Multiagent Decision-Making Dynamics Inspired by Honeybees

Gray, Rebecca; Franci, Alessio; Srivastava, Vaibhav; Leonard, Naomi Ehrich

doi:10.1109/tcns.2018.2796301

Cited by 77 publications

(102 citation statements)

References 30 publications

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“…For a fixed N , a large enough n, i.e., a large enough number of agents with disparity in thresholds, is necessary for the cascade. For n large enough that y 0 exists, we can expect that for ∈ [0, (y 0 , N, n)], the bifurcation is supercritical, since it is for = 0 [10]. As increases to greater than the critical value = (y 0 , N, n), we expect to see the transition from no cascade to cascade.…”

Section: Conditions For Cascadementioning

confidence: 99%

“…1 shows a network with N = 11 and n = 4. With an approach similar to that in Theorem 4 of [10], it can be shown that the trajectories of (1) converge exponentially to the three-dimensional manifold where all the states in the same cluster are the same. Let y k be the average state of cluster k = 1, 2, 3.…”

Section: Continuous Threshold Modelmentioning

confidence: 99%

“…Although the transition from supercritical pitchfork to subcritical pitchfork has been observed in [10], it is unclear for what parameter values the transition exists in the CTM. In this section, we first show conditions for existence of a pitchfork bifurcation and then for existence of the transition.…”

Section: Conditions For Cascadementioning

confidence: 99%

“…We propose a continuous threshold model (CTM) that introduces continuous-time, real-valued state dynamics with nonlinearity. The CTM is adapted from nonlinear consensus dynamics [10], which exhibit very rapid transitions in system This research was supported by ARO grant W911NF-18-1-0325 and ONR grants N00014-14-1-0635, N00014-19-1-2556. The authors are with the Department of Mechanical and Aerospace Engineering, Princeton University, Princeton, NJ 08544, USA.…”

Section: Introductionmentioning

confidence: 99%

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A Continuous Threshold Model of Cascade Dynamics

Zhong

Leonard

2019

2019 IEEE 58th Conference on Decision and Control (CDC)

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We present a continuous threshold model (CTM) of cascade dynamics for a network of agents with realvalued activity levels that change continuously in time. The model generalizes the linear threshold model (LTM) from the literature, where an agent becomes active (adopts an innovation) if the fraction of its neighbors that are active is above a threshold. With the CTM we study the influence on cascades of heterogeneity in thresholds for a network comprised of a chain of three clusters of agents, each distinguished by a different threshold. The system is most sensitive to change as the dynamics pass through a bifurcation point: if the bifurcation is supercritical the response will be contained, while if the bifurcation is subcritical the response will be a cascade. We show that there is a subcritical bifurcation, thus a cascade, in response to an innovation if there is a large enough disparity between the thresholds of sufficiently large clusters on either end of the chain; otherwise the response will be contained.

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Section: Conditions For Cascadementioning

confidence: 99%

Section: Continuous Threshold Modelmentioning

confidence: 99%

Section: Conditions For Cascadementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

A Continuous Threshold Model of Cascade Dynamics

Zhong

Leonard

2019

2019 IEEE 58th Conference on Decision and Control (CDC)

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“…For certain nonlinear dynamical networks, especially those in ecology, closed-loop control can be articulated and has been demonstrated to be effective [40]. Recently, how to exploit biologically inspired agent based control method to choose different alternative states in engineered multiagent network systems has been studied [41].…”

Section: Introductionmentioning

confidence: 99%

Irrelevance of linear controllability to nonlinear dynamical networks

Jiang

Lai

2019

Nat Commun

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There has been tremendous development in linear controllability of complex networks. Real-world systems are fundamentally nonlinear. Is linear controllability relevant to nonlinear dynamical networks? We identify a common trait underlying both types of control: the nodal “importance”. For nonlinear and linear control, the importance is determined, respectively, by physical/biological considerations and the probability for a node to be in the minimum driver set. We study empirical mutualistic networks and a gene regulatory network, for which the nonlinear nodal importance can be quantified by the ability of individual nodes to restore the system from the aftermath of a tipping-point transition. We find that the nodal importance ranking for nonlinear and linear control exhibits opposite trends: for the former large-degree nodes are more important but for the latter, the importance scale is tilted towards the small-degree nodes, suggesting strongly the irrelevance of linear controllability to these systems. The recent claim of successful application of linear controllability to Caenorhabditis elegans connectome is examined and discussed.

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The impact of irrational behaviors in the optional prisoner's dilemma with game‐environment feedback

Stella

Bauso

2021

Intl J Robust & Nonlinear

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In the optional prisoner's dilemma (OPD), players can choose to cooperate and defect as usual, but can also abstain as a third possible strategy. This strategy models the players' participation in the game and is a relevant aspect in many settings, for example, social networks or opinion dynamics, for example, during an election abstention is an option. In this article, we provide a formulation of the OPD where we consider irrational behaviors in the population, inspired by prospect theory. Prospect theory has gained increasing popularity in recent times because it can capture aspects such as reference dependence or loss aversion, which are common in human behavior. This element is original in our formulation of the game and is incorporated in our framework through pairwise comparison dynamics. Recently, the impact of the environment has been studied in the form of feedback on the population dynamics. Another element of novelty in our work is the extension of the game-environment feedback to the OPD in two forms of dynamics, the replicator and the pairwise comparison. The contribution of this article is threefold. First, we propose a modeling framework where prospect theory is used to capture irrational behaviors in an evolutionary game with game-environment feedback. Second, we carry out the stability analysis of the system equilibria and discuss the oscillating behaviors arising from the game-environment feedback. Finally, we extend our previous results to the OPD and we discuss the main differences between the model resulting from the replicator dynamics and the one resulting from the pairwise comparison dynamics.

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Multiagent Decision-Making Dynamics Inspired by Honeybees

Cited by 77 publications

References 30 publications

A Continuous Threshold Model of Cascade Dynamics

A Continuous Threshold Model of Cascade Dynamics

Irrelevance of linear controllability to nonlinear dynamical networks

The impact of irrational behaviors in the optional prisoner's dilemma with game‐environment feedback

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