Extending the Hegselmann-Krause Model II

Hegselmann and Krause have developed a computational model for studying the dynamics of belief formation in a population of epistemically interacting agents who try to determine, and also get evidence concerning, the value of some unspecified parameter. In a previous paper, we extended the Hegselmann-Krause (HK) model in various ways, using the extensions to investigate whether, in situations in which random noise affects the evidence the agents receive, certain forms of epistemic interaction can help the agents to approach the true value of the relevant parameter. This paper presents an arguably more radical extension of the HK model. Whereas in the original HK model each agent is solely characterized by its belief, in the model described in the current paper, the agents also have a location in a discrete two-dimensional space in which they are able to move and to meet with other agents; their epistemic interactions depend in part on who they happen to meet. We again focus on situations in which the evidence is noisy. The results obtained in the new model will be seen to agree qualitatively with the results obtained in our previous extensions of the HK model.