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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Bibliography

Latin Rectangle, https://en.wikipedia.org/wiki/Latin rectangle, 2021.
F. Antoneli and I. Stewart, Symmetry and synchrony in coupled cell networks 2: Group networks, Internat. J. Bifur. Chaos, 17 (2007), pp. 935-951.
D. Biro, D. J. T. Sumpter, J. Meade, and T. Guilford, From compromise to leadership in pigeon homing, Current Biol., 16 (2006), pp. 2123-2128.
A. Bizyaeva, A. Franci, and N. E. Leonard, Nonlinear opinion dynamics with tunable sensitivity, IEEE Trans. Automat. Control, 68 (2022), pp. 1415-1430.
M. Brambilla, E. Ferrante, M. Birattari, and M. Dorigo, Swarm robotics: A review from the swarm engineering perspective, Swarm Intell., 7 (2013), pp. 1-41.
G. Cicogna, Symmetry breakdown from bifurcations, Lett. Nuovo Cimento, 31 (1981), pp. 600-602.
P. Cisneros-Velarde, K. S. Chan, and F. Bullo, Polarization and Fluctuations in Signed Social Networks, preprint, arXiv:1902.00658, 2019.
J. Cohen and I. Stewart, Polymorphism viewed as phenotypic symmetry-breaking, in Nonlinear Phenomena in Biological and Physical Sciences, S. K. Malik, M. K. Chandrasekharan, and N. Pradhan, eds., Indian National Science Academy, New Delhi, 2000, pp. 1-63.
I. D. Couzin, C. C. Ioannou, G. Demirel, T. Gross, C. J. Torney, A. Hartnett, L. Conradt, S. A. Levin, and N. E. Leonard, Uninformed individuals promote democratic consensus in animal groups, Science, 334 (2011), pp. 1578-1580.
I. D. Couzin, J. Krause, N. R. Franks, and S. A. Levin, Effective leadership and decision-making in animal groups on the move, Nature, 433 (2005), pp. 513-516.
P. Dandekar, A. Goel, and D. T. Lee, Biased assimilation, homophily, and the dynamics of polarization, Proc. Natl. Acad. Sci. USA, 110 (2013), pp. 5791-5796.
G. Deffuant, D. Neau, F. Amblard, and G. Weisbuch, Mixing beliefs among interacting agents, Adv. Complex Syst., 3 (2000), pp. 87-98.
M. H. DeGroot, Reaching a consensus, J. Amer. Statist. Assoc., 69 (1974), pp. 121-132.
A. P. S. Dias and I. Stewart, Secondary bifurcations in systems with all-to-all coupling, Proc. R. Soc. Lond. A, 459 (2003), pp. 1969-1986.
A. P. S. Dias and I. Stewart, Linear equivalence and ODE-equivalence for coupled cell networks, Nonlinearity, 18 (2005), pp. 1003-1020.
M. Dworkin and D. Kaiser, Cell interactions in myxobacterial growth and development, Science, 230 (1985), pp. 18-24.
T. Elmhirst, Symmetry and Emergence in Polymorphism and Sympatric Speciation, Ph.D. thesis, University of Warwick, 2002.
M. Field and R. Richardson, Symmetry breaking and the maximal isotropy subgroup conjecture for reflection groups, Arch. Ration. Math. Mech., 105 (1989), pp. 61-94.
A. Franci, A. Bizyaeva, S. Park, and N. E. Leonard, Analysis and control of agreement and disagreement opinion cascades, Swarm Intell., 15 (2021), pp. 47-82.
A. Franci, M. Golubitsky, A. Bizyaeva, and N. E. Leonard, A Model-Independent Theory of Consensus and Dissensus Decision Making, preprint, arXiv:1909.05765, 2020.
N. E. Friedkin, A. V. Proskurnikov, R. Tempo, and S. E. Parsegov, Network science on belief system dynamics under logic constraints, Science, 354 (2016), pp. 321-326.
N. E. Friedkin and E. C. Johnsen, Social influence networks and opinion change, in Advances in Group Processes 16, S. R. Thye, E. J. Lawler, M. W. Macy, and H. A. Walker, eds., Emerald Group, Bingley, UK, 1999, pp. 1-29.
M. Golubitsky and D. G. Schaeffer, Singularities and Groups in Bifurcation Theory, Vol. 1, Springer, New York, 1985.
M. Golubitsky and I. Stewart, The Symmetry Perspective: From Equilibria to Chaos in Phase Space and Physical Space, Progress in Mathematics 200, Birkhäuser, Basel, 2002.
M. Golubitsky and I. Stewart, Nonlinear dynamics of networks: The groupoid formalism, Bull. Amer. Math. Soc., 43 (2006), pp. 305-364.
M. Golubitsky and I. Stewart, Dynamics and Bifurcation in Networks, SIAM, Philadelphia, 2023.
M. Golubitsky, I. Stewart, and D. G. Schaeffer, Singularities and Groups in Bifurcation Theory, Vol. 2, Springer, New York, 1988.
M. Golubitsky, I. Stewart, and A. Török, Patterns of synchrony in coupled cell networks with multiple arrows, SIAM J. Appl. Dyn. Syst., 4 (2005), pp. 78-100.
