We regard global warming as a cooperative game and examine the conditions under which the core of the global warming game is nonempty. It is carried out within the framework introduced in the previous chapters, where the economic welfare of each country may be expressed by the utility, which depends on the vector of goods consumed in that country and the total amount of carbon dioxide emitted by all the countries involved.

The players of the cooperative game of global warming are countries in the world. Each country may choose as a strategy a combination of the vector of goods to be consumed by that country and the amount of carbon dioxide to be emitted in that country from productive and other processes, and the payoff for each country is simply its utility.

A coalition for the global warming game is any group of countries, and the value of each coalition is the maximum of the sum of the utilities of the countries in the coalition on the assumption that those countries not belonging to the coalition form their own coalition and try to maximize the sum of their utilities.

The core of the global warming game consists of those allotments of the value of the game among individual countries that no coalition can block. The conditions under which the core of the global warming game with transferable utility is nonempty are examined. Then, an alternative definition of the value of coalition for the global warming game with transferable utility is introduced, and we show that the core of the global warming game under the alternative definition is always nonempty.