Aggregate learning in networks of strategic agents

We study the quality of aggregate learning in a networked dynamic quadratic game of incomplete information. We consider an ongoing generation of agents, where in each generation agents have access to a public history of noisy aggregate actions in previous generations. Each agent also receives a private noisy signal about the state in the current generation. We quantify the quality of aggregate learning as the asymptotic precision of the publicly learned signal about the current state, and study how the interactions among the agents affect the quality of aggregate learning. By characterizing the precision of aggregate learning for slow walks, we show the inefficiency of learning from 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 aggregate learning. As for the effect of the interaction structure, we show that the quality of aggregate learning for slow walks is mainly determined by the local structure of the graph: the denser the locality, the higher the quality of information aggregation. For fast dynamics, the quality of aggregate learning is positively affected by the average Bonacich centrality, and is negatively affected by its variance.