81 research outputs found
Distributed Coverage Verification in Sensor Networks Without Location Information
In this paper, we present three distributed algorithms for coverage verification in sensor networks with no location information. We demonstrate how, in the absence of localization devices, simplicial complexes and tools from algebraic topology can be used in providing valuable information about the properties of the cover. Our approach is based on computation of homologies of the Rips complex corresponding to the sensor network. First, we present a decentralized scheme based on Laplacian flows to compute a generator of the first homology, which represents coverage holes. Then, we formulate the problem of localizing coverage holes as an optimization problem for computing a sparse generator of the first homology. Furthermore, we show that one can detect redundancies in the sensor network by finding a sparse generator of the second homology of the cover relative to its boundary. We demonstrate how subgradient methods can be used in solving these optimization problems in a distributed manner. Finally, we provide simulations that illustrate the performance of our algorithms
Non-Bayesian Social Learning, Second Version
We develop a dynamic model of opinion formation in social networks. Relevant information is spread throughout the network in such a way that no agent has enough data to learn a payoff-relevant parameter. 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 (even though the neighbors’ views may be quite inaccurate). This non-Bayesian learning rule is motivated by the formidable complexity required to fully implement Bayesian updating in networks. We show that, under mild assumptions, repeated interactions lead agents to successfully aggregate information and to learn the true underlying state of the world. This result holds in spite of the apparent naıvite of agents’ updating rule, the agents’ need for information from sources (i.e., other agents) the existence of which they may not be aware of, the possibility that the most persuasive agents in the network are precisely those least informed and with worst prior views, and the assumption that no agent can tell whether their own views or their neighbors’ views are more accurate.Social networks, learning, information aggregation
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Consensus Over Ergodic Stationary Graph Processes
In this technical note, we provide a necessary and sufficient condition for convergence of consensus algorithms when the underlying graphs of the network are generated by an ergodic and stationary random process. We prove that consensus algorithms converge almost surely, if and only if, the expected graph of the network contains a directed spanning tree. Our results contain the case of independent and identically distributed graph processes as a special case. We also compute the mean and variance of the random consensus value that the algorithm converges to and provide a necessary and sufficient condition for the distribution of the consensus value to be degenerate
Variance Analysis of Randomized Consensus in Switching Directed Networks
In this paper, we study the asymptotic properties of distributed consensus
algorithms over switching directed random networks. More specifically, we focus
on consensus algorithms over independent and identically distributed, directed
Erdos-Renyi random graphs, where each agent can communicate with any other
agent with some exogenously specified probability . While it is well-known
that consensus algorithms over Erdos-Renyi random networks result in an
asymptotic agreement over the network, an analytical characterization of the
distribution of the asymptotic consensus value is still an open question. In
this paper, we provide closed-form expressions for the mean and variance of the
asymptotic random consensus value, in terms of the size of the network and the
probability of communication . We also provide numerical simulations that
illustrate our results.Comment: 6 pages, 3 figures, submitted to American Control Conference 201
Exchange rates and monetary policy uncertainty
We document that a trading strategy that is short the U.S. dollar and long other currencies exhibits significantly larger excess returns on days with scheduled Federal Open Market Committee (FOMC) announcements. We also show that these excess returns (i) are higher for currencies with higher interest rate differentials vis-Ă -vis the U.S.; (ii) increase with uncertainty about monetary policy; and (iii) intensify when the Federal Reserve adopts a policy of monetary easing. We interpret these excess returns as a compensation for monetary policy uncertainty within a parsimonious model of constrained financiers who intermediate global demand for currencies
The network origins of aggregate fluctuations
