American Institute of Mathematical Sciences

Advanced
doi: 10.3934/jimo.2019121

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

David W. K. Yeung 1,2,, , Yingxuan Zhang 1,3, , Hongtao Bai 4,5, and  Sardar M. N. Islam 3,

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.

Keywords: Transboundary Air pollution problems, cooperative game, time consistent solution, regional cooperation, environmental management.
Mathematics Subject Classification: Primary: 91A12, 91A35.
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, doi: 10.3934/jimo.2019121
References:
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F. Lera-Lopez, J. Faulin and M. Sanchez, Determinants of the willingness-to-pay for reducing the environmental impacts of road transportation, Transportation Research Part D Transport and Environment, 17 (2012), 215-220.  doi: 10.1016/j.trd.2011.11.002.  Google Scholar

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show all references

References:
[1]

A. Antoci, P. Russu and E. Ticci, Environmental externalities and immiserizing structural changes in an economy with heterogeneous agents, Ecological Economics, 81 (2012), 80-91.  doi: 10.1016/j.ecolecon.2012.06.004.  Google Scholar

[2]

M. Breton, G. Zaccour and M. Zahaf, A differential game of joint implementation of environmental projects, Automatica J., 41 (2005), 1737-1749.  doi: 10.1016/j.automatica.2005.05.004.  Google Scholar

[3]

M. Breton, G. Zaccour and M. Zahaf, A game-theoretic formulation of joint implementation of environmental projects, European J. Oper. Res., 168 (2005), 221-239.  doi: 10.1016/j.ejor.2004.04.026.  Google Scholar

[4]

A. J. Caplan and E. C. D. Silva, Federal acid rain games, J. of Urban Economics, 46 (1999), 25-52.  doi: 10.1006/juec.1998.2109.  Google Scholar

[5]

P. Chander and H. Tulkens, A core-theoretic solution for the design of cooperative agreements on transfrontier pollution, International Tax and Public Finance, 2 (1995), 279-294.  doi: 10.1007/BF00877502.  Google Scholar

[6]

P. Chander and H. Tulkens, (1997) The core of an economy with multilateral environmental externalities, Internat. J. Game Theory, 26 (1997), 379–401. doi: 10.1007/BF01263279.  Google Scholar

[7]

B. R. Copeland, Pollution content tariffs, environmental rent shifting, and the control of cross border pollution, J. of International Economics, 40 (1996), 459-476.  doi: 10.1016/0022-1996(95)01415-2.  Google Scholar

[8]

P. Courtois and T. Tazdaït, Bargaining over a climate deal: Deadline and delay, Ann. Oper. Res., 220 (2014), 205-221.  doi: 10.1007/s10479-011-1018-9.  Google Scholar

[9]

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[10]

E. J. Dockner and N. V. Long, International pollution control: Cooperative versus noncooperative strategies, J. of Environmental Economics and Management, 25 (1993), 13-29.  doi: 10.1006/jeem.1993.1023.  Google Scholar

[11]

M. Finus, P. Cooper and C. Almer, The use of international agreements in transnational environmental protection, Oxford Economic Papers, 69 (2017), 333-344.  doi: 10.1093/oep/gpx018.  Google Scholar

[12]

K. Fredj, G. Martín-Herrán and G. Zaccour, Slowing deforestation pace through subsidies: A differential game, Automatica J., 40 (2004), 301-309.  doi: 10.1016/j.automatica.2003.10.020.  Google Scholar

[13]

M. Germaina, H. Tulkens and A. Magnus, Dynamic core-theoretic cooperation in a two-dimensional international environmental model, Math. Social Sci., 59 (2010), 208-226.  doi: 10.1016/j.mathsocsci.2009.10.003.  Google Scholar

[14]

L. P. Hildebrand, V. Pebbles and D. A. Fraser, Cooperative ecosystem management across the Canada–US border: Approaches and experiences of transboundary programs in the Gulf of Maine, Great Lakes and Georgia Basin/Puget Sound, Ocean & Coastal Management, 45 (2002), 421-457.  doi: 10.1016/S0964-5691(02)00078-9.  Google Scholar

