Strategic control for a Boltzmann like decision-making model

TL;DR

This paper analyzes a decision-making model where agents switch between exploiting an expensive resource and a cheaper renewable source, using a Boltzmann-like policy and bifurcation analysis to design controllers for rapid strategy transitions.

Contribution

It introduces a Boltzmann-like exploration policy with sigmoidal cost-profit relations and applies geometric singular perturbation theory to analyze bifurcations and control strategies.

Findings

Identification of parameter ranges with bifurcations

Design of controllers for rapid strategy transitions

Enhanced modeling accuracy with sigmoidal functions

Abstract

We study a prototypical non-polynomial decision-making model for which agents in a population potentially alternate between two consumption strategies, one related to the exploitation of an unlimited but considerably expensive resource and the other a comparably cheaper but restricted and slowly renewable source. In particular, we study a model following a Boltzmann-like exploration policy, enhancing the accuracy at which the exchange rates are captured with respect to classical polynomial approaches by considering sigmoidal functions to represent the cost-profit relation in both exploit strategies. Additionally, given the intrinsic timescale separation between the decision-making process and recovery rates of the renewable resource, we use geometric singular perturbation theory to analyze the model. We further use numerical analysis to determine parameter ranges for which the model undergoes bifurcations. These bifurcations, being related to critical states of the system, are relevant to the fast transitions between strategies. Hence, we design controllers to regulate such rapid transitions by taking advantage of the system's criticality.