The efficacy of international environmental agreements when adaptation matters: Nash-Cournot vs Stackelberg leadership

We analyze the paradox of cooperation, as established by Barrett (1994), and later reiterated by many others, in a more general framework. That is, we show that stable coalitions are either small or if they are large, the potential gains from cooperation are small. First, we argue that the extension to a mitigation-adaptation game is a generalization of Barrett's pure mitigation game. Second, we consider for this extension not only the Nash-Cournot scenario, as in Bayramoglu et al. (2018), but also the Stackelberg scenario. Third, we show generally that if mitigation levels in different countries are strategic substitutes, stable coalitions are larger in the Stackelberg than in the Nash-Cournot scenario. Fourth, this is reversed if mitigation levels are strategic complements, which is possible if the strategic interaction between mitigation and adaptation is sufficiently strong. Fifth, for all possible combination of assumptions, we demonstrate that the paradox of cooperation is robust, except if mitigation and adaptation were strategic complements, which we argue is an assumption not supported by empirical evidence.