Stubborn Agent Research Articles

Multidimensional Friedkin-Johnsen model with increasing stubbornness in social networks

In most previous opinion dynamics research, the opinion evolution is usually defaulted to evolving over a single topic; however, in more general scenarios, agents often discuss several topics at the same time. This paper adopts a multidimensional opinion dynamics model in which the opinions are represented by vectors to reveal the multi-topic opinion pattern. To be more in line with reality, this paper employs a multidimensional version of the Friedkin-Johnsen (FJ) model, where each stubborn agent has a time-evolving stubbornness level. The theoretical analysis finds that the proposed model is convergent if the interpersonal influence matrix is stochastic indecomposable and aperiodic. To achieve unified consensus, opinion leaders are introduced, after which the consensus conditions for the proposed model are given. The theoretical conclusions suggest that in the proposed model, the stubborn agents are as prominent as the opinion leaders in the opinion formation process. Simulations are then conducted in two types of artificial networks, from which it is found that compared with the scalar version of the proposed model and standard multidimensional FJ models in which agents’ stubbornness levels remain unchanged, the proposed model produce a more compact final opinion space. The results show that to generate smaller opinion distance and higher opinion correctness degree, it is necessary to ensure a lower proportion of stubborn agents and higher network connectivity. This is consistent with people’s intuition. The population size is found to have little effect on the results, but larger number of topics result in larger opinion distances. These findings are enlightening and helpful to opinion managers.

Social Influence of Competing Groups and Leaders in Opinion Dynamics

This paper explores the influence of two competing stubborn agent groups on the opinion dynamics of normal agents. Computer simulations are used to investigate the parameter space systematically in order to determine the impact of group size and extremeness on the dynamics and identify optimal strategies for maximizing numbers of followers and social influence. Results show that (a) there are many cases where a group that is neither too large nor too small and neither too extreme nor too central achieves the best outcome, (b) stubborn groups can have a moderating, rather than polarizing, effect on the society in a range of circumstances, and (c) small changes in parameters can lead to transitions from a state where one stubborn group attracts all the normal agents to a state where the other group does so. We also explore how these findings can be interpreted in terms of opinion leaders, truth, and campaigns.

A Laplacian approach to stubborn agents and their role in opinion formation on influence networks

Within the framework of a simple model for social influence, the Taylor model, we analytically investigate the role of stubborn agents in the overall opinion dynamics of networked systems. Similar to zealots, stubborn agents are biased towards a certain opinion and have a major effect on the collective opinion formation process. Based on a modified version of the network Laplacian we derive quantities capturing the transient dynamics of the system and the emerging stationary opinion states. In the case of a single stubborn agent we characterize his/her ability to coherently change a prevailing consensus. For two antagonistic stubborn agents we investigate the opinion heterogeneity of the emerging non-consensus states and describe their statistical properties using a graph metric similar to the resistance distance in electrical networks. Applying the model to synthetic and empirical networks we find while opinion diversity is decreased by small-worldness and favored in the case of a pronounced community structure the opposite is true for the coherence of opinions during a consensus change.

Disruption via Grounding and Countermeasures in Discrete-Time Consensus Networks

We investigate the disruption of discrete-time consensus problems via grounding. Loosely speaking, grounding a network occurs if the state of one agent no longer responds to inputs from other agents and/or changes its dynamics. Then, the agent becomes a leader or a so-called stubborn agent. The disruption of the agent can be caused by internal faults, safety protocols or externally due to a malicious attack. In this paper we investigate how the grounding affects the eigenratio of expander graph families that usually exhibit good scaling properties with increasing network size. It is shown that the algebraic connectivity and eigenratio of the network decrease due to the grounding causing the performance and scalability of the network to deteriorate, even to the point of losing consensusability. We then present countermeasures to such disruptions in both passive and active manners. Our findings are supported by numerical simulations given within the paper.

Competitive diffusion in signed social networks: A game-theoretic perspective

Signed network can be used to effectively characterize both collaborative and antagonistic interactions among individuals in networks. In this paper, we consider a setting in which two stubborn agents compete to maximize the expected number of non-stubborn agents adopting their opinions in a signed network. Here, two stubborn agents hold two competing opinions which never change. They propagate their opinions by selecting some non-stubborn agents (who can change their opinions) to connect to. The payoff of each stubborn agent is denoted by the expected number of non-stubborn agents adopting its opinion. We model the competitive problem as a zero-sum game, where players are the two stubborn agents. Firstly, several properties of this game are presented. Secondly, the signed network with structurally balanced property is investigated, and we find that the number of non-stubborn agents in a subgroup can equal the payoff of one stubborn agent. Moreover, for the signed cycle graph, a necessary and sufficient condition is given to determine whether a strategy profile is Nash equilibrium. Finally, we show that the stubborn agent can increase its payoff by selecting a suitable non-stubborn agent to connect to.

Control of Network Opinion Dynamics by a Selfish Agent with Limited Visibility

Abstract Manipulation of a linear network opinion dynamics by a single selfish agent is considered. The selfish agent is modeled as measuring a projection (statistic) of current network opinions, which may be either myopic or global. The agent then enacts a local feedback control using this measurement. The selfish agent’s ability to manipulate network-wide opinions to a desired reference is assessed, both under nominal conditions and in the presence of a second, stubborn agent. Specifically, it is shown that low-gain proportional and proportional-integral controllers can be applied to manipulate network-wide opinions or opinion statistics. A nonlinear variant on the opinion-dynamics model, where the agents’ opinions are capped, is also briefly studied. The control strategies are illustrated using a 62-node dolphin social network model.

Multiagent Opinion Dynamics of Bounded Confidence with Nonlocal Aggregative Interaction

In this paper, we propose nonlocal aggregative opinion interactions for a bounded-confidence opinion model to demonstrate the fluctuation mechanism, and then study this opinion fluctuation mechanism by both theoretical analyses and numerical simulations. In this proposed agent-based opinion model, there are stubborn agents and regular agents: while each stubborn agent never changes its opinion, a regular agent updates his/her opinion based on selected agents' opinion values and his/her confidence bound. At first, we show that the global fluctuation for opinions of regular agents occurs almost surely if and only if the confidence bound of regular agents is larger than a critical value. Next, we give an estimated probability bound of the local fluctuation for regular agent opinions when the confidence bound is sufficiently small. Finally, we provide upper and lower bounds on the fluctuation strength and the regular agent opinion mean in the case when the global fluctuation occurs almost surely.

Evolution of Bounded Confidence Opinion in Social Networks

We investigate opinion dynamics as a stochastic process in social networks. We introduce the stubborn agent in order to determine the impact of network structure on the emergence of consensus. Depending on the fraction of undirected long-range connections, we observe fascinatingly rich dynamical behavior and transitions from disordered to ordered states. In general, we find that the stubborn agent promotes the emergence of consensus due to the so-called “group effect” that facilitates coalescence between separated network components. Agents are also behaviorally constrained Shannon information entropy in networks. However, since agents want to evolve their opinion with Brownian motion, which may in turn impede full consensus, sufficiently frequent long-range links are in such situations crucial for the network to converge into an absorbing phase. Our experimental findings indicate that, for a large range of control parameters, our model yields stable and fluctuating polarized states.

Keynote Summary: Half a century on huanglongbing: learning about the disease, trying to control it

Keynote Summary: Half a century on huanglongbing: learning about the disease, trying to control it

Aspects of Transmission of the Citrus Stubborn Agent by Scaphytopius Nitridus (DeLong)

Aspects of Transmission of the Citrus Stubborn Agent by Scaphytopius Nitridus (DeLong)