium exploration cutoff; $\underline{\pi}^*$ is the optimal exploitation cutoff; $\bar{\pi}^*$ is the optimal exploration cutoff; $\tau$ is the second-period exploration cutoff; In equilibrium (bottom), over-exploitation ($\underline{\pi} > \underline{\pi}^*$) and under-exploration ($\bar{\pi} > \bar{\pi}^*$) shift the thresholds rightward relative to the social optimum.
• Figure 4: Social surplus
• Figure 5: Limiting fraction of explorers

Theorems & Definitions (30)

• Definition 1
• Proposition 1
• Proposition 2
• Proposition 3
• Theorem 1: Exploration equilibrium
• Lemma 1
• Theorem 2: Asymmetric pure-strategy equilibrium
• Theorem 3: Symmetric mixed-strategy equilibrium
• Lemma 2
• Lemma 3