2026-09-19T01:16:24Zhttps://dspace.mit.edu/server/oai/requestoai:dspace.mit.edu:1721.1/748992022-01-13T07:54:29Zcom_1721.1_7582com_1721.1_7581col_1721.1_131023
Munther A. Dahleh and Asuman Ozdaglar.
Adam, Elie M
Massachusetts Institute of Technology. Dept. of Electrical Engineering and Computer Science.
Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science
2012-11-19T19:16:40Z
2012-11-19T19:16:40Z
2012
2012
http://hdl.handle.net/1721.1/74899
815410301
Thesis (S.M.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 2012.
Cataloged from PDF version of thesis.
Includes bibliographical references (p. 109-110).
We study a model for cascade effects over finite networks based on a deterministic binary linear threshold model. Our starting point is a networked coordination game where each agent's payoff is the sum of the payoffs coming from pairwise interaction with each of the neighbors. We first establish that the best response dynamics in this networked game is equivalent to the linear threshold dynamics with heterogeneous thresholds over the agents. While the previous literature has studied such linear threshold models under the assumption that each agent may change actions at most once, a study of best response dynamics in such networked games necessitates an analysis that allows for multiple switches in actions. In this thesis, we develop such an analysis and construct a combinatorial framework to understand the behavior of the model. To this end, we establish that the agents behavior cycles among different actions in the limit and provide three sets of results. We first characterize the limiting behavioral properties of the dynamics. We determine the length of the limit cycles and reveal bounds on the time steps required to reach such cycles for different network structures. We then study the complexity of decision/counting problems that arise within the context. Specifically, we consider the tractability of counting the number of limit cycles and fixed-points, and deciding the reachability of action profiles. We finally propose a measure of network resilience that captures the nature of the involved dynamics. We prove bounds and investigate the resilience of different network structures under this measure.
by Elie M. Adam.
S.M.
110 p.
eng
Massachusetts Institute of Technology
M.I.T. theses are protected by
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http://dspace.mit.edu/handle/1721.1/7582
Electrical Engineering and Computer Science.
On threshold models over finite networks
Thesis
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Publication
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<Abstract>We study a model for cascade effects over finite networks based on a deterministic binary linear threshold model. Our starting point is a networked coordination game where each agent's payoff is the sum of the payoffs coming from pairwise interaction with each of the neighbors. We first establish that the best response dynamics in this networked game is equivalent to the linear threshold dynamics with heterogeneous thresholds over the agents. While the previous literature has studied such linear threshold models under the assumption that each agent may change actions at most once, a study of best response dynamics in such networked games necessitates an analysis that allows for multiple switches in actions. In this thesis, we develop such an analysis and construct a combinatorial framework to understand the behavior of the model. To this end, we establish that the agents behavior cycles among different actions in the limit and provide three sets of results. We first characterize the limiting behavioral properties of the dynamics. We determine the length of the limit cycles and reveal bounds on the time steps required to reach such cycles for different network structures. We then study the complexity of decision/counting problems that arise within the context. Specifically, we consider the tractability of counting the number of limit cycles and fixed-points, and deciding the reachability of action profiles. We finally propose a measure of network resilience that captures the nature of the involved dynamics. We prove bounds and investigate the resilience of different network structures under this measure.</Abstract>
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