Opinion Dynamics for Utility Maximizing Agents: Exploring the Impact of Resource Penalty
arxiv(2024)
摘要
We propose a continuous-time nonlinear model of opinion dynamics with
utility-maximizing agents connected via a social influence network. A
distinguishing feature of the proposed model is the inclusion of an
opinion-dependent resource-penalty term in the utilities, which limits the
agents from holding opinions of large magnitude. The proposed utility functions
also account for how the relative resources within the social group affect both
an agent's stubbornness and social influence. Each agent myopically seeks to
maximize its utility by revising its opinion in the gradient ascent direction
of its utility function, thus leading to the proposed opinion dynamics. We show
that, for any arbitrary social influence network, opinions are ultimately
bounded. For networks with weak antagonistic relations, we show that there
exists a globally exponentially stable equilibrium using contraction theory. We
establish conditions for the existence of consensus equilibrium and analyze the
relative dominance of the agents at consensus. We also conduct a game-theoretic
analysis of the underlying opinion formation game, including on Nash equilibria
and on prices of anarchy in terms of satisfaction ratios. Additionally, we also
investigate the oscillatory behavior of opinions in a two-agent scenario.
Finally, simulations illustrate our findings.
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