Breaking Indecision in Multiagent, Multioption Dynamics

decision making; opinion dynamics; symmetry-breaking; synchrony-breaking; Bifurcation (mathematics); Multi agent systems; Network architecture; Bird flocks; Breakings; Decisions makings; Influence networks; Mathematical theory; Multi agent; Opinion dynamics; Performance; Symmetry breakings; Synchrony-breaking; Decision making

Abstract :

[en] How does a group of agents break indecision when deciding about options with qualities that are hard to distinguish? Biological and artificial multiagent systems, from honeybees and bird flocks to bacteria, robots, and humans, often need to overcome indecision when choosing among options in situations in which the performance or even the survival of the group is at stake. Breaking indecision is also important because in a fully indecisive state, where agents are not biased toward any specific option, the agent group is maximally sensitive and prone to adapt to inputs and changes in its environment. Here, we develop a mathematical theory to study how decisions arise from the breaking of indecision. Our approach is grounded in both equivariant and network bifurcation theory. We model decision from indecision as synchrony-breaking in influence networks in which each node is the value assigned by an agent to an option. First, we show that three universal decision behaviors, namely, deadlock, consensus, and dissensus, are the generic outcomes of synchrony-breaking bifurcations from a fully synchronous state of indecision in influence networks. Second, we show that all deadlock and consensus value patterns and some dissensus value patterns are predicted by the symmetry of the influence networks. Third, we show that there are also many "exotic"dissensus value patterns. These patterns are predicted by network architecture but not by network symmetries through a new synchrony-breaking branching lemma. This is the first example of exotic solutions in an application. Numerical simulations of a novel influence network model illustrate our theoretical results. © 2023 Society for Industrial and Applied Mathematics.

Disciplines :

Mathematics

Author, co-author :

Franci, Alessio ; Université de Liège - ULiège > Département d'électricité, électronique et informatique (Institut Montefiore) > Brain-Inspired Computing ; Department of Mathematics, National Autonomous University of Mexico, Mexico City, 04510, Mexico

Golubitsky, Martin; Department of Mathematics, Ohio State University, Columbus, 43210-1174, OH, United States

Stewart, Ian; Mathematics Institute, University of Warwick, Coventry, CV4 7AL, United Kingdom

Bizyaeva, Anastasia; Department of Mechanical and Aerospace Engineering, Princeton University, Princeton, 08544, NJ, United States

Leonard, Naomi E; Department of Mechanical and Aerospace Engineering, Princeton University, Princeton, 08544, NJ, United States

Language :

English

Title :

Breaking Indecision in Multiagent, Multioption Dynamics

Publication date :

2023

Journal title :

SIAM Journal on Applied Dynamical Systems

eISSN :

1536-0040

Publisher :

Society for Industrial and Applied Mathematics Publications

Volume :

Issue :

Pages :

1780 - 1817

Peer reviewed :

Peer Reviewed verified by ORBi

Available on ORBi :

since 02 July 2024

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