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Information flows and crashes in dynamic social networks

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Abstract

We develop a dynamic model of information transmission and aggregation in social networks in which continued membership in the network is contingent on the accuracy of opinions. Agents have opinions about a state of the world and form links to others in a directed fashion probabilistically. Agents update their opinions by averaging those of their connections, weighted by how long their connections have been in the system. Agents survive or die based on how far their opinions are from the true state. In contrast to the results in the extant literature on DeGroot learning, we show through simulations that for some parameterizations the model cycles stochastically between periods of high connectivity, in which agents arrive at a consensus opinion close to the state, and periods of low connectivity, in which agents’ opinions are widely dispersed.

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Notes

  1. Absent detailed information about the network topology, such as the links among analysts, we use the number of agents in the network as a proxy for the relative magnitudes of the numbers of connections.

  2. This condition on \(k^*\) ensures that the probability of death in (3) is bounded by zero and one.

  3. The model is written in the Python programming language (Python xxx) using the NetworkX (Hagberg et al. 2008) and Pandas (McKinney 2012) packages. Seed values for runs are randomly chosen but are stored for potential later use. We establish a “burn-in” period at the beginning of a run of the model. At the beginning of the burn-in period, all agents have uniformly drawn k-values and zero connections. The burn-in period ends when all agents have died at least once, after which the model run is considered to begin and time is reset to \(t=0\).

  4. Using the terminology in Golub and Jackson (2010), the singleton set containing the last agent is the only “closed group,” and thus the only minimal closed group, relative to \({\mathbf {W}}\) in (9). Then, (10) follows from Theorem 3 in Golub and Jackson (2010).

  5. Other cutoff values for state classification produce similar results.

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Authors and Affiliations

  1. Federal Reserve Board of Governors, 20th Street and Constitution Avenue N.W., Washington, DC, 20551, USA

    Phillip J. Monin

  2. Office of the Chief Investment Officer, University of California, 1111 Broadway, Oakland, CA, 94607, USA

    Richard Bookstaber

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  1. Phillip J. Monin
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  2. Richard Bookstaber
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Correspondence to Phillip J. Monin.

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Monin, P.J., Bookstaber, R. Information flows and crashes in dynamic social networks. J Econ Interact Coord 16, 471–495 (2021). https://doi.org/10.1007/s11403-020-00310-5

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