Learning Through Fictitious Play in a Game-Theoretic Model of Natural Resource Consumption

Understanding the emergence of sustainable behavior in dynamic models of resource consumption is essential for control of coupled human and natural systems. In this letter, we analyze a mathematical model of resource exploitation recently reported by the authors. The model incorporates the cognitive decision-making process of consumers and has previously been studied in a game-theoretic context as a static two-player game. In this letter, we extend the analysis by allowing the agents to adapt their psychological characteristics according to simple best-response learning dynamics. We show that, under the selected learning scheme, the Nash Equilibrium is reachable provided certain conditions on the psychological attributes of the consumers are fulfilled. Moreover, the equilibrium solution obtained is found to be sustainable in the sense that no players exhibit free-riding behavior, a phenomenon which occurs in the original open-loop system. In the process, via a Lyapunov-function based approach, we also provide a proof for the asymptotic global stability of the original system which was previously known to be only locally stable.

I. Introduction

Systems such as complex Coupled Human And Natural Systems (CHANS) pose a notable challenge in being examined and ultimately controlled, owing to the fact that they span across multiple disciplines such as social sciences, engineering disciplines and the environmental sciences. The advent of technology and the realization of new control and sensing applications in such settings [1], [2] have especially accentuated the technical aspect of these systems. The Cyber-Physical Social Systems (CPSS) [2], [3] concept provides an integrative language which not only covers the environmental and technical aspects, but also addresses the social aspect in CHANS. Such systems are now garnering the interest of not only the controls community but also other communities, albeit under different contexts and subtle differences in ideology [4], [5]. In this letter, we focus on the issue of sustainability of socio-ecological systems, a particular instance of CHANS. In particular we analyze the dynamics of a single renewable resource harvested by multiple consumers, recently proposed and studied by Manzoor et al. [6], [7].