Bottom-up linking of carbon markets under far-sighted cap coordination and reversibility

A Publisher Correction to this article was published on 19 April 2018

This article has been updated


The Paris Agreement relies on nationally determined contributions to reach its targets and asks countries to increase ambitions over time, leaving open the details of this process. Although overcoming countries’ myopic ‘free-riding’ incentives requires cooperation, the global public good character of mitigation makes forming coalitions difficult. To cooperate, countries may link their carbon markets1, but is this option beneficial2? Some countries might not participate, not agree to lower caps, or not comply to agreements. While non-compliance might be deterred3, countries can hope that if they don’t participate, others might still form a coalition. When considering only one coalition whose members can leave freely, the literature following the publication of refs 4,5 finds meagre prospects for effective collaboration6. Countries also face incentives to increase emissions when linking their markets without a cap agreement7,8. Here, we analyse the dynamics of market linkage using a game-theoretic model of far-sighted coalition formation. In contrast to non-dynamic models and dynamic models without far-sightedness9,10, in our model an efficient global coalition always forms eventually if players are sufficiently far-sighted or caps are coordinated immediately when markets are linked.

Access options

Rent or Buy article

Get time limited or full article access on ReadCube.


All prices are NET prices.

Fig. 1: Illustration of the model in a fictitious situation with three symmetric players A, B, and C, linear mitigation benefits, and quadratic mitigation costs.
Fig. 2: Typical model results for the six major emitters.
Fig. 3: Alternative scenario to Fig. 2 with typical complications occurring if players are highly far-sighted (δ = 0.9) and agreements are irreversible.
Fig. 4: Alternative scenario to Fig. 2 in a world where caps cannot immediately be coordinated when markets are linked but only later in separate moves.

Change history

  • 19 April 2018

    In the PDF version of this Article originally published, in equation (6) \(g^{\prime}_{i}\) was incorrectly formatted as gi′, and at the end of the Methods section w i was incorrectly formatted as wi. These have now been corrected.


  1. 1.

    Adoption of the Paris Agreement FCCC/CP/2015/L.9/Rev.1 (UNFCCC, 2015);

  2. 2.

    Green, J. F., Sterner, T. & Wagner, G. A balance of bottom-up and top-down in linking climate policies. Nat. Clim. Change 4, 1064–1067 (2014).

    Article  Google Scholar 

  3. 3.

    Heitzig, J., Lessmann, K. & Zou, Y. Self-enforcing strategies to deter free-riding in the climate change mitigation game and other repeated public good games. Proc. Natl Acad. Sci. USA 108, 15739–15744 (2011).

  4. 4.

    Carraro, C. & Siniscalco, D. Strategies for the international protection of the environment. J. Public Econ. 52, 309–328 (1993).

    Article  Google Scholar 

  5. 5.

    Barrett, S. Self-enforcing international environmental agreements. Oxford Econ. Pap. 46, 878–894 (1994).

  6. 6.

    Finus, M. in Environmental Policy in an International Perspective (eds Marsiliani, L., Rauscher, M. & Withagen, C.) 19–49 (Kluwer, Dordrecht, Holland, 2003).

  7. 7.

    Helm, C. International emissions trading with endogenous allowance choices. J. Public Econ. 87, 2737–2747 (2003).

    Article  Google Scholar 

  8. 8.

    Carbone, J. C., Helm, C. & Rutherford, T. F. The case for international emission trade in the absence of cooperative climate policy. J. Environ. Econ. Manag. 58, 266–280 (2009).

    Article  Google Scholar 

  9. 9.

    Smead, R., Sandler, R. L., Forber, P. & Basl, J. A bargaining game analysis of international climate negotiations. Nat. Clim. Change 4, 442–445 (2014).

    Article  Google Scholar 

  10. 10.

    Verendel, V., Johansson, D. J. A. & Lindgren, K. Strategic reasoning and bargaining in catastrophic climate change games. Nat. Clim. Change 6, 6–10 (2015).

    Google Scholar 

  11. 11.

    Ray, D. & Vohra, R. Equilibrium binding agreements. J. Econ. Theory 73, 30–78 (1997).

    Article  Google Scholar 

  12. 12.

    Ray, D. & Vohra, R. A theory of endogenous coalition structures. Games Econ. Behav. 26, 286–336 (1999).

    Article  Google Scholar 

  13. 13.

    Konishi, H. & Ray, D. Coalition formation as a dynamic process. J. Econ. Theory 110, 1–41 (2003).

    Article  Google Scholar 

  14. 14.

    de Zeeuw, A. Dynamic effects on the stability of international environmental agreements. J. Environ. Econ. Manag. 55, 163–174 (2008).

    Article  Google Scholar 

  15. 15.

