One of my bibles for climate negotiation research is Scott Barrett's Environment and Statecraft, which is a tome filled with a very, very great deal of discussion of the game theory that people have used to think about environmental negotiation. I've fought my way through one read of it, and it's one of those books that I'm clearly going to have to go through multiple times to make sure I've worked through it thoroughly.
Here's one initial thought, however. Barrett's game theoretic models suggest that when looking at multilateral environmental treaty-making, the ability to get more and more people to sign on is decreasing with relationship to the benefit of the environmental mitigation in question, and increasing with relationship to the cost of the mitigation. That is, the larger the benefits of mitigation action required by a treaty, the fewer signatories you'll get, while the greater the costs of mitigation, the more signatories you'll get.
This at first seems counter-intuitive (it did to me, at least) but I think the intuition is this: all parties are assumed to be behaving strategically. Parties know that if the benefits of mitigation are greater, they can more confidently assume that other actors will choose to mitigate in order to attain those benefits. Therefore, they can more confidently choose not to sign, planning to free-ride. Conversely, when the costs are higher, you need more total benefits to balance out costs (remember, the benefits of mitigation are assumed to be public goods, so each party to a treaty pays only for its own share but receives benefit equal to the total benefits created by all parties), and treaties will fail to occur if they don't get enough signatories. Since potential signatories know this and (we assume) desire the total potential payoffs from a successful treaty, more will sign, in order to reach the tipping point.
There's a wrinkle to this, though, that Barrett doesn't address but which I think is important to climate negotiations. That is that if parties are facing an existential threat, the benefits of mitigation are essentially infinite. Logically, therefore, by Barrett's model, if willingness to sign treaties decreases as size of benefits to mitigation increases, it should be nearly impossible to get countries to sign on to treaties in cases where the treaties deal with an existential threat. Each country should be able to confidently expect that, even absent a treaty, each other country must nonetheless rationally choose to take every possible action to mitigate, because if the risk of not doing so is an existential one, it would be suicidal not to. The implication of this is that persuasive tactics at the international level that involve emphasizing the possible existential nature of the costs of failure to mitigate (and hence the size of potential benefits to mitigation) could actually be counter-productive.
I'm not sure I believe this as a representation of how states think in general - I'm not convinced states will typically play chicken in this way. But I think there's a variant that's plausible that assumes ambiguity. Let's say you're a Chinese government official, and you're negotiating with European diplomats over an emissions reduction treaty. The European officials, along with a bunch of Western NGOs, are busily trying to convince you that climate change represents an existential threat and therefore you should do something about it - in spite of the fact that it could damage you materially by slowing growth and destabilizing you politically. You believe in a general sense in the problem, but are uncertain how seriously you take the immediacy and scale of it. You're a rising world power and don't want to get played, either into taking action that isn't really necessary, or into taking on more than your share of efforts that are necessary (thus assuming a competitive disadvantage). You think it's entirely possible that your negotiating partners might be exaggerating their true beliefs about costs in order to convince you to cooperate.
Under these conditions, refusal to cooperate is potentially the right move strategically. If the threat is truely existential, then it would be rational for the Europeans to do everything in their power to mitigate, whether or not you cooperate. If the threat is truely existential, they will be forced into shouldering the higher costs of early-learning-curve action. If they do, you have learned something about the real seriousness of the threat (and avoided early high costs - a bonus!). If they don't, you've learned something else - namely, that their own actions suggest they are in fact misrepresenting their beliefs about the real magnitude of the threat.
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