title: Networks of conforming or nonconforming individuals tend to reach satisfactory decisions.
abstract: Binary decisions of agents coupled in networks can often be classified into two types: "coordination," where an agent takes an action if enough neighbors are using that action, as in the spread of social norms, innovations, and viral epidemics, and "anticoordination," where too many neighbors taking a particular action causes an agent to take the opposite action, as in traffic congestion, crowd dispersion, and division of labor. Both of these cases can be modeled using linear-threshold-based dynamics, and a fundamental question is whether the individuals in such networks are likely to reach decisions with which they are satisfied. We show that, in the coordination case, and perhaps more surprisingly, also in the anticoordination case, the agents will indeed always tend to reach satisfactory decisions, that is, the network will almost surely reach an equilibrium state. This holds for every network topology and every distribution of thresholds, for both asynchronous and partially synchronous decision-making updates. These results reveal that irregular network topology, population heterogeneity, and partial synchrony are not sufficient to cause cycles or nonconvergence in linear-threshold dynamics; rather, other factors such as imitation or the coexistence of coordinating and anticoordinating agents must play a role.
authors: Engineering and Technology Institute Groningen (ENTEG), Faculty of Mathematics and Natural Sciences, University of Groningen, 9747 AG Groningen, The Netherlands p.ramazi@gmail.com m.cao@rug.nl.
authors: Pouria
authors: 0000-0003-4906-0090
authors: P
authors: Ramazi
authors: Engineering and Technology Institute Groningen (ENTEG), Faculty of Mathematics and Natural Sciences, University of Groningen, 9747 AG Groningen, The Netherlands.
authors: James
authors: J
authors: Riehl
authors: Engineering and Technology Institute Groningen (ENTEG), Faculty of Mathematics and Natural Sciences, University of Groningen, 9747 AG Groningen, The Netherlands p.ramazi@gmail.com m.cao@rug.nl.
authors: Ming
authors: M
authors: Cao
mesh_terms: D003657:Decision Making; D005716:Game Theory; D006801:Humans; D008962:Models, Theoretical; D012919:Social Behavior
keywords: best-response dynamics; equilibrium convergence; evolutionary game theory; linear-threshold model; network games