Nonlinear model reference adaptive control approach for governance of the commons in a feedback-evolving game

TL;DR

This paper introduces a nonlinear model reference adaptive control method to manage uncertainties in the enforcement of policies for common-pool resource governance within feedback-evolving game models, enhancing sustainability strategies.

Contribution

It develops a novel adaptive control protocol to handle implementation uncertainties in resource management games, ensuring desired outcomes are achieved.

Findings

The proposed control law guarantees convergence to target outcomes under certain conditions.

Numerical examples validate the effectiveness of the adaptive control approach.

The method improves management of renewable resources with uncertain enforcement.

Abstract

The governance of common-pool resources has vital importance for sustainability. However, in the realistic management systems of common-pool resources, the institutions do not necessarily execute the management policies completely, which will induce that the real implementation intensity is uncertain. In this paper, we consider a feedback-evolving game model with the inspection for investigating the management of renewable resource and assume that there exists the implementation uncertainty of inspection. Furthermore, we use the nonlinear model reference adaptive control approach to handle this uncertainty. We accordingly design a protocol, which is an update law of adjusting the institutional inspection intensity. We obtain a sufficient condition under which the update law can drive the actual system to reach the expected outcome. In addition, we provide several numerical examples, which can confirm our theoretical results. Our work presents a novel approach to address the implementation uncertainty in the feedback-evolving games and thus our results can be helpful for effectively managing the common-pool resources in the human social systems.