R. Gray, A. Franci, V. Srivastava, and N. E. Leonard, Multi-agent decision-making dynamics inspired by honeybees, IEEE Trans. Control Netw. Syst., 5 (2018), pp. 793-806.
M. Grötschel, L. Lovász, and A. Schrijver, Geometric Algorithms and Combinatorial Optimization, Vol. 2, Springer-Verlag, Berlin, 2012.
J. Guckenheimer and P. Holmes, Structurally stable heteroclinic cycles, Math. Proc. Cambridge Philos. Soc., 103 (1988), pp. 189-192.
R. Hegselmann and U. Krause, Opinion dynamics and bounded confidence models, analysis, and simulations, J. Artif. Soc. Soc. Simul., 5 (2002), pp. 121-132.
M. J. B. Krieger, J.-B. Billeter, and L. Keller, Ant-like task allocation and recruitment in cooperative robots, Nature, 406 (2000), pp. 992-995.
T. H. Labella, M. Dorigo, and J.-L. Deneubourg, Division of labor in a group of robots inspired by ants' foraging behavior, ACM Trans. Auton. Adapt. Syst., 1 (2006), pp. 4-25.
N. E. Leonard, T. Shen, B. Nabet, L. Scardovi, I. D. Couzin, and S. A. Levin, Decision versus compromise for animal groups in motion, Proc. Natl. Acad. Sci. USA, 16 (2012), pp. 227-232.
E. Ihrig and M. Golubitsky, Pattern selection with fO (3) symmetry, Phys. D, 12 (1984), pp. 1-33.
M. B. Miller and B. L. Bassler, Quorum sensing in bacteria, Ann. Rev. Microbiol., 55 (2001), pp. 165-199.
B. Nabet, N. E. Leonard, I. D. Couzin, and S. A. Levin, Dynamics of decision making in animal group motion, J. Nonlinear Sci., 19 (2009), pp. 399-435.
D. Pais, P. M. Hogan, T. Schlegel, N. R. Franks, N. E. Leonard, and J. A. R. Marshall, A mechanism for value-sensitive decision-making, PLoS One, 8 (2013), e73216.
S. E. Parsegov, A. V. Proskurnikov, R. Tempo, and N. E. Friedkin, Novel multidimensional models of opinion dynamics in social networks, IEEE Trans. Automat. Control, 62 (2016), pp. 2270-2285.
T. D. Seeley, S. Camazine, and J. Sneyd, Collective decision-making in honey bees: How colonles choose among nectar sources, Behav. Ecol. Sociobiol., 28 (1991), pp. 277-290.
T. D. Seeley, Honey bee colonies are group-level adaptive units, Amer. Natur., 150 (1997), pp. S22-S41.
T. D. Seeley, P. K. Visscher, T. Schlegel, P. M. Hogan, N. R. Franks, and J. A. R. Marshall, Stop signals provide cross inhibition in collective decision-making by honeybee swarms, Science, 335 (2012), pp. 108-111.
E. A. Shank and R. Kolter, Extracellular signaling and multicellularity in Bacillus subtilis, Curr. Opin. Microbiol., 14 (2011), pp. 741-747.
V. H. Sridhar, L. Li, D. Gorbonos, M. Nagy, B. R. Schell, R. Bianca, T. Sorochkin, N. S. Gov, and I. D. Couzin, The geometry of decision-making in individuals and collectives, Proc. Natl. Acad. Sci. USA, 118 (2021), e2102157118.
I. Stewart, Balanced colorings and bifurcations in rivalry and opinion networks, Internat. J. Bifur. Chaos, 31 (2021), 2130019.
I. Stewart, T. Elmhirst, and J. Cohen, Symmetry-breaking as an origin of species, in Bifurcations, Symmetry, and Patterns, J. Buescu, S. Castro, A. P. S. Dias, and I. Labouriau, eds., Birkhäuser, Basel, 2003, pp. 3-54.
I. Stewart and M. Golubitsky, Synchrony-breaking bifurcation at a simple real eigenvalue for regular networks 1: 1-dimensional cells, SIAM J. Appl. Dyn. Syst., 10 (2011), pp. 1404-1442.
I. Stewart, M. Golubitsky, and M. Pivato, Symmetry groupoids and patterns of synchrony in coupled cell networks, SIAM J. Appl. Dyn. Syst., 2 (2003), pp. 609-646.
UN General Assembly, High-Level Thematic Debate on Delivering Climate Action: For People, Planet and Prosperity, https://www.un.org/pga/76/wp-content/uploads/sites/101/2022/01/Delivering-Climate-Action-Summary.pdf, 2021.
A. Vanderbauwhede, Local Bifurcation and Symmetry, Research Notes in Mathematics 75, Pitman, Boston, 1982.
P. K. Visscher, Group decision making in nest-site selection among social insects, Ann. Rev. Entomol., 52 (2007), pp. 255-275.
M. Ye, M. H. Trinh, Y.-H. Lim, B. D. O. Anderson, and H.-S. Ahn, Continuous-time opinion dynamics on multiple interdependent topics, Automatica, 115 (2020), 108884.
C. M. Waters and B. L. Bassler, Quorum sensing: Cell-to-cell communication in bacteria, Ann. Rev. Cell Dev. Biol., 21 (2005), pp. 319-346.