Passivity-based analysis and design for population dynamics with conformity biases

Abstract

This paper focuses on conformity bias, a kind of bounded rationality of humans, and addresses the two fundamental questions: How does the bias affect decision making by large population from a control theoretic viewpoint, and how can we lead the biased decision makers to a desired state? We approach these issues based on the notion of passivity. To this end, we first formulate two population dynamics with conformity biases. The models are then analyzed based on so-called δ-passivity, where it is revealed that the conformity biases work to break passivity of decision makers. Based on the passivity perspective, we propose mechanisms so as to lead decision makers to a desired population state. Furthermore, we analyze convergence properties of the designed mechanisms while revealing conditions for guaranteeing stable inducements.