Tractable Bayesian social learning on trees

Kanoria, Yashodhan; Tamuz, Omer

doi:10.1109/isit.2012.6284016

Cited by 25 publications

(37 citation statements)

References 30 publications

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“…Mathematically modeling learning in networks by actors who update their beliefs on the profitability of choices has been a goal of theoretical economists for the past few decades (cf. Goyal, 2007;Kanoria and Tamuz, 2011). However, to our knowledge, this is the first study to examine the influence of network structure and positions on solutions to multi-armed bandit problems empirically.…”

Section: An Experimental Approachmentioning

confidence: 96%

Learning in social networks: Selecting profitable choices among alternatives of uncertain profitability in various networks

2015

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Section: An Experimental Approachmentioning

confidence: 96%

Learning in social networks: Selecting profitable choices among alternatives of uncertain profitability in various networks

2015

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“…where we included the ith element inside the maximum operator to obtain the first equality. Note that the second equality follows by the norm definition in (6). Consider the second term in (l3), note that by Levy's 0-1 law <l> t (O" �) --+ <l> 00 (0" �) and by the definition in (l0), <l> 00 (0" �) = O" �.…”

Section: T -+Oomentioning

confidence: 97%

“…Because of such computational intractability, Bayesian leaming models often focus on asymptotic char acterizations of agents' behavior [3]- [5]. Only under some structural assumptions on the network or distribution of information, Bayesian updating can be performed tractably [6]- [8]. The mathematical intractability of Bayesian learning in the general case motivates the introduction of bounded rational approaches that resort to simplified Bayesian updates and heuristic rules to keep computations tractable.…”

Section: Introductionmentioning

confidence: 99%

Dynamic games with side information in economic networks

Eksin

Molavi

Ribeiro

et al. 2012

2012 Conference Record of the Forty Sixth Asilomar Conference on Signals, Systems and Computers (ASILOMAR)

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We consider a dynamic game with payoff exter nalities. Agents' utility depends on an unknown true state of the world and actions of everyone in the network. Each agent has an initial private information about the underlying state and repeatedly observes actions of its neighbors. We analyze the asymptotic behavior of agents' actions and beliefs in a connected network when it is common knowledge that the agents are myopic and rational. Given a quadratic payoff function, we provide a new proof for an existing result that claims almost sure consensus in actions asymptotically. Given consensus in actions, we show that agents have the same mean estimate of the true state of the world in the limit. We justify these results in a numerical example motivated by a socio economic scenario. I. IN TRODUCTIONThe model discussed in this paper belongs to the class of repeated games of incomplete information. Agents repeatedly play a game where the payoffs depend on a parameter ("state of the world") as well as the actions taken by other agents. In a game of incomplete information the payoff-relevant parameter is unknown to the agents; rather, they make private noisy observations about the parameter that can be used when deciding on an action. In such a setting, on the one hand, agents' optimal actions depend on their private observations as well as how they expect others to play, and on the other hand, by selecting certain actions agents are revealing perhaps unwillingly-pieces of private information about the unknown parameter [1]. As a result, the actions chosen by "rational" agents are influenced by both an information externality pertaining to the flow of information about the unknown parameter and a payoff externality corresponding to the dependence of the payoff on actions taken by other agents. Rational agents need to select actions that are optimal given their information while also taking into account the effect of their decisions on the future play. They also need to try the leam about the underlying parameter as much as possible by incorporating the new information revealed to them optimally, i.e., using the Bayes rule. This kind of strategic leaming is relevant to the vast literature on learning in games; refer to [2] and references therein.There exists an extensive literature on learning over net works. Bayesian leaming stands as the normative behavioral model for agents in social networks; however, it is often computationally intractable even for networks with small IEEE 520 number of agents. This is since a Bayesian update requires an agent to infer not only about the information of her neighbors but also that of the neighbors of her neighbors and so on. Because of such computational intractability, Bayesian leaming models often focus on asymptotic char acterizations of agents' behavior [3]- [5]. Only under some structural assumptions on the network or distribution of information, Bayesian updating can be performed tractably [6]- [8]. The mathematical intractability of Bayesian learning in the general case motivate...

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“…A model of Bayesian social learning where agents receive a private information about state of the nature and observe the actions of their neighbors is investigated in [5]. They proposed an algorithm for agents' calculations on tree-based social networks and analyzed their algorithm in terms of efficiency and convergence.…”

Section: Related Work and Organization Of Papermentioning

confidence: 99%

“…In the benchmark protocol, we assume that instead of transmitting posterior distribution , each node transmits its own private observations and all raw observations received over the network. Thus each node has the entire available observation history from previous nodes, which we will denote as 5 . Therefore, the estimation of each node is free of mis-information.…”

Section: Remarksmentioning

confidence: 99%

Mis-Information Removal in Social Networks: Constrained Estimation on Dynamic Directed Acyclic Graphs

Krishnamurthy

Hamdi

2013

IEEE J. Sel. Top. Signal Process.

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A key issue in the multi agent state estimation presented in social networks is the inadvertent multiple re-use of data also known as mis-information propagation or data incest. We formulate this mis-information propagation in a graph theoretic setting and give a necessary and sufficient conditions on the topology of information flow network so that the underlying state can be estimated optimally. A distributed fusion algorithm is proposed so that the social network has incest free estimates. We also provide a discussion on mis-information removal algorithm for information exchange protocols where people learn from actions of others in a social network. A sub-optimal algorithm is also presented when the information flow graph is not known. Numerical examples are provided to illustrate the performance of the proposed optimal and sub-optimal algorithms.

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Tractable Bayesian social learning on trees

Cited by 25 publications

References 30 publications

Learning in social networks: Selecting profitable choices among alternatives of uncertain profitability in various networks

Learning in social networks: Selecting profitable choices among alternatives of uncertain profitability in various networks

Dynamic games with side information in economic networks

Mis-Information Removal in Social Networks: Constrained Estimation on Dynamic Directed Acyclic Graphs

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