Watts, Duncan J.
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Publication Resilient Cooperators Stabilize Long-run Cooperation In The Finitely Repeated Prisoner’s Dilemma(2017-01-13) Mao, Andrew; Suri, Siddharth; Watts, Duncan J.; Dworkin, LiliLearning in finitely repeated games of cooperation remains poorly understood in part because their dynamics play out over a timescale exceeding that of traditional lab experiments. Here, we report results of a virtual lab experiment in which 94 subjects play up to 400 ten-round games of Prisoner’s Dilemma over the course of twenty consecutive weekdays. Consistent with previous work, the typical round of first defection moves earlier for several days; however, this unravelling process stabilizes after roughly one week. Analysing individual strategies, we find that approximately 40% of players behave as resilient cooperators who avoid unravelling even at significant cost to themselves. Finally, using a standard learning model we predict that a sufficiently large minority of resilient cooperators can permanently stabilize unravelling among a majority of rational players. These results shed hopeful light on the long-term dynamics of cooperation, and demonstrate the importance of long-run experiments.Publication Evaluating the Fake News Problem at the Scale of the Information Ecosystem(2020-04-03) Allen, Jennifer; Howland, Baird; Mobius, Markus; Rothschild, David; Watts, Duncan J.“Fake news,” broadly defined as deliberately false or misleading information masquerading as legitimate news, is frequently asserted to be pervasive on the web, and on social media in particular, with serious consequences for public opinion, political polarization, and ultimately democracy. Using a unique multimode data set that comprises a nationally representative sample of mobile, desktop, and television consumption across all categories of media content, we refute this conventional wisdom on three levels. First, news consumption of any sort is heavily outweighed by other forms of media consumption, comprising at most 14.2% of Americans’ daily media diets. Second, to the extent that Americans do consume news, it is overwhelmingly from television, which accounts for roughly five times as much as news consumption as online, while a supermajority of Americans consume little or no news online at all. Third, fake news comprises only about 1% of overall news consumption and 0.15% of Americans’ daily media diet. Although consumption data alone cannot determine that online misinformation in any dose is not dangerous to democracy, our results suggest that the origins of public mis-informedness and polarization are more likely to lie in the content of ordinary news--especially on television--or alternatively in the avoidance of news altogether as they are in overt fakery.Publication Scaling and Percolation in the Small-World Network Model(1999-05-06) Newman, M E.J.; Watts, Duncan J.In this paper we study the small-world network model of Watts and Strogatz, which mimics some aspects of the structure of networks of social interactions. We argue that there is one non-trivial length-scale in the model, analogous to the correlation length in other systems, which is well-defined in the limit of infinite system size and which diverges continuously as the randomness in the network tends to zero, giving a normal critical point in this limit. This length-scale governs the cross-over from large- to small-world behavior in the model, as well as the number of vertices in a neighborhood of given radius on the network. We derive the value of the single critical exponent controlling behavior in the critical region and the finite size scaling form for the average vertex-vertex distance on the network, and, using series expansion and Pade approximants, find an approximate analytic form for the scaling function. We calculate the effective dimension of small-world graphs and show that this dimension varies as a function of the length-scale on which it is measured, in a manner reminiscent of multifractals. We also study the problem of site percolation on small-world networks as a simple model of disease propagation, and derive an approximate expression for the percolation probability at which a giant component of connected vertices first forms (in epidemiological terms, the point at which an epidemic occurs). The typical cluster radius satisfies the expected finite size scaling form with a cluster size exponent close to that for a random graph. All our analytic results are confirmed by extensive numerical simulations of the modelPublication Random Graphs With Arbitrary Degree Distributions and Their Applications(2001-07-24) Newman, M. E.J.; Strogatz, S. H.; Watts, Duncan J.Recent work on the structure of social networks and the internet has focussed attention on graphs with distributions of vertex degree that are significantly different from the Poisson degree distributions that have been widely studied in the past. In this paper we develop in detail the theory of random graphs with arbitrary degree distributions. In addition to simple undirected, unipartite graphs, we examine the properties of directed and bipartite graphs. Among other results, we derive exact expressions for the position of the phase transition at which a giant component first forms, the mean component size, the size of the giant component if there is one, the mean number of vertices a certain distance away from a randomly chosen vertex, and the average vertex-vertex distance within a graph. We apply our theory to some real-world graphs, including the world-wide web and collaboration graphs of scientists and Fortune 1000 company directors. We demonstrate that in some cases random graphs with appropriate distributions of vertex degree predict with surprising accuracy the behavior of the real world, while in others there is a measurable discrepancy between theory and reality, perhaps indicating the presence of additional social structure in the network that is not captured by the random graph.