    Biancardi, M. & Villani, G. Largest consistent set in international environmental agreements. Comput. Econ. 38, 407–423 (2011).

    Article  Google Scholar 

  16. 16.

    Osmani, D. A Note on Computational Aspects of Far-sighted Coalitional Stability. Hamburg University, Sustainability and Global Change Research Unit Working Papers FNU–176 1–18 (2011).

  17. 17.

    Godal, O. & Holtsmark, B. On the efficiency gains of emissions trading when climate deals are non-cooperative. Bergen Inst. Res. Econ. Bus. Adm. Work. Pap. 17, 1–24 (2011).

    Google Scholar 

  18. 18.

    Flachsland, C., Marschinski, R. & Edenhofer, O. To link or not to link: benefits and disadvantages of linking cap-and-trade systems. Clim. Policy 9, 358–372 (2009).

    Article  Google Scholar 

  19. 19.

    Tuerk, A., Mehling, M., Flachsland, C. & Sterk, W. Linking carbon markets: concepts, case studies and pathways. Clim. Policy 9, 341–357 (2009).

    Article  Google Scholar 

  20. 20.

    Jaffe, J. & Stavins, R. N. L inkage of Tradable Permit Systems in International Climate Policy Architecture. NBER Working Paper 14432 (2008).

  21. 21.

    Flachsland, C., Marschinski, R. & Edenhofer, O. Global trading versus linking: Architectures for international emissions trading. Energy Policy 37, 1637–1647 (2009).

    Article  Google Scholar 

  22. 22.

    Ranson, M. & Stavins, R. N. Linkage of greenhouse gas emissions trading systems: learning from experience. Clim. Policy 16, 284–300 (2016).

    Article  Google Scholar 

  23. 23.

    Ellerman, A. D. & Decaux, A. Analysis of Post-Kyoto CO 2 Emissions Trading Using Marginal Abatement Curves. MIT Joint Program on the Science and Policy of Global Change Report 40 (1998).

  24. 24.

    Finus, M., van Ierland, E. & Dellink, R. Stability of climate coalitions in a cartel formation game. Econ. Gov. 7, 271–291 (2006).

    Article  Google Scholar 

  25. 25.

    Kalai, E. Nonsymmetric Nash solutions and replications of 2-person bargaining. Int. J. Game Theory 6, 129–133 (1977).

    Article  Google Scholar 

  26. 26.

    Barrett, S. in Conflicts and Cooperation in Managing Environmental Resources (ed. Pethig, R.) 11–37 (Springer: Berlin, Heidelberg, 1992).

  27. 27.

    Heitzig, J. Efficiency in face of externalities when binding hierarchical agreements are possible. Game Theory Bargain. Theory eJournal 3, 1–16 (2011).

  28. 28.

    Heitzig, J. & Simmons, F. W. Some chance for consensus: Voting methods for which consensus is an equilibrium. Social. Choice Welf. 38, 43–57 (2012).

    Article  Google Scholar 

  29. 29.

    Nordhaus, W. D. Managing the Global Commons: the Economics of Climate Change (MIT Press, Cambridge, MA, 1994).

  30. 30.

    Nordhaus, W. D. Economic aspects of global warming in a post-Copenhagen environment. Proc. Natl Acad. Sci. USA 107, 11721–11726 (2010).

  31. 31.

    Kalai, E. & Samet, D. On weighted Shapley values. Int. J. Game Theory 16, 205–222 (1987).

    Article  Google Scholar 

Download references


The authors thank K. Lessmann, R. Marschinski, O. Edenhofer, the Policy Instruments Group and the COPAN Flagship Project at the Potsdam Institute for Climate Impact Research for many intense discussions; B. Holtsmark, M. Greaker, C. Hagem, R. Schmidt, and the CREW project for inspiring work; and R. Vohra, P. Menck, N. Marwan, J. Donges and C.-F. Schleussner for helpful comments.

Author information




J.H. developed the model and conducted the numerical experiments. Both authors interpreted the study, and wrote and edited the text.

Corresponding author

Correspondence to Jobst Heitzig.

Ethics declarations

Competing interests

The authors have no competing interests.

Additional information

Publisher’s note: Springer Nature remains neutral with regard to jurisdictional claims inpublished maps and institutional affiliations.

Supplementary information

Supplementary Information

Supplementary Methods, Supplementary Literature and Approaches, Supplementary Results, Supplementary References, Supplementary Figures 1–10, Supplementary Tables 1–2

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Heitzig, J., Kornek, U. Bottom-up linking of carbon markets under far-sighted cap coordination and reversibility. Nature Clim Change 8, 204–209 (2018).

Download citation

Further reading


Nature Briefing

Sign up for the Nature Briefing newsletter — what matters in science, free to your inbox daily.

Get the most important science stories of the day, free in your inbox. Sign up for Nature Briefing