Characterizing Strategic Cascades on Networks

Transmission of disease, spread of information and rumors, adoption of new products, and many other network phenomena can be fruitfully modeled as cascading processes, where actions chosen by nodes influence the subsequent behavior of neighbors in the network graph. Current literature on cascades tends to assume nodes choose myopically based on the state of choices already taken by other nodes. We examine the possibility of strategic choice, where agents representing nodes anticipate the choices of others who have not yet decided, and take into account their own influence on such choices. Our study employs the framework of Chierichetti et al. [2012], who (under assumption of myopic node behavior) investigate the scheduling of node decisions to promote cascades of product adoptions preferred by the scheduler. We show that when nodes behave strategically, outcomes can be extremely different. We exhibit cases where in the strategic setting 100% of agents adopt, but in the myopic setting only an arbitrarily small epsilon % do. Conversely, we present cases where in the strategic setting 0% of agents adopt, but in the myopic setting (100-epsilon)% do, for any constant epsilon > 0. Additionally, we prove some properties of cascade processes with strategic agents, both in general and for particular classes of graphs.Comment: To appear in EC 201

Theoretical Tools for Network Analysis: Game Theory, Graph Centrality, and Statistical Inference.

A computer-driven data explosion has made the difficulty of interpreting large data sets of interconnected entities ever more salient. My work focuses on theoretical tools for summarizing, analyzing, and understanding network data sets, or data sets of things and their pairwise connections. I address four network science issues, improving our ability to analyze networks from a variety of domains. I first show that the sophistication of game-theoretic agent decision making can crucially effect network cascades: differing decision making assumptions can lead to dramatically different cascade outcomes. This highlights the importance of diligence when making assumptions about agent behavior on networks and in general. I next analytically demonstrate a significant irregularity in the popular eigenvector centrality, and propose a new spectral centrality measure, nonbacktracking centrality, showing that it avoids this irregularity. This tool contributes a more robust way of ranking nodes, as well as an additional mathematical understanding of the effects of network localization. I next give a new model for uncertain networks, networks in which one has no access to true network data but instead observes only probabilistic information about edge existence. I give a fast maximum-likelihood algorithm for recovering edges and communities in this model, and show that it outperforms a typical approach of thresholding to an unweighted network. This model gives a better tool for understanding and analyzing real-world uncertain networks such as those arising in the experimental sciences. Lastly, I give a new lens for understanding scientific literature, specifically as a hybrid coauthorship and citation network. I use this for exploratory analysis of the Physical Review journals over a hundred-year period, and I make new observations about the interplay between these two networks and how this relationship has changed over time.PhDComputer Science and EngineeringUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/133463/1/travisbm_1.pd