This paper argues that in the presence of intersectoral input-output linkages, microeconomic idiosyncratic shocks may lead to aggregate fluctuations. In particular, it shows that, as the economy becomes more disaggregated, the rate at which aggregate volatility decays is determined by the structure of the network capturing such linkages. Our main results provide a characterization of this relationship in terms of the importance of different sectors as suppliers to their immediate customers as well as their role as indirect suppliers to chains of downstream sectors. Such higher-order interconnections capture the possibility of "cascade effects" whereby productivity shocks to a sector propagate not only to its immediate downstream customers, but also indirectly to the rest of the economy. Our results highlight that sizable aggregate volatility is obtained from sectoral idiosyncratic shocks only if there exists significant asymmetry in the roles that sectors play as suppliers to others, and that the "sparseness" of the input-output matrix is unrelated to the nature of aggregate fluctuations.Business cycle, aggregate volatility, diversification, input-output linkages, intersectoral network, cascades
Cascades in Networks and Aggregate Volatility
We provide a general framework for the study of cascade effects created by interconnections between sectors, firms or financial institutions. Focusing on a multi sector economy linked through a supply network, we show how structural properties of the supply network determine both whether aggregate volatility disappears as the number of sectors increases (i.e., whether the law of large numbers holds) and when it does, the rate at which this happens. Our main results characterize the relationship between first order interconnections (captured by the weighted degree sequence in the graph induced by the input-output relations) and aggregate volatility, and more importantly, the relationship between higher-order interconnections and aggregate volatility. These higher-order interconnections capture the cascade effects, whereby low productivity or the failure of a set of suppliers propagates through the rest of the economy as their downstream sectors/firms also suffer and transmit the negative shock to their downstream sectors/firms. We also link the probabilities of tail events (large negative deviations of aggregate output from its mean) to sector-specific volatility and to the structural properties of the supply network
Systemic Risk and Stability in Financial Networks
We provide a framework for studying the relationship between the financial network architecture and the likelihood of systemic failures due to contagion of counterparty risk. We show that financial contagion exhibits a form of phase transition as interbank connections increase: as long as the magnitude and the number of negative shocks affecting financial institutions are sufficiently small, more “complete” interbank claims enhance the stability of the system. However, beyond a certain point, such interconnections start to serve as a mechanism for propagation of shocks and lead to a more fragile financial system. We also show that, under natural contracting assumptions, financial networks that emerge in equilibrium may be socially inefficient due to the presence of a network externality: even though banks take the effects of their lending, risk-taking and failure on their immediate creditors into account, they do not internalize the consequences of their actions on the rest of the network.We are grateful to David Brown, Ozan Candogan, Gary Gorton, Ali Jadbabaie, Jean-Charles Rochet, Alp Simsek, Ali Shourideh and Rakesh Vohra for useful feedback and suggestions. We also thank seminar participants at the 2012 and 2013 AEA Conferences, Chicago Booth, MIT, Stanford GSB, and the Systemic Risk conference at the Goethe University. Acemoglu and Ozdaglar gratefully acknowledge financial support from the Army Research Office, Grant MURI W911NF-12-1-0509
The Network Origins of Large Economic Downturns
This paper shows that large economic downturns may result from the propagation of microeconomic shocks over the input-output linkages across different firms or sectors within the economy. Building on the framework of Acemoglu et al. (2012), we argue that the economy’s input-output structure can fundamentally reshape the distribution of aggregate output, increasing the likelihood of large downturns from infinitesimal to substantial. More specifically, we show that an economy with non-trivial intersectoral input-output linkages that is subject to thin-tailed productivity shocks may exhibit deep recessions as frequently as economies that are subject to heavy-tailed shocks. Moreover, we show that in the presence of input-output linkages, aggregate volatility is not necessarily a sufficient statistic for the likelihood of large downturns. Rather, depending on the shape of the distribution of the idiosyncratic shocks, different features of the economy’s input-output network may be of first-order importance. Finally, our results establish that the effects of the economy’s input-output structure and the nature of the idiosyncratic firm level shocks on aggregate output are not separable, in the sense that the likelihood of large economic downturns is determined by the interplay between the two
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