# Essays on observational learning

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People's payoffs are often jointly determined by their action and an unobserved common payoff relevant state. To adopt a promising technology is profitable; to adopt an incompetent technology is a waster of money. By observing other people's choices, one person could infer the hidden information behind these choices and make a potentially better decision. In the meanwhile, his/her choice gives out his/her private information as well. Economists are interested in whether private information spread among the entire society could aggregate if only actions rather than information are observable. In other words, economists care about whether the society can learn the true payoff relevant state after observing a large number of informed actions.

In the first chapter, we analyze the question of information aggregation when a fraction of players are naive and act based exclusively on their private information. Rational players are uncertain about the true proportion of naive players. They simultaneously learn about this proportion and about the payoff-relevant state. We find that confounded learning emerges as a robust phenomenon in this environment. That is, in the long run, positive weights are assigned to more than one states. Any observable actions happen with equal probabilities across these states. Thus, even if players still use private information to decide, this information is lost by just observing actions. We further studied the dynamic property of a confounded learning belief and find that it could be globally stable-there're environments where public beliefs eventually settle down to confounded learning with positive probability, starting from almost all current beliefs. We also show that correct learning is always globally stable. In contrast, correct learning may not be globally stable when it arises due to heterogeneous preferences as in [24] In the second chapter, we study the robustness of confounded learning. We found that confounded learning is fragile in presence of public random payoff shocks. For a quite general set-up, we prove the existence of a public shock that can make any confounded learning belief instationary, and hence cannot be a long run limit belief. In practice, this means that a social planner can create a tax/subsidy scheme to eliminate confounded learning in most observational learning environments. In the third chapter, we studies the convergence property of public beliefs. It is a standard technique to explore the martingale property of public beliefs λ [subscript t] to obtain almost surely convergence. We restrict ourselves to a two states two action model and ask whether we can strength the almost surely convergence to convergence in L¹. This is not true if the model is not biased in some sense. We invent a method to show that [mathematical equation].