Post Kyoto

26.3.1 Post-Kyoto and coalition formation theory

Negotiation over the post-Kyoto (or post-2012) scheme is occurring currently, as the Bali roadmap set 2009 as the deadline for a conclusion to be reached and carried out through several levels including an AWG (ad hoc working group) of the CMP (conference of parties serving as meeting of parties) of KP and the COP (conference of parties) of UNFCCC, and G7 (or G8). Several proposals have been made by several parties, ranging from an expansion of the current Kyoto scheme to reinstituting a new scheme that completely replaces the Kyoto schemes, and also there are several intermediate proposals such as sector by sector methods and the addition of regional schemes to current frameworks. One of the biggest disagreements, between the EU and USA, stems from the differing priority regarding adaptation vs mitigation. Yet another big issue is how to make developing countries become involved with the stricter international arrangement.

The extent of the size of cooperating nations is a classical issue studied by the branch of game theory called coalition formation, and there is a vast literature even for international environmental agreements alone (for a general overview, see Barrett (2005), for example, and also see the references in Rubio and Ulph (2007), which consider this problem from a dynamic perspective). One conclusion frequently reached is that there is not much hope of having many countries join a cooperative ring. Several devices to enlarge the extent of cooperation have been examined and proposed, but the sovereignty and limited commitment ability of nations severely restricts such a possibility.

As an illustration, let us go back to the model described earlier in which we show a simple example of a two-stage analysis (initiated by Barrett (1994) and Carraro and Siniscalco (1993). Now, we separate out the term representing the benefit from the world emission reduction, V (X), where X = Z xl is now a variable determined by each nation. Accordingly, the rest of the net benefit is written as Ki (xi) , so that V i (X) - Ki (xi) = B i (x i) . In addition, we adopt a specific functional form: linear public benefit and quadratic costs and assume that each nation is symmetric to each other. That is, we assume that V (X) = X - X and K (x i) = (xi - x t )2 / 2 , where X = X X;, and Xi is the natural level of emission, which is the emission level if no benefit from the total emission reduction is reflected, i.e., K'( X) = 0. It would be more convenient to express things in terms of emission reduction y t = xi - xi and Y = X y . Then, the benefit from the total reduction is Y and the individual abatement cost for i is k (y i) = y ¡2 / 2 . Given an emission reduction of other nations, the best emission reduction level is given by 1 = ki (y i) or y i = 1, which is the dominant strategy.

Without coordination, each nation reduces its own emission by 1 and the total reduction is N. The situation is inefficient because, if each nation reduces by one more unit, then the total benefit increases by N2 while the total cost of doing so would be N2 / 2, meaning that such an attempt is beneficial for every nation.

Cooperative game theory considers the possibility of making binding agreements among a subset of players called a coalition. If s players agree to form a coalition S and decide on the best actions for them to take, then, from the maximization of XfeS(Y-k(y;)) = sXy, -XfeSX(yZ/2) in terms of (yi)feS, one obtains yi = s . Thus, their target increases by forming a coalition or they agree to internalize their parts of the externalities. Obviously, forming a grand coalition including all members and reducing emissions by N each would be the optimal solution yielding a net benefit of N2 / 2 each.

Coalition formation theory, however, predicts that the chance of forming a grand coalition is not that great in many instances. In the above example, suppose that N equals 4. If one nation leaves the coalition and changes its reduction level to just one unit, while the other three nations remain in the coalition, the departing nation obtains a net benefit of 9:5 > 8, where 8 is the net benefit level when it joined the grand coalition. Thus, there is an incentive to leave the grand coalition. At the other extreme, when no genuine coalition (consisting of at least two nations) exists, each nation's net benefit is 4-0.5 = 3.5, whereas, by joining with one nation to form a coalition of size 2, a nation's net benefit becomes 4, and hence there is an incentive to form a coalition. Supposing that there is at most one coalition, one finds that coalitions of 2 and 3 are "stable" in the sense that no insider wishes to leave and, at the same time, no outsider wishes to join (except for the case that they are indifferent between the two options), and this fact holds regardless of N, in this example (cf. Fig. 26.2). Thus, it indicates that a relatively small coalition forms, and many remain as free-riders.

