In game theory, there are a number of solution concepts, such as the Nash equilibrium, and the subgame perfect equilibrium, that help us to understand strategic behaviour. What role do these concepts have when looking at how to facilitate international cooperation on climate change?

When using a model to help understand a problem, it is important to be aware of the limitations of the model. Many applications of game theory require that decision makers are rational. That is, they have clear preferences, form expectations about unknowns, and make decisions that are consistent with these preferences and expectations. These assumptions may not be consistent with experimental psychology. Elinor Ostrom has considered the the role that human behaviour considerations relate to cooperation problems, and applied this to climate change. She found that a `surprisingly large number of individuals facing collective action problems do cooperate’. She also found that cooperation is more likely if people gain reputations for being trustworthy reciprocators; reliable information is available about costs and benefits of action; individuals have a long-term time horizon; and are not in a highly competitive environment.

So the application of game-theoretic solutions concepts should be taken with a pinch of salt. For example, there is Nash equilibrium that arises from a basic model where countries make a continuous choice about how much to reduce their emissions. As one would expect, this involves small amounts of emission reductions (that reflect the damage that a country will do to itself from its greenhouse gas emissions), but much less than would occur in a fully cooperative situation. But what if one country were to go first, and reduce its emissions by more than the Nash equilibrium choice? If the marginal damage from a tonne of emissions increase with respect to total emissions, then the Nash equilibrium response of other countries would be for them to reduce their emissions by less than they otherwise would (see e.g. Finus, 2001, Chapter 9). But behavioural considerations suggest that other countries would be likely to reciprocate, and reduce emissions by more than they otherwise would.

Eric Maskin, in a paper published in 2009, argues that “the principal theoretical and practical drawbacks of Nash equilibrium as a solution concept are far less troublesome in problems of mechanism design than in most other applications of game theory”. Mechanism design is focused on how to design games whose solution concepts lead to cooperative outcomes. One reason why game theoretic solution concepts are less troublesome in mechanism design, is that the rules of the game are clear to players, and to analysts. Another reason given by Maskin is that one can design games that do not have multiple equilibria or have equilibria that are stronger than the Nash equilibrium.

If humans are more cooperative than assumed in our models, the models could work as a ‘lower benchmark’, and at least as much cooperation as predicted by the models could be observed. When mechanisms have game theoretic solution concepts that could lead to more cooperation on climate change, such mechanisms ought to be given serious consideration.