If the goal is to understand which international regime is likely to emerge to control GHG emissions, game theory is certainly the best tool. Indeed, game theory has been used extensively to analyze the possibility of coalition formation in the presence of free riding (i.e., when parties have to agree on the provision of a public good). Early contributions (see Hardin and Baden, 1977) characterized the environmental game among countries as a prisoners’ dilemma, inevitably leading to the so-called “tragedy” of the common property goods. However, in the real world, at the same time, many international environmental agreements on the commons were signed, often involving subgroups of negotiating countries and sometimes involving economic and technological transfers and other links to other policies (trade, technological co-operation, etc.). It was therefore necessary to develop new models to help understand the logic of coalition formation in the presence of spillovers, and the possibility to increase welfare by means of appropriate mechanisms and strategies. These new models were developed in the 1990s within a non-co-operative game-theory framework, and provide interesting indications on the likely outcomes of climate negotiations.

Consider first the case in which countries negotiate on a single worldwide agreement. Most papers in the game-theory literature on coalition formation applied to environmental agreements (Hoel, 1991, 1992; Carraro and Siniscalco, 1992, 1993; Barrett, 1994, 1997b; Heal, 1994; Parson and Zeckhauser, 1995) propose the following conclusions:

• the presence of asymmetries⁷ across countries and the incentive to free-ride makes the existence of global self-enforcing agreements, that is agreements which are profitable to all signatories and stable, quite unlikely (Carraro and Siniscalco, 1993);
  
• when self-enforcing international environmental agreements exist, they are signed by a limited number of countries (Hoel, 1991, 1994; Carraro and Siniscalco, 1992; Barrett, 1994); and
  
• when the number of signatories is large, the difference between the co-operative behaviour adopted by the coalition and the non-co-operative one is very small (Barrett, 1997b; Hammitt and Adams, 1996).

The results are robust with respect to different specifications of countries’ welfare function, and with respect to the burden-sharing rule⁸ used in the asymmetric case (Barrett, 1997a; Botteon and Carraro, 1997a). They suggest that the attempt to negotiate effective emission reductions is unlikely to lead to a coalition formed by all or by almost all countries, unless more complex policy strategies, in which environmental policy interacts with other policy measures, are adopted⁹. This is why in the game-theoretic environmental economics literature two main sets of instruments are proposed to expand environmental coalitions, that is to increase the number of signatories of an environmental agreement. These instruments are “economic and technological transfers” and “issue linkage”. The potential of these instruments is analyzed in Section 10.2.5, which deals with partial agreements and ways to broaden them.

Consider the case in which countries are free to sign the agreement proposed by a group of countries or to propose themselves a different agreement to the same or to other countries (Carraro, 1998). This may lead to the formation of multiple climate agreements, as happens with trade blocs (Bloch, 1997; Yi, 1997; Carraro and Moriconi, 1998). The multiplicity of coalitions may allow region-specific agreements in which the characteristics of countries in the region are better reflected by the contents of the agreement. Even in this case, game theory provides a clear analysis of the outcome of climate negotiations. Despite the large number of equilibrium concepts¹⁰, some conclusions seem to be quite robust:

• the equilibrium coalition structure is not formed by a single coalition, but usually by many coalitions;
  
• the grand coalition, in which all countries sign the same environmental agreement, is unlikely to be in equilibrium; and
  
• coalitions of different sizes may emerge at the equilibrium (even when countries are symmetric).

The specific results on the size of the coalitions depend on the model structure and, in particular, on the slope of countries’ reaction functions (i.e., on the presence of carbon leakage). If there is no or little leakage and countries are symmetric, then the Nash equilibrium of the multicoalition game is characterized by many small coalitions, each one satisfying the properties of internal and external stability (this result is shown in Carraro and Moriconi, 1998).

The remaining question is therefore a policy one. Is a country’s welfare larger when one or when several coalitions form? And what happens with environmental effectiveness? The answer is still uncertain, both because theory provides examples in which a single agreement is preferred, at least from an environmental viewpoint, to many small regional agreements (and vice versa), and because empirical studies have not yet convincingly addressed this issue. Moreover, the conclusion crucially depends on the choice of the equilibrium concept and on the size of leakage.

The consequence of the results discussed above is that the structure of the international environmental agreements is a crucial dimension of the negotiating process. If all countries negotiate on a single agreement, the incentives to sign are lower than those that characterize a multiple-agreement negotiating process. But at the equilibrium, the environmental benefit (quality) may be higher.

Can more precise conclusions be made on the likely coalition(s) that can emerge at the equilibrium? Can existing studies be used, albeit not in their design, to address the above issues, and to increase our understanding of the implications of different policy strategies? In the next section, the aim is to provide, at least partially, a synthesis, by exploring the outcomes of the combinations of different coalition structures (international regimes) and of different policy options (with focus on different degrees of adoption of emissions trading and other Kyoto mechanisms). Table 10.2 summarizes the main combinations for which impact is explored. The papers indicated in each cell are examples and do not cover the literature in total.

Table 10.2: Coalition structures and policy options
	Policy options
		Domestic measures only	Co-ordinated carbon tax	Flexibility mechanisms with ceilings	Free flexibility mechanisms	Flexibility mechanisms with banking	Flexibility mechanisms with R&D	Flexibility mechanisms with monopoly power
C o a l i t i o n s t r u c t u r e s	No participation	IPCC (1995)
	Unilateral participation	Jorgensen et al. (1993) Barrett (1992)
	EU only	Carraro and Siniscalco (1992)	Bosello and Carraro (1999) Barker (1999)
	OECD only	Burniaux et al. (1992)	Capros (1998)		Harrison and Rutherford (1999) Holtsmark (1998) Capros (1998)
	Annex-1 countries	McKibbin et al. (1998)	Mensbrugghe (1998) Buonnano	Ellerman et al. (1998) Holtsmark (1998) et al. (1999) Manne and Richels (1998)	Ellerman et al.(1998) Grubb and Vrolijk (1998) Westkog (1999) McKibbin et al. (1998) Manne and Richels (1999a, 1999b) Mensbrugghe (1998) Nordhaus and Boyer (1999) Shackleton (1998)	Bosello and Roson (1999) (1999)	Nordhaus (1997) Buonnano et al.	Burniaux (1998) Ellerman et al. (1998)
	Double umbrella				McKibbin et al. (1998) Shackleton (1998)			Ellerman et al.(1998)
	All countries	Nordhaus and Yang (1996)		Ellerman et al. (1998) Buonnano et al. (1999)	Bohm (1999) Ellerman et al. (1998) Manne and Richels (1998; 1999a, 1999b) Nordhaus and Boyer (1999) Shackleton (1998)	Bosello and Roson (1998) Westkog (1999)	Nordhaus (1997) Buonnano et al. (1999)

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