# American Institute of Mathematical Sciences

March  2021, 17(2): 517-531. doi: 10.3934/jimo.2019121

## Collaborative environmental management for transboundary air pollution problems: A differential levies game

 1 SRS Consortium for Advanced Study in Dynamic Cooperative Games, Hong Kong Shue Yan University, Hong Kong 2 Center of Game Theory, St Petersburg State University, St Petersburg, 198904, Russia 3 Decision Sciences and Modelling Program, Victoria University, Australia 4 College of Environmental Science and Engineering, Nankai University, China 5 MOE Key Laboratory of Pollution Processes and Environmental Criteria, Nankai University, China

* Corresponding author: David W. K. Yeung

Received  June 2018 Revised  June 2019 Published  October 2019

This paper develops a new cooperative dynamic time consistent model for studying regional air pollution management issues in a cooperative game framework for formulating pollution control policies and dynamically consistent compensation mechanisms. As air pollution is a transboundary issue, unilateral response on the part of one region is generally ineffective. Regional cooperation is essential to resolve serious environmental problems. In addition, the long-term environmental impacts are closely related to the building up existing air pollution stocks in Sulfur Dioxide (SO2), Nitrogen Dioxide (NO2), Respirable suspended particulates (RSP) and Ozone (O3). A cooperative dynamic game with different types of pollutants is developed. We characterize the non-cooperative outcomes, and examine the cooperative arrangements, group optimal actions, and individually rational imputations. In particular, an air pollution levy consisting of four components involving damage charges on emissions of sulfur dioxide, nitrogen dioxide, respirable suspended particulates and ozone depletion materials. Cooperative games offer the possibility of socially optimal and group efficient solutions to the lack of cooperation among different regions involving decision problems among strategic actors. This paper makes a valuable contribution to the literature as this is the first cooperative dynamic time consistent model for regional management of different types of air pollutants.

Citation: David W. K. Yeung, Yingxuan Zhang, Hongtao Bai, Sardar M. N. Islam. Collaborative environmental management for transboundary air pollution problems: A differential levies game. Journal of Industrial & Management Optimization, 2021, 17 (2) : 517-531. doi: 10.3934/jimo.2019121
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