We propose a two-stage noncooperative game theoretic model to describe the coalition formation of countries which decide to jointly invest in research and developments projects to mitigate the damages induced by climate changes.The first-stage game is a finite game where each country has only two strategies: sign or not an international agreement with other countries, while the second-stage game is a generalized Nash equilibrium problem, where each country aims to find the optimal levels of pollutant emission and effort in research and development projects.The variational equilibrium of the second-stage game is reformulated as an equivalent variational inequality with a reduced number of variables and the monotonicity of the corresponding operator is investigated.Finally, the impact of the coalition on the reduction of the environmental damage is numerically investigated.

In mathematical economics, the used functions are, in general, considered to be quasiconcave. Moreover, they are, in many cases, separable of nature. It is known that a local maximum of a quasiconcave function is not, in general, a global maximum. In this paper we will show that this property is true when the quasiconcave function is furthermore separable. Sufficient optimality conditions for a separable quasiconcave programming will be studied in both differentiable and nondifferentiable cases. Thanks to separability condition, quasiconcave functions have nice properties in optimization problems.