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.

INTRODUCTION

Among the many institutional arrangements and policy measures proposed to control the emission of carbon dioxide and other greenhouse gases and effectively abate the processes of global warming, the institution of international markets for tradable emission permits is probably the one that has most attracted the attention of the economist, as typically argued by Tietenberg (1985, 1992), Bertram (1992), and Barrett et al.(1992), Barrett and Taylor (1995) and others.

Bertram, Stephens, and Wallace (1989) argued that a worldwide system of tradable emission permits could be an effective way of advancing the interests of developing countries in harmony with the global community's interest in protecting the atmosphere. This egalitarian view was expounded and reinforced further by Grubb (1989, 1990), Hoel (1991), Tietenberg (1992), Rose and Stevens (1993), and others.

The main advantages of markets for tradable emission permits are their ability to achieve environmental aims with a minimal bureaucratic apparatus. One of the central problems with most such schemes is the allocation of the initial allotments among the countries involved. The “license to pollute” tends to be granted to those countries that are already major polluters with the result that the rents associated with a growing scarcity of pollution entitlements fall into the hands of these countries. However, as argued by Grubb (1989), of all the instruments examined, the system of tradable emission permits is the most promising. It is flexible in operation and effectively and efficiently abates global warming. The costs of alternative permit allocations have been tentatively calculated by Larsen and Shah (1992, 1994), and others.

The unremitting processes of industrialization and urbanization in the last several decades have disrupted and destabilized the global environment to a degree unprecedented in the history of mankind. Not only have global environmental issues such as global warming, acid rain, the loss of biodiversity, pollution of the oceans, and desertification become real threats to the stability of the environmental equilibrium, but they also tend to impair economic development in many developing countries and to lower the welfare of people in all future generations decisively.

The processes by which global environmental issues have arisen are interwoven with natural, historical, cultural, social, and political factors, but the predominant forces behind them are economic. Any analysis of environmental issues must involve a careful examination of the economic motives behind the activities responsible for the disruption of the natural environment, and any institutional arrangements or policy measures intended to restore environmental equilibrium must take into account the resulting economic impact on human activities.

Global environmental issues have three aspects that have not been satisfactorily addressed by orthodox economic theory until quite recently.

First, all phenomena involved with global environmental issues exhibit externalities of one kind or another. That is, as is typical with the case of global warming, what each individual decides to do is affected by the behavior of other members of the society, and vice versa. The questions of externalities certainly are of great interest to the economist as exemplified by Cecil Pigou's classic work The Economics of Welfare (Pigou 1925) and Paul Samuelson's seminal paper, “The Pure Theory of Public Expenditures” (Samuelson 1954).