Pooya Molavi

Non-Bayesian social learning

We develop a dynamic model of opinion formation in social networks when the information required for learning a parameter may not be at the disposal of any single agent. Individuals engage in communication with their neighbors in order to learn from their experiences. However, instead of incorporating the views of their neighbors in a fully Bayesian manner, agents use a simple updating rule which linearly combines their personal experience and the views of their neighbors. We show that, as long as individuals take their personal signals into account in a Bayesian way, repeated interactions lead them to successfully aggregate information and learn the true parameter. This result holds in spite of the apparent naivete of agentsʼ updating rule, the agentsʼ need for information from sources the existence of which they may not be aware of, worst prior views, and the assumption that no agent can tell whether her own views or those of her neighbors are more accurate.

Information Heterogeneity and the Speed of Learning in Social Networks

This paper examines how the structure of a social network and the quality of information available to different agents determine the speed of social learning. To this end, we study a variant of the seminal model of DeGroot (1974), according to which agents linearly combine their personal experiences with the views of their neighbors. We show that the rate of learning has a simple analytical characterization in terms of the relative entropy of agents’ signal structures and their eigenvector centralities. Our characterization establishes that the way information is dispersed throughout the social network has non-trivial implications for the rate of learning. In particular, we show that when the informativeness of different agents’ signal structures are comparable in the sense of Blackwell (1953), then a positive assortative matching of signal qualities and eigenvector centralities maximizes the rate of learning. On the other hand, if information structures are such that each individual possesses some information crucial for learning, then the rate of learning is higher when agents with the best signals are located at the periphery of the network. Finally, we show that the extent of asymmetry in the structure of the social network plays a key role in the long-run dynamics of the beliefs.

Learning in network games with incomplete information: asymptotic analysis and tractable implementation of rational behavior

The role of social networks in learning and opinion formation has been demonstrated in a variety of scenarios such as the dynamics of technology adoption [1], consumption behavior [2], organizational behavior [3], and financial markets [4]. The emergence of network-wide social phenomena from local interactions between connected agents has been studied using field data [5]?[7] as well as lab experiments [8], [9]. Interest in opinion dynamics over networks is further amplified by the continuous growth in the amount of time that individuals spend on social media Web sites and the consequent increase in the importance of networked phenomena in social and economic outcomes. As quantitative data become more readily available, a research problem is to identify metrics that could characterize emergent phenomena such as conformism or diversity in individuals? preferences for consumer products or political ideologies [10]. With these metrics available, a natural follow-up research goal is the study of mechanisms that lead to diversity or conformism and the role of network properties like neighborhood structures on these outcomes. All of these questions motivate the development of theoretical models of opinion formation through local interactions in different scenarios.

Foundations of Non-Bayesian Social Learning

In this paper, we study the problem of non-Bayesian learning over social networks by taking an axiomatic approach. As our main behavioral assumption, we postulate that agents follow social learning rules that satisfy imperfect recall, according to which they treat the current beliefs of their neighbors as sufficient statistics for all the information available to them. We establish that as long as imperfect recall represents the only point of departure from Bayesian rationality, agents’ social learning rules take a log-linear form. Our approach also enables us to provide a taxonomy of behavioral assumptions that underpin various non-Bayesian models of learning, including the canonical model of DeGroot. We then show that for a fairly large class of learning rules, the form of bounded rationality represented by imperfect recall is not an impediment to asymptotic learning, as long as agents assign weights of equal orders of magnitude to every independent piece of information. Finally, we show how the dispersion of information among different individuals in the social network determines the rate of learning.

Bayesian Quadratic Network Game Filters

A repeated network game where agents have quadratic utilities that depend on information externalities-an unknown underlying state-as well as payoff externalities-the actions of all other agents in the network-is considered. Agents play Bayesian Nash Equilibrium strategies with respect to their beliefs on the state of the world and the actions of all other nodes in the network. These beliefs are refined over subsequent stages based on the observed actions of neighboring peers. This paper introduces the Quadratic Network Game (QNG) filter that agents can run locally to update their beliefs, select corresponding optimal actions, and eventually learn a sufficient statistic of the networks state. The QNG filter is demonstrated on a Cournot market competition game and a coordination game to implement navigation of an autonomous team.

Aggregate observational distinguishability is necessary and sufficient for social learning

We study a model of information aggregation and social learning recently proposed by Jadbabaie, Sandroni, and Tahbaz-Salehi, in which individual agents try to learn a correct state of the world by iteratively updating their beliefs using private observations and beliefs of their neighbors. No individual agents private signal might be informative enough to reveal the unknown state. As a result, agents share their beliefs with others in their social neighborhood to learn from each other. At every time step each agent receives a private signal, and computes a Bayesian posterior as an intermediate belief. The intermediate belief is then averaged with the beliefs of neighbors to form the individuals belief at next time step. We find a set of necessary and sufficient conditions under which agents will learn the unknown state and reach consensus on their beliefs without any assumption on the private signal structure. The key enabler is a result that shows that using this update, agents will eventually forecast the indefinite future correctly.

A topological view of estimation from noisy relative measurements

In this paper we study the problem of estimating the state of sensors in a sensor network from noisy pairwise relative measurements. The underlying sensor network is typically modeled by a graph whose edges correspond to pairwise relative measurements and nodes represent sensors. Using tools from algebraic topology and cohomology theory, we present a new model in which the higher order relations between measurements are captured as simplicial complexes. This allows us to address the fundamental tension between two conflicting goals: finding estimates that are close to obtained measurements, and at the same time are consistent around any sequence of pairwise measurements that form a cycle. By defining a measure of inconsistency around each cycle, we present a one-parameter family of algorithms that solves the estimation problem by identifying and removing the smallest fraction of measurements that make the estimates globally inconsistent. We demonstrate that the inconsistencies are due to topological obstructions and can be decomposed into local and global components that have interesting geometric interpretations. Furthermore, we show that the proposed algorithm is naturally distributed and will provably result in consistent estimates, and more importantly, recovers two sparse estimation algorithms as special cases.

Information aggregation in a beauty contest game

We consider a repeated game in which a team of agents share a common, but only partially known, task. The team also has the goal to coordinate while completing the task. This creates a trade-off between estimating the task and coordinating with others reminiscent of the kind of trade-off exemplified by the Keynesian beauty contest game. The agents thus can benefit from learning from others. This paper provides a survey of results from [1-4]. We first present a recent result that states repeated play of the game by myopic but Bayesian agents, who observe the actions of their neighbors over a connected network, eventually yield coordination on a single action. Furthermore, the coordinated action is equal to the mean estimate of the common task given individuals information. This indicates that agents in the network have the same mean estimate in the limit despite the differences in the quality of local information. Finally, we state that if the space of signals is a finite set, the coordinated action is equal to the estimate of the common task given full information, that is, agents eventually aggregate the information available throughout the network on the common task optimally.