The above observation seems to parallel the process leading to the current configuration of the KP, in that only a limited number of nations are accepting the emission quota. Remedies for this situation to increase the size of the coalition have been investigated, such as linking environmental issues with other policy issues (Russia was said to be induced to ratify the KP in return for the EU's support for Russia joining the WTO), providing a side payment as an inducement to recruit new participants, and creating other commitment devices such as a minimum participation requirement (55% requirement in terms of emission levels among Annex B nations in the case of the KP). (For references, see the literature cited in Carraro, Eyckmans, and Finus (2006), for example.)

Among these options, the use of transfers (interpreted broadly to include changes of rules in favor of new participants, etc.) seems to be of wider use, especially for the negotiation within the framework of the CMP of the KP or the COP of UNFCCC. Funding and technology transfer are discussed at the meetings in parallel to discussions on the scheme after 2012 (although developing countries constantly claim that those discussions should not be combined with the involvement of those countries in the quota scheme).

The above example is too simple in many respects. One important element is that of asymmetry among nations, which affects the composition of members of the coalition to form and the identification of necessary inducement to expand a coalition becomes more player specific.

Another important element is the fact that both climate problems and international cooperation together with its negotiation are dynamic issues. In fact, formulating the problem dynamically expands the possibility of cooperation substantially. The basic logic is that the possibility of future failure of cooperation would prevent countries from not cooperating. Such "sanction" is within the ordinary policy choice rather than a new action created to force other nations to obey an international agreement or to participate in a treaty, which would have grave consequences in the international relations.

Following Barrett (1999), researchers focused on equilibria that satisfy dynamic rationality conditions called subgame perfectness and renegotiation proofness. The former condition yields many outcomes whereas the latter condition can reduce the number of solutions. Renegotiation proofness is appropriate in this context because, in the international negotiation, it would be difficult to implement inefficient sanctions for a long time and also any agreement reached has a time limit and so renegotiation actually takes place similar to the KP. However, requiring this condition in terms of efficiency in any event so that there is no room to renegotiate is too strong and a weaker criterion is utilized. For more details, refer to Weikard and Dellink (2008) where finitely many periods with a prefixed allocation for each potential coalition is examined, Asheim et al. (2006) where it is shown that multiple coalitions can attain better allocations, and also Rubio and Ulph (2007) and De Zeeuw (2008) which examine the effects of stock pollutants utilizing dynamic programming methods, and references therein.

26.3.2 Negotiation

As shown in the examples of analyses in the papers listed above, game theory can serve as a device to simulate the negotiation process as well as to evaluate options to be proposed in the course of negotiation. As mentioned above, several proposals have been made for a scheme after 2012, some of which were proposals proposed before the KP was adopted or before the KP entered into force. These range from a simple expansion of the Kyoto regime with tighter targets to diverse alternative schemes including fragmentizing the Kyoto approach by sectors or regions, voluntary commitment schemes, world carbon taxes, establishing global technological standards, and setting emission intensity targets. Many agree that the key factors are uncertainty and enhancement of the chance of technological breakthrough. Beyond that, there seems to remain a big gap in the ranking of policy alternatives. This discrepancy in subjective beliefs, together with the Kyoto mechanism being in a position of quasi status quo, seems to make agreement among broader participants very difficult.

To illustrate the issue, take the simple case of negotiation between two countries. They can agree on some scheme so that both become better off, whereas, if they fail to reach agreement, they are left with the "status quo." This setup is known as a two-person pure bargaining problem. If the two people disagree on the best option, possibly because of future probabilities of events and future costs and benefits, then agreement would become harder. (In general, a discrepancy in subjective probability helps agreement when contingent payments based on future events, probabilities of which the parties disagree on, is possible.) However, in the post-2012 negotiation, it seems that adoption of one scheme (e.g., starting mitigation now) may change the likelihood of one event (technological breakthrough) occurring. Under common expectations (and complete information) and when the number of potential cooperators is known and fixed, bargaining theory provides the solution as a predictor or a focal point for negotiation. Under the possibility of each player joining or leaving a coalition, the analysis is slightly more complicated, but the resulting outcome often corresponds to solutions in cooperative game theory.