[15]

J. Hu, Research on Local Government Collaboration in Transboundary Environmental Governance, Thesis for Doctor's Degree, Fudan University, Shanghai, China, (2010). Google Scholar

[16]

S. Jorgensen and G. Zaccour, Time consistent side payments in a dynamic game of downstream pollution, J. Econom. Dynam. Control, 25 (2001), 1973-1987.  doi: 10.1016/S0165-1889(00)00013-0.  Google Scholar

[17]

V. Kaitala, M. Pohjola and O. Tahvonen, Transboundary air pollution between Finland and the USSR - a dynamic acid rain game, in Dynamic Games in Economic Analysis, Lecture Notes in Control and Information Sciences, 157, Springer, 1991, 183–192. doi: 10.1007/BFb0006240.  Google Scholar

[18]

V. Kaitala, M. Pohjola and O. Tahvonen, An economic analysis of transboundary air pollution between Finland and the Soviet Union, Scandinavian J. of Economics, 94 (1992), 409-424.   Google Scholar

[19]

V. Kaitala, M. Pohjola and O. Tahvonen, Transboundary air pollution and soil acidification: A dynamic analysis of an acid rain game between Finland and the USSR, Environmental and Resource Economics, 2 (1992), 161-181.  doi: 10.1007/BF00338241.  Google Scholar

[20]

V. Kaitala, K. G. Maler and H. Tulkens, The acid rain game as a resource allocation process, with application to negotiations between Finland, Russia and Estonia, in Public Goods, Environmental Externalities and Fiscal Competition, 97, Springer, Boston, MA, 1995, 135–152. doi: 10.1007/978-0-387-25534-7_9.  Google Scholar

[21]

T. R. Lakshmanan and F. Lo, A regional economic model for the assessment of effects of air pollution abatement, Environment and Planning, 4 (1972), 73-97.   Google Scholar

[22]

F. Lera-Lopez, J. Faulin and M. Sanchez, Determinants of the willingness-to-pay for reducing the environmental impacts of road transportation, Transportation Research Part D Transport and Environment, 17 (2012), 215-220.  doi: 10.1016/j.trd.2011.11.002.  Google Scholar

[23]

S. Li, A differential game of transboundary industrial pollution with emission permits trading, J. Optim. Theory Appl., 163 (2014), 642-659.  doi: 10.1007/s10957-013-0384-7.  Google Scholar

[24]

M. C. Liu, L. Yang, Q. W. Min and Y. Y. Bai, Eco-compensation standards for agricultural water conservation: A case study of the paddy land-to-dry land program in China, Agricultural Water Management, 204 (2018), 192-197.  doi: 10.1016/j.agwat.2018.04.004.  Google Scholar

[25]

K. G. Mäler, The acid rain game, in Valuation Methods and Policy Making in Environmental Economics, Elsevier, Amsterdam, 1989, 231–252. Google Scholar

[26]

J. R. Markusen, International externalities and optimal tax structures, J. of International Economics, 5 (1975), 15-29.  doi: 10.1016/0022-1996(75)90025-2.  Google Scholar

[27]

Y. Nagase and E. C. D. Silva, Acid rain in China and Japan: A game-theoretic analysis, Regional Science and Urban Economics, 37 (2007), 100-120.  doi: 10.1016/j.regsciurbeco.2006.08.001.  Google Scholar

[28]

T. Paksoy and E. Ozceylan, Environmentally conscious optimization of supply chain networks, J. of the Operational Research Society, 65 (2013), 855-872.  doi: 10.1057/jors.2012.95.  Google Scholar

[29]

T. Paksoy, N. Y. Pehlivan and E. Ozceylan, Fuzzy multi objective optimization of a green supply chain network with risk management of that includes environmental hazards, Human and Ecological Risk Assessment, 18 (2012), 1120-1151.  doi: 10.1080/10807039.2012.707940.  Google Scholar

[30]

L. Petrosyan and G. Zaccour, Time-consistent Shapley value allocation of pollution cost reduction, J. Econom. Dynam. Control, 27 (2003), 381-398.  doi: 10.1016/S0165-1889(01)00053-7.  Google Scholar

