Invitation Games: An Experimental Approach to Coalition Formation
Round 1
Reviewer 1 Report
The paper is well written and the results are clearly described. I also believe that understanding the role of sequentiality in coalition formation from an empirical perspective is an important question. The paper looks into the problem with some new angle with its focus on actions (and hence it delivers new insights).
My main concern is with the conclusions. The difference between the sequential and the simultaneous treatments could originate in how easy it is for player C (and player B to a lesser extent) to make computations in the sequential treatment, but not necessarily be related to the fact that they can observe the previous players' actions. Or most likely both effects at are simultaneously at work. I therefore think that it would be nice if the authors could investigate this issue and disentangle both effects in explaining e.g. the efficiency gap between the two procedures, or at the very least advance some hypotheses. This issue could be discussed at the conclusion section.
Author Response
We are very grateful to Reviewer 1 for the helpful comments. Please see the attachment for our reply to the provided comments.
Author Response File: 
Author Response.pdf
Reviewer 2 Report
This paper studies coalition formation and introduces what the authors claim is a new game, based on invitations and staggered decision-making. The paper speaks to a wide academic and policy debate about coalition formation, especially concerning international cooperation around climate change.
My appraisal is rather positive concerning the theoretical setting, although the authors did not make much effort to connect to strands of literature closely connected to their paper. I have more concerns regarding the execution, which however can be addressed by going back to the (physical or online) lab. In what follows, I elaborate on all these points.
- The paper contributes to a literature on coalition formation, which has seen a lot of prolificacy especially related with climate change negotiations (Hoel 1992; Carraro and Siniscalco 1993; Barrett 1994; Carraro and Siniscalco 1998; Barrett 2006; Harstad 2012; Battaglini and Harstad 2015; Nordhaus 2015; Harstad 2016). In particular, the staggered approach seems to reflect the pledge and review process to the Paris Agreement, when Switzerland first pledged a 50% reduction compared to the 1990 baseline in early 2015 and then the European Union pledged a 40% reduction compared to the 1990 baseline, with both ambitious pledges setting the stage for a cascade of cooperation, which eventually led to a successful agreement in Paris, as highlighted in Carattini, Levin, and Tavoni (2019). Further, the paper speaks to an interdisciplinary literature on club approaches and strategies to manage momentum in climate negotiations, including Nordhaus (2015), Keohane and Victor (2016), Buchholz and Sandler (2017), Helland, Hovi, and Sælen (2018).
- My main concern with the execution relates with the use of very small samples, so that in my opinion a return to the lab is in order, which should now be increasingly feasible – while online labs have never stopped operating and still represent a viable alternative. The fact that participants’ actions align very well with theory is not, in my opinion, a good reason not to collect further data until getting reasonable sample sizes. Going back to the lab would also allow randomizing treatments instead of playing them consecutively, which is more in line with the state of the art in the literature (between-subject design).
References
Barrett, Scott. 1994. “Self-Enforcing International Environmental Agreements.” Oxford Economic Papers 46: 878–94.
———. 2006. Environment and Statecraft: The Strategy of Environmental Treaty-Making. Oxford ; New York: Oxford University Press.
Battaglini, Marco, and Bård Harstad. 2015. “Participation and Duration of Environmental Agreements.” Journal of Political Economy 124 (1): 160–204.
Buchholz, Wolfgang, and Todd Sandler. 2017. “Successful Leadership in Global Public Good Provision: Incorporating Behavioural Approaches.” Environmental & Resource Economics 67 (3): 591–607.
Carraro, Carlo, and Domenico Siniscalco. 1993. “Strategies for the International Protection of the Environment.” Journal of Public Economics 52 (3): 309–28.
———. 1998. “International Institutions and Environmental Policy: International Environmental Agreements: Incentives and Political Economy.” European Economic Review 42 (3–5): 561–72. https://doi.org/10.1016/S0014-2921(97)00118-9.
Harstad, Bård. 2012. “Climate Contracts: A Game of Emissions, Investments, Negotiations, and Renegotiations.” The Review of Economic Studies 79 (4): 1527–57.
———. 2016. “The Dynamics of Climate Agreements.” Journal of the European Economic Association 14 (3): 719–52.
Helland, Leif, Jon Hovi, and Håkon Sælen. 2018. “Climate Leadership by Conditional Commitments.” Oxford Economic Papers 70 (2): 417–42.
Hoel, Michael. 1992. “International Environment Conventions: The Case of Uniform Reductions of Emissions.” Environmental and Resource Economics 2 (2): 141–59.
Keohane, Robert O., and David G. Victor. 2016. “Cooperation and Discord in Global Climate Policy.” Nature Climate Change 6 (6): 570–75.
Nordhaus, William. 2015. “Climate Clubs: Overcoming Free-Riding in International Climate Policy.” American Economic Review 105 (4): 1339–70.
Author Response
We are very grateful to Reviewer 2 for the helpful comments. Please see the attachment for our reply to the provided comments.
Author Response File: Author Response.pdf
Reviewer 3 Report
My opinion is that the proposed experiments would be interesting if the model, purpose and conclusions were explained more clearly.
1) First of all there is a problem from the beginning: the author/s aim to compare two different games and not the same game played in a different way, as, in one case, the strategies depend on the path (the SEQ model), and, in the other one, they do not (the SIM model). So, what author/s really compare are the strategy profiles of the SIM model with the sequence of actions "along the path" in the SEQ model, as these two kind of vectors have the same dimension. So, when the author/s talk about subgame Nash equilibrium consistency then it means that the corresponding path is a "part of the subgame Nash equilibrium" or that the "path is prescribed by a SPNE". Now these things must be clearly fixed from the beginning because otherwise the reader expects something different.
For instance, the sentence in the introduction saying that a SPNE is not a NE of the simultaneous game is false. It becomes true only if it is specified what I told you before: Authors are comparing strategies profiles of one game with paths of another game!
2) Once the game is clearly explained, what the authors want to show? It is obvious that if you play different games, then the outcomes can be different; so, this observation cannot be the final purpose of the experiments. The authors should focus on fewer results, the most intriguing ones. In the present form, the reader is confused by the so many different details and does not really understand what is the contribution of the experiments.
3) Finally, my opinion is that problem of coalition formation appears a bit oversimplified. First of all, authors are considering games with only 3 players. Moreover, authors don't take into account externalities: the utility of A to be alone may change depending on B and C are forming a coalition or not. However these comments might be suggestions for future research
Author Response
We are very grateful to Reviewer 3 for the helpful comments. Please see the attachment for our reply to the provided comments.
Author Response File: Author Response.pdf
Reviewer 4 Report
Please find attached.
Comments for author File: Comments.pdf
Author Response
We are very grateful to Reviewer 4 for the helpful comments. Please see the attachment for our reply to the provided comments.
Author Response File: Author Response.pdf
Round 2
Reviewer 2 Report
I find the response by the authors extremely minimalist and unsatisfactory.
Author Response
We have revised our manuscript based on the academic editor's comments. Please contact the academic editor for the revisions.
Reviewer 4 Report
While I understand that this paper is interested in testing the efficiencies of two mechanisms. However, the two mechanisms you suggest are thought processes, and so unless you can establish/elicit that you have successfully invoked the two different processes by means of a suitable experiment design, I am not sure how I should evaluate the final results. I remain worried that the experiment design does not confirm to the conditions for any of the underlying equilibrium predictions that are being used.
Author Response
We have revised our manuscript based on the academic editor's comments. Please contact the academic editor for the revisions.
