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Register a new userModeling limited attention in opinion dynamics by topological interactions
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This work explores models of opinion dynamics with opinion-dependent connectivity. Our starting point is that individuals have limited capabilities to engage in interactions with their peers. Motivated by this observation, we propose a continuous-time opinion dynamics model such that interactions take place with a limited number of peers: we refer to these interactions as topological, as opposed to metric interactions that are postulated in classical bounded-confidence models. We observe that topological interactions produce equilibria that are very robust to perturbations.
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We study generalizations of the Hegselmann-Krause (HK) model for opinion dynamics, incorporating features and parameters that are natural components of observed social systems. The first generalization is one where the strength of influence depends on the distance of the agents opinions. Under this setup, we identify conditions under which the opinions converge in finite time, and provide a qualitative characterization of the equilibrium. We interpret the HK model opinion update rule as a quadratic cost-minimization rule. This enables a second generalization: a family of update rules which possess different equilibrium properties. Subsequently, we investigate models in which a external force can behave strategically to modulate/influence user updates. We consider cases where this external force can introduce additional agents and cases where they can modify the cost structures for other agents. We describe and analyze some strategies through which such modulation may be possible in an order-optimal manner. Our simulations demonstrate that generalized dynamics differ qualitatively and quantitatively from traditional HK dynamics.
In this paper, a general nonlinear 1st-order consensus-based solution for distributed constrained convex optimization is considered for applications in network resource allocation. The proposed continuous-time solution is used to optimize continuously-differentiable strictly convex cost functions over weakly-connected undirected multi-agent networks. The solution is anytime feasible and models various nonlinearities to account for imperfections and constraints on the (physical model of) agents in terms of their limited actuation capabilities, e.g., quantization and saturation constraints among others. Moreover, different applications impose specific nonlinearities to the model, e.g., convergence in fixed/finite-time, robustness to uncertainties, and noise-tolerant dynamics. Our proposed distributed resource allocation protocol generalizes such nonlinear models. Putting convex set analysis together with the Lyapunov theorem, we provide a general technique to prove convergence (i) regardless of the particular type of nonlinearity (ii) with weak network-connectivity requirement (i.e., uniform-connectivity). We simulate the performance of the protocol in continuous-time coordination of generators, known as the economic dispatch problem (EDP).
Pursuit-evasion games are ubiquitous in nature and in an artificial world. In nature, pursuer(s) and evader(s) are intelligent agents that can learn from experience, and dynamics (i.e., Newtonian or Lagrangian) is vital for the pursuer and the evader in some scenarios. To this end, this paper addresses the pursuit-evasion game of intelligent agents from the perspective of dynamics. A bio-inspired dynamics formulation of a pursuit-evasion game and baseline pursuit and evasion strategies are introduced at first. Then, reinforcement learning techniques are used to mimic the ability of intelligent agents to learn from experience. Based on the dynamics formulation and reinforcement learning techniques, the effects of improving both pursuit and evasion strategies based on experience on pursuit-evasion games are investigated at two levels 1) individual runs and 2) ranges of the parameters of pursuit-evasion games. Results of the investigation are consistent with nature observations and the natural law - survival of the fittest. More importantly, with respect to the result of a pursuit-evasion game of agents with baseline strategies, this study achieves a different result. It is shown that, in a pursuit-evasion game with a dynamics formulation, an evader is not able to escape from a slightly faster pursuer with an effective learned pursuit strategy, based on agile maneuvers and an effective learned evasion strategy.
Structural balance theory has been developed in sociology and psychology to explain how interacting agents, e.g., countries, political parties, opinionated individuals, with mixed trust and mistrust relationships evolve into polarized camps. Recent results have shown that structural balance is necessary for polarization in networks with fixed, strongly connected neighbor relationships when the opinion dynamics are described by DeGroot-type averaging rules. We develop this line of research in this paper in two steps. First, we consider fixed, not necessarily strongly connected, neighbor relationships. It is shown that if the network includes a strongly connected subnetwork containing mistrust, which influences the rest of the network, then no opinion clustering is possible when that subnetwork is not structurally balanced; all the opinions become neutralized in the end. In contrast, it is shown that when that subnetwork is indeed structurally balanced, the agents of the subnetwork evolve into two polarized camps and the opinions of all other agents in the network spread between these two polarized opinions. Second, we consider time-varying neighbor relationships. We show that the opinion separation criteria carry over if the conditions for fixed graphs are extended to joint graphs. The results are developed for both discrete-time and continuous-time models.
It is known that individual opinions on different policy issues often align to a dominant ideological dimension (e.g. left vs. right) and become increasingly polarized. We provide an agent-based model that reproduces these two stylized facts as emergent properties of an opinion dynamics in a multi-dimensional space of continuous opinions. The mechanisms for the change of agents opinions in this multi-dimensional space are derived from cognitive dissonance theory and structural balance theory. We test assumptions from proximity voting and from directional voting regarding their ability to reproduce the expected emerging properties. We further study how the emotional involvement of agents, i.e. their individual resistance to change opinions, impacts the dynamics. We identify two regimes for the global and the individual alignment of opinions. If the affective involvement is high and shows a large variance across agents, this fosters the emergence of a dominant ideological dimension. Agents align their opinions along this dimension in opposite directions, i.e. create a state of polarization.
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