[31]

K. Prager, Agri-environmental collaboratives for landscape management in Europe, Current Opinion in Environmental Sustainability, 12 (2015), 59-66.  doi: 10.1016/j.cosust.2014.10.009.  Google Scholar

[32]

K. Prager, Agri-environmental collaboratives as bridging organisations in landscape management, J. of Environmental Management, 161 (2015), 375-384.  doi: 10.1016/j.jenvman.2015.07.027.  Google Scholar

[33]

O. Tahvonen, V. Kaitala and M. Pohjola, A Finnish-Soviet acid rain game: Noncooperative equilibria, cost efficiency, and sulphur agreements, J. of Environmental Economics and Management, 24 (1993), 87-100.  doi: 10.1006/jeem.1993.1006.  Google Scholar

[34]

H. Tulkens, An economic model of international negotiations relating to transfrontier pollution, in Public Goods, Environmental Externalities and Fiscal Competition, Springer, Boston, MA, 2006, 107–121. doi: 10.1007/978-0-387-25534-7_7.  Google Scholar

[35]

P. Usta, S. Ergun and S. Z. Alparslan-Gok, A cooperative game theory approach to post disaster housing problem, in Handbook of Research on Emergent Applications of Optimization Algorithms, IGI Global, USA, 2018, 314–325. Google Scholar

[36]

A. A. Vasin, Game-theoretic study of electricity market mechanisms, Procedia Computer Science, 31 (2014), 124-132.  doi: 10.1016/j.procs.2014.05.252.  Google Scholar

[37]

A. A. Vasin and A. G. Gusev, Game-theoretical control models for electric power and capacity market, J. Comput. Syst. Sci. Int., 51 (2012), 792-801.  doi: 10.1134/S1064230712060135.  Google Scholar

[38]

G. W. Weber, S. Z. Alparslan-Gok and B. Soyler, A new mathematical approach in environmental and life sciences: gene-environment networks and their dynamics, Environmental Modelling and Assessment, 14 (2009), 267-288.  doi: 10.1007/s10666-007-9137-z.  Google Scholar

[39]

G. W. Weber, P. Taylan, S. Z. Alparslan-Gok, S. Ozogue and B. Akteke-Ozturk, Optimization of gene-environment networks in the presence of errors and uncertainty with Chebychev approximation, TOP, 16 (2008), 284-318.  doi: 10.1007/s11750-008-0052-5.  Google Scholar

[40]

J. Westerink, R. Jongeneel, N. Polman, K. Prager, J. Franks, P. Dupraz and E. Mettepenningen, Collaborative governance arrangements to deliver spatially coordinated agri-environmental management, Land Use Policy, 69 (2017), 176-192.  doi: 10.1016/j.landusepol.2017.09.002.  Google Scholar

[41]

D. Yaron and A. Ratner, Regional cooperation in the use of irrigation water: Efficiency and income distribution, Agricultural Economics, 4 (1990), 45-58.  doi: 10.1016/0169-5150(90)90019-W.  Google Scholar

[42]

D. W. K. Yeung, Dynamically consistent cooperative solution in a differential game of transboundary industrial pollution., J. Optim. Theory Appl., 134 (2007), 143-160.  doi: 10.1007/s10957-007-9240-y.  Google Scholar

[43]

D. W. K. Yeung, Dynamically consistent solution for a pollution management game in collaborative abatement with uncertain future payoffs, Int. Game Theory Rev., 10 (2008), 517-538.  doi: 10.1142/S0219198908002072.  Google Scholar

[44]

D. W. K. Yeung, Dynamically consistent collaborative environmental management with production technique choices, Ann. Oper. Res., 220 (2014), 181-204.  doi: 10.1007/s10479-011-0844-0.  Google Scholar

[45]

D. W. K. Yeung and L. A. Petrosyan, Subgame consistent solution of a cooperative stochastic differential game with nontransferable payoffs, J. Optim. Theory Appl., 124 (2005), 701-724. doi: 10.1007/s10957-004-1181-0.  Google Scholar

[46]

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