Technological Change in Water Use: A Mean-Field Game Approach to Optimal Investment Timing

30 Pages Posted: 1 Jul 2020 Last revised: 29 Oct 2020

See all articles by Géraldine Bouveret

Géraldine Bouveret

Nanyang Technological University (NTU); University of Oxford - Smith School of Enterprise and the Environment

Roxana Dumitrescu

King's College London

Peter Tankov

ENSAE Paris

Date Written: July 1, 2020

Abstract

The need for clean water is expected to substantially increase while further reductions of water availability in sufficient quantity and quality are projected owing to climate change and anthropogenic activities. Accordingly, the debate on water security has recently intensified and reached the intergovernmental arena. Industry is, in particular, one of the largest (non-consumptive) water users, accountable for massive toxic wastewater discharges and facing stringent and costly environmental oversight. However, the management of reservoirs is intricate and operational research must be further expanded to design tools that enhance water security while improving operators’ profitability. We therefore consider a game-theoretic framework to study the strategies adopted by a large group of similar producers sharing a water reservoir for their manufacturing activities. Each operator faces random demand for its outputs and chooses the optimal time to invest in a technology that ends its reliance on the reservoir. This technology introduces cost saving opportunities for the operator and benefits for the environment. Each producer therefore solves a so-called optimal stopping problem, and all problems are coupled through the reservoir level. We formulate the problem of finding a Nash equilibrium as a mean-field game (MFG) of optimal stopping. We then apply the model to the paper milling industry, an extensive water user facing a tightening of environmental regulations. This paper provides fresh insights into how to rethink the problem of technological change and water management, by offering an innovative application of operational research that builds on recent mathematical developments made in MFG theory.

Keywords: OR in Natural Resources, Mean-Field Game, Technology Investment, Strategic Timing

Suggested Citation

Bouveret, Géraldine and Dumitrescu, Roxana and Tankov, Peter, Technological Change in Water Use: A Mean-Field Game Approach to Optimal Investment Timing (July 1, 2020). Available at SSRN: https://ssrn.com/abstract=3640181 or http://dx.doi.org/10.2139/ssrn.3640181

Géraldine Bouveret (Contact Author)

Nanyang Technological University (NTU) ( email )

S3 B2-A28 Nanyang Avenue
Singapore, 639798
Singapore

University of Oxford - Smith School of Enterprise and the Environment ( email )

United Kingdom

Roxana Dumitrescu

King's College London ( email )

Strand
London, England WC2R 2LS
United Kingdom

Peter Tankov

ENSAE Paris ( email )

92245 Malakoff Cedex
France
91400 (Fax)

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