IDEAS home Printed from https://ideas.repec.org/a/spr/topjnl/v28y2020i2d10.1007_s11750-020-00539-0.html
   My bibliography  Save this article

Sharing pollution permits under welfare upper bounds

Author

Listed:
  • Jin Li

    (International Academy of Business and Economics, Tianjin University of Finance and Economics)

  • Sang-Chul Suh

    (University of Windsor)

  • Yuntong Wang

    (University of Windsor)

Abstract

We consider a pollution permit sharing problem: there are a finite number of countries and each country owns a fixed amount of permits and a technology. Each country’s output production is limited by the amount of permits it has and the permit is the only input for the technology. Permits are considered as rival goods and are perfectly transferable between countries. Technologies are nonrival but exclusive. Efficiency requires the permits to be able to be reallocated between countries so that the joint total production is optimal. The main question is how to share the total optimal output. A solution assigns to each permit sharing problem an allocation of the optimal output between the countries. In this paper, we consider two upper bounds for a solution. We define two coalitional games. The aspiration upper bound with given technologies (AUBT) game assigns to each coalition the optimal output the coalition can generate using the permits available from all the countries with the technologies available to the coalition. The aspiration upper bound with given permits (AUBP) game, on the other hand, assigns to each coalition the optimal output the coalition can generate using the technologies available from all countries with the permits available to the coalition. These two games define two natural welfare upper bounds for a solution. We show that both the AUBT and the AUBP games are concave (Theorems 1, 2). The Shapley values of these two games satisfy the two welfare upper bounds, respectively.

