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Dynamic public learning in networks of strategic agents: The role of inter/intra-community ties

We study the quality of information aggregation in a dynamic quadratic game of incomplete information. Agents in each generation have access to a public history of noisy aggregate actions in previous generations. Each agent also belongs to an information community, where they share a private noisy signal about the state. We quantify the quality of information aggregation as the asymptotic precision of the publicly learned signal about the state, and study how the interactions between/within information communities affect the quality of learning. By characterizing the precision of aggregate learning for random walks with low volatility, we show the inefficiency of learning from the public history: while for a static state, public history fully reveals the state, a small perturbation in the state from generation to generation significantly degrades the quality of public learning. As for the effect of information-action structure, we show that the intercommunity interactions exhibit a double-edged effect: while the inter-community interaction of local influencers and influences improves the quality of learning for slow dynamics, the intercommunity interaction of global influencers and influences hampers learning for fast dynamics. As a result, we may observe phase transition in the quality of learning between different information-action structures.