On the behavior of threshold models over finite networks
Author(s)Adam, Elie M.; Dahleh, Munther A.; Ozdaglar, Asuman E.
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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 paper, we develop such an analysis. We establish that agent behavior cycles among different actions in the limit, we characterize the length of such limit cycles, and reveal bounds on the time steps required to reach them. 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.
DepartmentMassachusetts Institute of Technology. Department of Electrical Engineering and Computer Science; Massachusetts Institute of Technology. Engineering Systems Division; Massachusetts Institute of Technology. Laboratory for Information and Decision Systems
Proceedings of the 2012 IEEE 51st IEEE Conference on Decision and Control (CDC)
Institute of Electrical and Electronics Engineers (IEEE)
Adam, Elie M., Munther A. Dahleh, and Asuman Ozdaglar. “On the Behavior of Threshold Models over Finite Networks.” 2012 IEEE 51st IEEE Conference on Decision and Control (CDC) (n.d.).
Author's final manuscript