Technological change in water use: A mean-field game approach to optimal investment timing

Géraldine Bouveret; Roxana Dumitrescu; Peter Tankov

doi:10.1016/j.orp.2022.100225

Technological change in water use: A mean-field game approach to optimal investment timing

Géraldine Bouveret^*, Roxana Dumitrescu, Peter Tankov

^*Corresponding author for this work

Mathematics

Research output: Contribution to journal › Article › peer-review

3 Citations (Scopus)

207 Downloads (Pure)

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.

Original language	English
Article number	100225
Journal	Operations Research Perspectives
Volume	9
Early online date	7 Feb 2022
DOIs	https://doi.org/10.1016/j.orp.2022.100225
Publication status	E-pub ahead of print - 7 Feb 2022

Keywords

Mean-field game
OR in natural resources
Strategic timing
Technology investment

UN SDGs

This output contributes to the following UN Sustainable Development Goals (SDGs)

Access to Document

10.1016/j.orp.2022.100225Licence: CC BY-NC-ND

Technological change in water_BOUVERET_Publishedonline7Feb2022_GOLD VoR (CC BY)Final published version, 1.45 MBLicence: CC BY-NC-ND

Cite this

@article{757feb7ff72e4ec9ae9954ef0bfc2995,

title = "Technological change in water use: A mean-field game approach to optimal investment timing",

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{\textquoteright} 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 = "Mean-field game, OR in natural resources, Strategic timing, Technology investment",

author = "G{\'e}raldine Bouveret and Roxana Dumitrescu and Peter Tankov",

note = "Funding Information: The authors are grateful to the Wisconsin Department of Natural Resources for having provided some of the data for the case study. Publisher Copyright: {\textcopyright} 2022 The Author(s)",

year = "2022",

month = feb,

day = "7",

doi = "10.1016/j.orp.2022.100225",

language = "English",

volume = "9",

journal = "Operations Research Perspectives",

issn = "2214-7160",

publisher = "Elsevier BV",

}

TY - JOUR

T1 - Technological change in water use

T2 - A mean-field game approach to optimal investment timing

AU - Bouveret, Géraldine

AU - Dumitrescu, Roxana

AU - Tankov, Peter

PY - 2022/2/7

Y1 - 2022/2/7

N2 - 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.

AB - 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.

KW - Mean-field game

KW - OR in natural resources

KW - Strategic timing

KW - Technology investment

UR - http://www.scopus.com/inward/record.url?scp=85125371222&partnerID=8YFLogxK

U2 - 10.1016/j.orp.2022.100225

DO - 10.1016/j.orp.2022.100225

M3 - Article

AN - SCOPUS:85125371222

SN - 2214-7160

VL - 9

JO - Operations Research Perspectives

JF - Operations Research Perspectives

M1 - 100225

ER -

Technological change in water use: A mean-field game approach to optimal investment timing

Abstract

Keywords

UN SDGs

Access to Document

Other files and links

Fingerprint

Cite this