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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
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    References listed on IDEAS

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    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.

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    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

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