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Sharing pollution permits under welfare upper bounds. (English) Zbl 1443.91027
Summary: 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.
91A12 Cooperative games
91B76 Environmental economics (natural resource models, harvesting, pollution, etc.)
Full Text: DOI
[1] Ambec, S.; Sprumont, Y., Sharing a river, J Econ Theory, 107, 453-462 (2002) · Zbl 1033.91503
[2] Bahel, E.; Trudeau, C., Stable cost sharing in production allocation games, Rev Econ Des, 22, 25-53 (2018) · Zbl 1422.91384
[3] Borm, P.; Hamers, H.; Hendrickx, R., Operations research games: a survey, TOP, 9, 139-216 (2001) · Zbl 1006.91009
[4] Chander P, Tulkens H (2011) The Kyoto Protocol, the Copenhagen Accord, the Cancun Agreements, and beyond: an economic and game theoretical exploration and interpretation. CORE DISCUSSION PAPER 2011/51, Center for Operations Research and Econometrics, Voie du Roman Pays, 34, B-1348 Louvain-la-Neuve, Belgium
[5] Claus, A.; Kleitman, D., Cost allocation for a spanning tree, Networks, 3, 289-304 (1973) · Zbl 0338.90031
[6] Grundel, S.; Borm, P.; Hamers, H., Resource allocation games: a compromise stable extension of bankruptcy games, Math Methods Oper Res, 78, 149-169 (2013) · Zbl 1280.91013
[7] Grundel, S.; Borm, P.; Hamers, H., Resource allocation problems with concave reward functions, TOP, 27, 37-54 (2019) · Zbl 1410.91311
[8] Ichiishi, T., Super-modularity: applications to convex games and to the greedy algorithm for LP, J Econ Theory, 25, 283-286 (1981) · Zbl 0478.90092
[9] Montgomery, WD, Markets in licenses and efficient pollution control programs, J Econ Theory, 5, 395-418 (1972)
[10] Moulin, H., Welfare bounds in the fair division problem, J Econ Theory, 54, 321-337 (1991) · Zbl 0743.90007
[11] Moulin, H., Cooperative microeconomics (1995), Princeton: Princeton University Press, Princeton
[12] Moulin, H.; Arrow, KJ; Sen, AK; Suzumura, K., Axiomatic cost and surplus sharing, Handbook of social choice and welfare (2002), Amsterdam: North-Holland, Amsterdam
[13] Moulin, H.; Sprumont, Y., Fair allocation of production externalities: recent results, Rev Econ Polit, 117, 7-36 (2007)
[14] Raupach, MR; Davis, ST; Peters, GP; Andrew, RM; Canadell, JG; Ciais, P.; Friedlingstein, P.; Jotzo, F.; van Vuuren, DP; Le Quéré, C., Sharing a quota on cumulative carbon emissions, Nat Clim Change (2014)
[15] Shapley LS (1953) A value for n-person games. In: Kuhn HW, Tucker AW (eds) Contributions to the theory of games II. Annals of mathematics, vol 28, pp 307-317 · Zbl 0050.14404
[16] Shapley, LS, Cores of convex games, Int J Game Theory, 1, 11-26 (1971) · Zbl 0222.90054
[17] Suh, S., Non-manipulable solutions in a permit sharing problem: equivalence between non-manipulability and monotonicity, Rev Econ Des, 6, 447-460 (2001) · Zbl 1008.91064
[18] Suh S, Wang Y (2019) The proportional solution in a permit sharing problem. Working Paper, University of Windsor
[19] Weber R (1988) Probabilistic values for games. In: Values The Shapley (ed) A. Cambridge University Press, Cambridge
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