Passivity-based Analysis and Design for Population Dynamics with Conformity Biases

TL;DR

This paper introduces mathematical models of population dynamics with conformity biases, analyzes their passivity properties, and proposes mechanisms to steer decision makers toward desired states while ensuring stability.

Contribution

It provides a passivity-based framework for analyzing and designing mechanisms in population dynamics with conformity biases, a novel approach in this context.

Findings

Conformity biases break passivity of decision makers.

Proposed mechanisms can induce desired population states.

Conditions for stable convergence are established.

Abstract

This paper addresses mechanisms for boundedly rational decision makers in discrete choice problem. First, we introduce two mathematical models of population dynamics with conformity biases. We next analyze the models in terms of delta-passivity, and show that the conformity biases work to break passivity of decision makers. Based on the passivity perspective, we propose mechanisms so as to induce decision makers to a desired population state. Furthermore, we analyze a convergence property of designed mechanisms, and present parameter conditions to guarantee stable inducements.