Mathematical Methods for Optimal Resource Allocation in Common-Pool Resources

Abstract

Humans and the environment are inherently coupled. Understanding these socio-ecological systems (SESs) is important for creating solutions to global crises such as wealth inequality, antibiotic resistance, and ecosystem collapse. Often these problems require decision-making from either individuals or a governing body to allocate resources for an optimal social outcome. This thesis develops and utilizes mathematical modelling to advance the understanding, prediction, and management of SESs in the context of resource allocation problems.

The following three chapters are each self-contained projects using and/or evaluating a mathematical model for various systems from different scientific fields. The first chapter details a dynamic programming model of intergenerational resource transfer and the impact of heterogeneity on the distribution of resources. The second chapter investigates the design of subsidies to encourage institutions to cooperate to control the spread of nosocomial infections. The final chapter evaluates a technique from system dynamics called Loop Eigenvalue Elasticity Analysis (LEEA) which allows the decomposition of the influence of feedback loops on system behaviour. This tool is then applied to a case study SES involving resource extraction.