@article{e25a43ce49e444da90dfff22b3b82e72,
title = "Consensus and information cascades in game-theoretic imitation dynamics with static and dynamic network topologies",
abstract = "We construct a model of strategic imitation in an arbitrary network of players who interact through an additive game. Assuming a discrete time update, we show a condition under which the resulting difference equations converge to consensus. Two conjectures on general convergence are also discussed. We then consider the case where players not only may choose their strategies, but also affect their local topology. We show that for the prisoner{\textquoteright}s dilemma, the graph structure converges to a set of disconnected cliques and strategic consensus occurs in each clique. Several examples from various matrix games are provided. A variation of the model is then used to create a simple model for the spreading of trends, or information cascades in (e.g., social) networks. We provide theoretical and empirical results on the trend-spreading model.",
author = "Christopher Griffin and Sarah Rajtmajer and Anna Squicciarini and Andrew Belmonte",
note = "Funding Information: The work of the first, second, and third authors was partially supported by the Army Research Office under grant W911NF-13-1-0271. The work of the first and fourth authors was partially supported by the National Science Foundation under grant CMMI-1463482. Funding Information: ∗Received by the editors October 3, 2016; accepted for publication (in revised form) by M. Golubitsky February 14, 2019; published electronically April 2, 2019. http://www.siam.org/journals/siads/18-2/M109675.html Funding: The work of the first, second, and third authors was partially supported by the Army Research Office under grant W911NF-13-1-0271. The work of the first and fourth authors was partially supported by the National Science Foundation under grant CMMI-1463482. †Applied Research Laboratory, Penn State University, University Park, PA 16802 (griffinch@ieee.org). ‡College of Information Science and Technology, Penn State University, University Park, PA 16802 (srajtmajer@ ist.psu.edu, asquicciarini@ist.psu.edu). §Department of Mathematics, Penn State University, University Park, PA 16802 (alb18@psu.edu). Publisher Copyright: {\textcopyright} 2019 Society for Industrial and Applied Mathematics.",
year = "2019",
doi = "10.1137/16M109675X",
language = "English (US)",
volume = "18",
pages = "597--628",
journal = "SIAM Journal on Applied Dynamical Systems",
issn = "1536-0040",
publisher = "Society of Industrial and Applied Mathematics",
number = "2",
}