The paper studies the problem of steering multi-dimensional opinion in a social network. Assuming the society of desire consists of stubborn and regular agents, stubborn agents are considered as leaders who specify the desired opinion distribution as a distributed reward or utility function. In this context, each regular agent is seen as a follower, updating its bias on the initial opinion and influence weights by averaging their observations of the rewards their influencers have received. Assuming random graphs with reducible and irreducible topology specify the influences on regular agents, opinion evolution is represented as a containment control problem in which stability and convergence to the final opinion are proven.

This paper introduces a new multidimensional extension of the Hegselmann-Krause (HK) opinion dynamics model, where opinion proximity is not determined by a norm or metric. Instead, each agent trusts opinions within the Minkowski sum $\xi+\mathcal{O}$, where $\xi$ is the agent's current opinion and $\mathcal{O}$ is the confidence set defining acceptable deviations. During each iteration, agents update their opinions by simultaneously averaging the trusted opinions. Unlike traditional HK systems, where $\mathcal{O}$ is a ball in some norm, our model allows the confidence set to be non-convex and even unbounded. We demonstrate that the new model, referred to as SCOD (Set-based Confidence Opinion Dynamics), can exhibit properties absent in the conventional HK model. Some solutions may converge to non-equilibrium points in the state space, while others oscillate periodically. These ``pathologies'' disappear if the set $\mathcal{O}$ is symmetric and contains zero in its interior: similar to the usual HK model, SCOD then converges in a finite number of iterations to one of the equilibrium points. The latter property is also preserved if one agent is "stubborn" and resists changing their opinion, yet still influences the others; however, two stubborn agents can lead to oscillations.

This paper investigates how interacting agents arrive to a consensus or a polarized state. We study the opinion formation process under the effect of a global steering mechanism (GSM), which aggregates the opinion-driven stochastic agent states at the network level and feeds back to them a form of global information. We also propose a new two-layer agent-based opinion formation model, called GSM-DeGroot, that captures the coupled dynamics between agent-to-agent local interactions and the GSM's steering effect. This way, agents are subject to the effects of a DeGroot-like local opinion propagation, as well as to a wide variety of possible aggregated information that can affect their opinions, such as trending news feeds, press coverage, polls, elections, etc. Contrary to the standard DeGroot model, our model allows polarization to emerge by letting agents react to the global information in a stubborn differential way. Moreover, the introduced stochastic agent states produce event stream dynamics that can fit to real event data. We explore numerically the model dynamics to find regimes of qualitatively different behavior. We also challenge our model by fitting it to the dynamics of real topics that attracted the public attention and were recorded on Twitter. Our experiments show that the proposed model holds explanatory power, as it evidently captures real opinion formation dynamics via a relatively small set of interpretable parameters.

Multi-agent systems driven by large language models (LLMs) have shown promising abilities for solving complex tasks in a collaborative manner. This work considers a fundamental problem in multi-agent collaboration: consensus seeking. When multiple agents work together, we are interested in how they can reach a consensus through inter-agent negotiation. To that end, this work studies a consensus-seeking task where the state of each agent is a numerical value and they negotiate with each other to reach a consensus value. It is revealed that when not explicitly directed on which strategy should be adopted, the LLM-driven agents primarily use the average strategy for consensus seeking although they may occasionally use some other strategies. Moreover, this work analyzes the impact of the agent number, agent personality, and network topology on the negotiation process. The findings reported in this work can potentially lay the foundations for understanding the behaviors of LLM-driven multi-agent systems for solving more complex tasks. Furthermore, LLM-driven consensus seeking is applied to a multi-robot aggregation task. This application demonstrates the potential of LLM-driven agents to achieve zero-shot autonomous planning for multi-robot collaboration tasks. Project website: westlakeintelligentrobotics.github.io/ConsensusLLM/.

We study a social learning model in which agents iteratively update their beliefs about the true state of the world using private signals and the beliefs of other agents in a non-Bayesian manner. Some agents are stubborn, meaning they attempt to convince others of an erroneous true state (modeling fake news). We show that while agents learn the true state on short timescales, they "forget" it and believe the erroneous state to be true on longer timescales. Using these results, we devise strategies for seeding stubborn agents so as to disrupt learning, which outperform intuitive heuristics and give novel insights regarding vulnerabilities in social learning.

Zero-sum games have long guided artificial intelligence research, since they possess both a rich strategy space of best-responses and a clear evaluation metric. What's more, competition is a vital mechanism in many real-world multi-agent systems capable of generating intelligent innovations: Darwinian evolution, the market economy and the AlphaZero algorithm, to name a few. In two-player zero-sum games, the challenge is usually viewed as finding Nash equilibrium strategies, safeguarding against exploitation regardless of the opponent. While this captures the intricacies of chess or Go, it avoids the notion of cooperation with co-players, a hallmark of the major transitions leading from unicellular organisms to human civilization. Beyond two players, alliance formation often confers an advantage; however this requires trust, namely the promise of mutual cooperation in the face of incentives to defect. Successful play therefore requires adaptation to co-players rather than the pursuit of non-exploitability. Here we argue that a systematic study of many-player zero-sum games is a crucial element of artificial intelligence research. Using symmetric zero-sum matrix games, we demonstrate formally that alliance formation may be seen as a social dilemma, and empirically that na\"ive multi-agent reinforcement learning therefore fails to form alliances. We introduce a toy model of economic competition, and show how reinforcement learning may be augmented with a peer-to-peer contract mechanism to discover and enforce alliances. Finally, we generalize our agent model to incorporate temporally-extended contracts, presenting opportunities for further work.

Abstract-- This paper considers a novel framework to detect communities in a graph from the observation of signals at its nodes. We model the observed signals as noisy outputs of an unknown network process -- represented as a graph filter -- that is excited by a set of low-rank inputs. Rather than learning the precise parameters of the graph itself, the proposed method retrieves the community structure directly; Furthermore, as in blind system identification methods, it does not require knowledge of the system excitation. The paper shows that communities can be detected by applying spectral clustering to the low-rank output covariance matrix obtained from the graph signals. The performance analysis indicates that the community detection accuracy depends on the spectral properties of the graph filter considered. Furthermore, we show that the accuracy can be improved via a low-rank matrix decomposition method when the excitation signals are known. Numerical experiments demonstrate that our approach is effective for analyzing network data from diffusion, consumers, and social dynamics. The emerging field of network science and availability of big data have motivated researchers to extend signal processing techniques to the analysis of signals defined on graphs, motivating a new area of research referred to as graph signal processing (GSP) [2]-[4].

This paper develops an active sensing method to estimate the relative weight (or trust) agents place on their neighbors' information in a social network. The model used for the regression is based on the steady state equation in the linear DeGroot model under the influence of stubborn agents, i.e., agents whose opinions are not influenced by their neighbors. This method can be viewed as a \emph{social RADAR}, where the stubborn agents excite the system and the latter can be estimated through the reverberation observed from the analysis of the agents' opinions. The social network sensing problem can be interpreted as a blind compressed sensing problem with a sparse measurement matrix. We prove that the network structure will be revealed when a sufficient number of stubborn agents independently influence a number of ordinary (non-stubborn) agents. We investigate the scenario with a deterministic or randomized DeGroot model and propose a consistent estimator of the steady states for the latter scenario. Simulation results on synthetic and real world networks support our findings.