Abstract:
We discuss the large time behavior of agent-based models for social dynamics. Mathematical tools to address this question can be classified into four classes, depending whether (i) the interactions of agents are local or global; and (ii) the interactions are symmetric or not.
When the interactions are global in the sense that every two agents influence each other, then there are two possible tools: spectral analysis in the case of symmetric interactions, and an energy method when interactions are not symmetric. Either way, all agents approach the same state of consensus. When the interactions are local, then there are again two choices: spectral analysis and an energy method. For spectral analysis, consensus amounts to tracing the propagation of graph connectivity. For the energy method, one needs to trace global contractivity. We shall mention these questions in light of our recent study of heterophilious dynamics. |