Suggested Citation

  • Jin Li & Sang-Chul Suh & Yuntong Wang, 2020. "Sharing pollution permits under welfare upper bounds," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 28(2), pages 489-505, July.
    • Handle: RePEc:spr:topjnl:v:28:y:2020:i:2:d:10.1007_s11750-020-00539-0
    DOI: 10.1007/s11750-020-00539-0
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s11750-020-00539-0
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s11750-020-00539-0?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Moulin, Herve, 2002. "Axiomatic cost and surplus sharing," Handbook of Social Choice and Welfare, in: K. J. Arrow & A. K. Sen & K. Suzumura (ed.), Handbook of Social Choice and Welfare, edition 1, volume 1, chapter 6, pages 289-357, Elsevier.
    2. Montgomery, W. David, 1972. "Markets in licenses and efficient pollution control programs," Journal of Economic Theory, Elsevier, vol. 5(3), pages 395-418, December.
    3. Soesja Grundel & Peter Borm & Herbert Hamers, 2013. "Resource allocation games: a compromise stable extension of bankruptcy games," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 78(2), pages 149-169, October.
    4. Peter Borm & Herbert Hamers & Ruud Hendrickx, 2001. "Operations research games: A survey," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 9(2), pages 139-199, December.
    5. Hervé Moulin & Yves Sprumont, 2007. "Fair allocation of production externalities : recent results," Revue d'économie politique, Dalloz, vol. 117(1), pages 7-36.
    6. CHANDER, Parkash & TULKENS, Henry, 2011. "The kyoto Protocol, the Copenhagen Accord, the Cancun Agreements, and beyond: an economic and game theoretical exploration and interpretation," LIDAM Discussion Papers CORE 2011051, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    7. Moulin, Herve, 1991. "Welfare bounds in the fair division problem," Journal of Economic Theory, Elsevier, vol. 54(2), pages 321-337, August.
    8. Eric Bahel & Christian Trudeau, 2018. "Stable cost sharing in production allocation games," Review of Economic Design, Springer;Society for Economic Design, vol. 22(1), pages 25-53, June.
    9. Soesja Grundel & Peter Borm & Herbert Hamers, 2019. "Resource allocation problems with concave reward functions," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 27(1), pages 37-54, April.
    10. Ichiishi, Tatsuro, 1981. "Super-modularity: Applications to convex games and to the greedy algorithm for LP," Journal of Economic Theory, Elsevier, vol. 25(2), pages 283-286, October.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Sang-Chul Suh & Yuntong Wang, 2023. "The equal share proportional solution in a permit sharing problem," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 60(3), pages 477-501, April.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Eric Bahel & Christian Trudeau, 2018. "Consistency requirements and pattern methods in cost sharing problems with technological cooperation," International Journal of Game Theory, Springer;Game Theory Society, vol. 47(3), pages 737-765, September.
    2. Fragnelli, V. & Llorca, N. & Sánchez-Soriano, J. & Tijs, S.H., 2006. "Convex Games with Countable Number of Players and Sequencing Situations," Discussion Paper 2006-119, Tilburg University, Center for Economic Research.
    3. Özen, Ulas & Norde, Henk & Slikker, Marco, 2011. "On the convexity of newsvendor games," International Journal of Production Economics, Elsevier, vol. 133(1), pages 35-42, September.
    4. Heuvel, Wilco van den & Borm, Peter & Hamers, Herbert, 2007. "Economic lot-sizing games," European Journal of Operational Research, Elsevier, vol. 176(2), pages 1117-1130, January.
    5. Bilbao, J.M. & Jiménez, N. & López, J.J., 2010. "The selectope for bicooperative games," European Journal of Operational Research, Elsevier, vol. 204(3), pages 522-532, August.
    6. Drechsel, J. & Kimms, A., 2010. "Computing core allocations in cooperative games with an application to cooperative procurement," International Journal of Production Economics, Elsevier, vol. 128(1), pages 310-321, November.
    7. Sebastián Marbán & Peter Ven & Peter Borm & Herbert Hamers, 2013. "ALOHA networks: a game-theoretic approach," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 78(2), pages 221-242, October.
    8. Soesja Grundel & Peter Borm & Herbert Hamers, 2013. "Resource allocation games: a compromise stable extension of bankruptcy games," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 78(2), pages 149-169, October.
    9. Ruud Hendrickx & Jacco Thijssen & Peter Borm, 2012. "Minimum cost spanning tree games and spillover stability," Theory and Decision, Springer, vol. 73(3), pages 441-451, September.
    10. Eric Bahel, 2011. "The implications of the ranking axiom for discrete cost sharing methods," International Journal of Game Theory, Springer;Game Theory Society, vol. 40(3), pages 551-589, August.
    11. Yves Sprumont, 2008. "Nearly serial sharing methods," International Journal of Game Theory, Springer;Game Theory Society, vol. 37(2), pages 155-184, June.
    12. Ozen, U. & Norde, H.W. & Slikker, M., 2005. "On the Convexity of News Vendor Games," Other publications TiSEM 2faeeb88-8d0b-4c36-9b08-5, Tilburg University, School of Economics and Management.
    13. Sang-Chul Suh & Yuntong Wang, 2016. "Pollution Permit Sharing Games," Working Papers 1604, University of Windsor, Department of Economics.
    14. Txus Ortells & Juan Santos, 2011. "The pseudo-average rule: bankruptcy, cost allocation and bargaining," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 73(1), pages 55-73, February.
    15. Estévez-Fernández, Arantza, 2012. "A game theoretical approach to sharing penalties and rewards in projects," European Journal of Operational Research, Elsevier, vol. 216(3), pages 647-657.
    16. Frans P. Vries & Nick Hanley, 2016. "Incentive-Based Policy Design for Pollution Control and Biodiversity Conservation: A Review," Environmental & Resource Economics, Springer;European Association of Environmental and Resource Economists, vol. 63(4), pages 687-702, April.
    17. Michel Grabisch, 2011. "Ensuring the boundedness of the core of games with restricted cooperation," Annals of Operations Research, Springer, vol. 191(1), pages 137-154, November.
    18. Lawrence H. Goulder, 2013. "Markets for Pollution Allowances: What Are the (New) Lessons?," Journal of Economic Perspectives, American Economic Association, vol. 27(1), pages 87-102, Winter.
    19. Nunez, Marina & Rafels, Carles, 2003. "Characterization of the extreme core allocations of the assignment game," Games and Economic Behavior, Elsevier, vol. 44(2), pages 311-331, August.
    20. Veith, Stefan & Werner, Jörg R. & Zimmermann, Jochen, 2009. "Capital market response to emission rights returns: Evidence from the European power sector," Energy Economics, Elsevier, vol. 31(4), pages 605-613, July.

    More about this item

    Keywords

    Pollution permits; Cooperative games; Aspiration upper bounds; Shapley value;
    All these keywords.

    JEL classification:

    • C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games
    • D70 - Microeconomics - - Analysis of Collective Decision-Making - - - General

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:topjnl:v:28:y:2020:i:2:d:10.1007_s11750-020-00539-0. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.