# Observational learning in an uncertain world

01 Dec 2010-pp 6645-6650

TL;DR: It is shown that information is correctly aggregated when preferences of different types are closely aligned, and even though learning is guaranteed to be incomplete ex ante, there are sample paths over which agents become certain about the underlying state of the world.

Abstract: We study a model of observational learning in social networks in the presence of uncertainty about agents' type distributions. Each individual receives a private noisy signal about a payoff-relevant state of the world, and can observe the actions of other agents who have made a decision before her. We assume that agents do not observe the signals and types of others in the society, and are also uncertain about the type distributions. We show that information is correctly aggregated when preferences of different types are closely aligned. On the other hand, if there is sufficient heterogeneity in preferences, uncertainty about type distributions leads to potential identification problems, preventing asymptotic learning. We also show that even though learning is guaranteed to be incomplete ex ante, there are sample paths over which agents become certain about the underlying state of the world.

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TL;DR: It is shown that the asymmetric flow of information hinders the learning abilities of certain agents regardless of their local observations, and useful closed-form expressions are derived which can be used to motivate design problems to control it.

Abstract: In this paper, we study diffusion social learning over weakly connected graphs. We show that the asymmetric flow of information hinders the learning abilities of certain agents regardless of their local observations. Under some circumstances that we clarify in this paper, a scenario of total influence (or “mind-control”) arises where a set of influential agents ends up shaping the beliefs of noninfluential agents. We derive useful closed-form expressions that characterize this influence, and which can be used to motivate design problems to control it. We provide simulation examples to illustrate the results.

51 citations

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TL;DR: It is shown that the diffusion algorithm converges almost surely to the true state and the superior convergence rate of the diffusion strategy over consensus-based strategies since diffusion schemes allow information to diffuse more thoroughly through the network.

Abstract: We propose a diffusion strategy to enable social learning over networks Individual agents observe signals influenced by the state of the environment The individual measurements are not sufficient to enable the agents to detect the true state of the environment on their own Agents are then encouraged to cooperate through a diffusive process of self-learning and social-learning We show that the diffusion algorithm converges almost surely to the true state Simulation results also illustrate the superior convergence rate of the diffusion strategy over consensus-based strategies since diffusion schemes allow information to diffuse more thoroughly through the network

42 citations

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TL;DR: In this paper, the authors examine a distributed learning problem where the agents of a network form their beliefs about certain hypotheses of interest each agent collects streaming (private) data and updates continually its belief by means of a diffusion strategy, which blends the agent's data with the beliefs of its neighbors.

Abstract: This work examines a distributed learning problem where the agents of a network form their beliefs about certain hypotheses of interest Each agent collects streaming (private) data and updates continually its belief by means of a diffusion strategy, which blends the agent's data with the beliefs of its neighbors We focus on weakly-connected graphs, where the network is partitioned into sending and receiving sub-networks, and we allow for heterogeneous models across the agents First, we examine what agents learn ( social learning ) and provide an analytical characterization for the long-term beliefs at the agents Among other effects, the analysis predicts when a leader-follower behavior is possible, where some sending agents control the beliefs of the receiving agents by forcing them to choose a particular and possibly fake hypothesis Second, we consider the dual or reverse learning problem that reveals how agents learn: given the beliefs collected at a receiving agent, we would like to discover the influence that any sending sub-network might have exerted on this receiving agent ( topology learning ) An unexpected interplay between social and topology learning emerges: given $H$ hypotheses and $S$ sending sub-networks, topology learning can be feasible when $H\geq S$ The latter being only a necessary condition, we then examine the feasibility of topology learning for two useful classes of problems The analysis reveals that a critical element to enable topology learning is a sufficient degree of diversity in the statistical models of the sending sub-networks

15 citations

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TL;DR: This work examines a distributed learning problem where the agents of a network form their beliefs about certain hypotheses of interest by means of a diffusion strategy and examines the feasibility of topology learning for two useful classes of problems.

