Stable International Environmental Agreements: Large Coalitions that Achieve Little

Round 1

Reviewer 1 Report

The paper deals with the topic of International Environmental Agreements in an endogenous coalition formation setting. The aim is to show as in some references that either the stable agreement is formed by few countries or, when the number of signatories is higher, that the abatement is, ultimately, very small. In addition, to convince countries to enter, signatories have to reduce the curvature of the abatement cost function when just entered. The setting is, in a way, standard for this literature, with a linear abatement benefit function and a quadratic abatement cost. However, there are several simplifying assumptions: only one coalition can form, and the coalition formation game is a restricted partition function game, since the only feasible coalition structures are those formed by one large coalition and all remaining countries playing independently. Also, countries’ abatement benefits are independent of their own decision, which yields a orthogonal best-responses. This assumptions should be justified. The introductory literature coverage is partial. For instance there exists an established literature with coalitions acting as Stackelberg leaders (see Currarini,  Marini 2003 and 2004, Marini (2013).

As for the paper results, author(s) need to be clearer in some passages. What does exactly mean a change in curvature of the abatement cost function? Is this not equivalent to a shift in the abatment technology? When is this reasonable and justifiable? Why environmental technology spillovers (or leakeages) are absent? Are all these matters of model simplification? A real life example could help the reader to grasp the meaning of the numerical results.

References:

Currarini, S. Marini, M. (2004) "A Conjectural Cooperative equilibrium in Strategic Form Games", in Carraro C.  Fragnelli V. (eds.) Game Practise and the Environment.  Edward Elgar.

Currarini, S. Marini, M. (2003) “A Sequential Approach to the Characteristic Function and  the Core in Games with Externalities”, in Koray S. and Sertel, M. R. (eds.), pp.233-250, Advances in Economic Design, Springer Verlag, Berlin & London. (with S. Currarini)

Marini, M. (2013) “The sequential core of an economy with environmental externalities”, Environmental Sciences 1 (2), 79-82.

Author Response

Dear referee,

thank you for your comments, which are very helpful.

I corrected some typos, but I am not sure whesther I detected all of them.

I extended the literature survey a bit, by adding two of the references you mentioned and some other ones related to issue linking. A longer discussion of the Stackelberg model would, in my view, be inappropriate since I assume Nash behaviour in my model. Issue linkage was missing in the first paper and I mentioned it as another way of achieving larger coalitions as well.

The linear damages indeed generate orthogonal  reaction functions, which are an essential ingredient for the derivation closed-form solutions for welfare and coalition size. Moreover the diagrams that help to understand the intuition behind the results require some simplifying assumptions. 

A change in the curvature of the cost function is a reflection of the properties of the underlying technology. This does not imply a shift from one to another technology (which would more probably result in a discontinuity). It is known that  total-cost curves are often S shaped. Here the marginal cost curve is S shaped such and I added a footnote explaining what this means. 

I agree that a real-life example would be great. However, this paper is more of the conceptional nature. What has to happen in a particular class of coalition-formation models to make large coalitions stable and what are consequences for the abatement levels? 

Kind regards,

Michael Rauscher

Reviewer 2 Report

This paper is well-written and the the analyses are free from serious errors. There are some minor suggestions and comments as follows:

There are no clear definitions of w_s^k and w_n^K in page 5. The proof of Proposition written in the footnote should be included in the main text.  In the analysis developed in page 7, the author can mention the welfare effects of IEA, that is, the ratio of world welfare under the stable IEA to that under the GC, although it is almost the same as the ratio of abatement. The author could make arguments on the meaning and reality of assumption made in Section 4 that MAC becomes linear once the stable IEA has been reached. It would be better if the author could mention some policy implications based on the results of analyses.

Author Response

Dear Referee,

thank you for your helpful comments.

w_s^k and w_n^K  are now explained.

I moved the proof from the footnote to the main text.

I added a footnote on what the change in the curvature means.

I added a paragraph in the summary and conclusions relating the paper to real world abatement cost curves and the Paris Agreement.

Some other small changes, in particular in the introduction, were suggested by the other referee.

Kind  regards

The author