Abstract: We consider a social learning problem, where a network of agents is interested in selecting one among a finite number of hypotheses. We focus on weakly-connected graphs where the network is partitioned into a sending part and a receiving part. The data collected by the agents might be heterogeneous. For example, some sub-networks might intentionally generate data from a fake hypothesis in order to influence other agents. The social learning task is accomplished via a diffusion strategy where each agent: i) updates individually its belief using its private data; ii) computes a new belief by exponentiating a linear combination of the log-beliefs of its neighbors. First, we examine what agents learn over weak graphs (social learning problem). We obtain analytical formulas for the beliefs at the different agents, which reveal how the agents' detection capability and the network topology interact to influence the beliefs. In particular, the formulas allow us to predict when a leader-follower behavior is possible, where some sending agents can control the mind of the receiving agents by forcing them to choose a particular hypothesis. Second, we consider the dual or reverse learning problem that reveals how agents learned: given a stream of beliefs collected at a receiving agent, we would like to discover the global influence that any sending component exerts on this receiving agent (topology learning problem). A remarkable and perhaps unexpected interplay between social and topology learning is observed: given $H$ hypotheses and $S$ sending components, topology learning can be feasible when $H\geq S$. The latter being only a necessary condition, we examine the feasibility of topology learning for two useful classes of problems. The analysis reveals that a critical element to enable faithful topology learning is the diversity in the statistical models of the sending sub-networks.

11 citations

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TL;DR: It is shown that the asymmetric flow of information hinders the learning abilities of certain agents regardless of their local observations, and useful closed-form expressions are derived which can be used to motivate design problems to control it.

Abstract: In this paper, we study diffusion social learning over weakly-connected graphs. We show that the asymmetric flow of information hinders the learning abilities of certain agents regardless of their local observations. Under some circumstances that we clarify in this work, a scenario of total influence (or "mind-control") arises where a set of influential agents ends up shaping the beliefs of non-influential agents. We derive useful closed-form expressions that characterize this influence, and which can be used to motivate design problems to control it. We provide simulation examples to illustrate the results.

9 citations

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##### References

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TL;DR: In this article, the authors analyze a sequential decision model in which each decision maker looks at the decisions made by previous decision makers in taking her own decision, and they show that the decision rules that are chosen by optimizing individuals will be characterized by herd behavior.

Abstract: We analyze a sequential decision model in which each decision maker looks at the decisions made by previous decision makers in taking her own decision. This is rational for her because these other decision makers may have some information that is important for her. We then show that the decision rules that are chosen by optimizing individuals will be characterized by herd behavior; i.e., people will be doing what others are doing rather than using their information. We then show that the resulting equilibrium is inefficient.

5,536 citations

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TL;DR: It is argued that localized conformity of behavior and the fragility of mass behaviors can be explained by informational cascades.

Abstract: An informational cascade occurs when it is optimal for an individual, having observed the actions of those ahead of him, to follow the behavior of the preceding individual without regard to his own information. We argue that localized conformity of behavior and the fragility of mass behaviors can be explained by informational cascades.

5,170 citations

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Duke University

^{1}TL;DR: In this paper, a comprehensive introduction to probability theory covering laws of large numbers, central limit theorem, random walks, martingales, Markov chains, ergodic theorems, and Brownian motion is presented.

Abstract: This book is an introduction to probability theory covering laws of large numbers, central limit theorems, random walks, martingales, Markov chains, ergodic theorems, and Brownian motion. It is a comprehensive treatment concentrating on the results that are the most useful for applications. Its philosophy is that the best way to learn probability is to see it in action, so there are 200 examples and 450 problems.

5,160 citations

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TL;DR: In this paper, the authors argue that localized conformity of behavior and the fragility of mass behaviors can be explained by informational cascades, where an individual, having observed the actions of those ahead of him, to follow the behavior of the preceding individual without regard to his own information.

Abstract: An informational cascade occurs when it is optimal for an individual, having observed the actions of those ahead of him, to follow the behavior of the preceding individual without regard to his own information. We argue that localized conformity of behavior and the fragility of mass behaviors can be explained by informational cascades.

4,428 citations

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