One focal solution concept is the Nash bargaining solution. To illustrate these points, consider the model discussed earlier with the membership of signatory nations fixed and a world quota A as given but its breakdown yet to be determined. Each nation i expects the given allocation of assignments a = (ai )N=1, with an associated competitive allocation x(a) = ("xi (a))N=1, where the equilibrium is as above and denoted by the induced level of net benefit as Bi (a). Furthermore, assume that there is a benefit level B0 corresponding to the case where each nation chooses its environment policy without an assigned quota (for this, we have to assume that each government is aware of the public good aspect of its own emission and chooses its policy from that point of view). The Nash bargaining solution approach assumes that a is chosen so that nN=1(Bi (a) - B°)is maximized provided that each term inside the multiplication operator is positive. This is a typical cooperative game solution, although there are many other solutions proposed.

Many modifications are necessary before applying this type of solution to the ongoing negotiation. For instance, one may question the validity of taking a laissez faire allocation of net benefits as the reference point of the solution and the equal weights given to each nation's net benefit, which means that bargaining power is equal. Another more serious need to modify the theory stems from the recognition of the moral or emotional factor. In particular, the historical process that led to today's position of each nation is not accounted for. In the ongoing negotiation, some claim that those who were eager to advance environmental regulation much earlier than other nations deserve consideration. Furthermore, the spirit in the UNFCCC is that some of the nations that emitted much more in the past should be given different obligations from those who need more emissions to catch up. These claims are often made in the political negotiation, and several proposals account for some of those data (cf. Brazilian proposal of COP8 (FCCC/SBSTA/2002/INF.14)). This would be an interesting topic to study from the viewpoints of both game theory and political science. (See references in Bohlinger and Helm (2008), for example.)

When one considers a process prior to the above negotiation so that the world community first agrees on the total emission quota A in a manner similar to the negotiation over individual quotas, with an expectation that the subsequent negotiation would be resolved as predicted by the Nash bargaining solution or any cooperative game solution, then there would be a trap that the overall choice of the quota a may turn out to be inefficient. The reason is that each nation considers only its share in the final outcome and would not take into account the entire gain for the world community. This sort of negotiation procedure is very common but involves a danger known as the problem posed by incomplete contracts, as pointed out by Tadenuma (2004) particularly for the emission quota problem.

One could go one step further and attempt to capture the fact that a nation is not a single objective maximizer. We have seen several policy changes following election results; from Democrat to Republican in 2000 leading to US secession from the KP, the Canadian election in 2005 resulting in the new government declaring intentional noncompliance, and the Australian election in 2007 was followed by an immediate ratification of the KP at the last minute.

This phenomenon cannot be accounted for even if one models the governmental policy position as a consequence of the Downsian voting game, which essentially points to the median voter theorem so that policy change becomes continuous. (Applications of the Downsian model are common in the discipline. See Roelfsema (2007), for example.) Recent developments in political economics introduced the probabilistic voting model, which has some chance of accommodating such discontinuous randomness in voters' preferences. Parties face uncertainty in voter's preference along with some policy-ideology dimension. Assume that the parties cannot choose their ideological traits themselves, and so they mostly compete with each other along a more deterministic policy dimension. After they chose their policy positions, uncertainty over the ideological dimension of voters' preferences is resolved. (It is assumed that the rate of substitution of ideology with the other policy is common across voters.) Then, the power is given to the party whose ideological position is closer to the realized position. One can create policy change with respect to the KP listed above or alike in this sort of model. Obviously, one needs more information on how the preference over environmental policy is affected, but this seems to be one plausible research agenda.

26.3.3 Role of CDM

In the same way that the agreement on the KP in 1997 was a surprise to some observers, we cannot predict the consequence of current negotiations with much confidence. At least because the time left is short and many parties have vested interests in the current scheme, a modification of the Kyoto scheme (with possibly a smaller number of participants) or a return to no scheme at all may have some chance. In this situation, the role of the CDM seems to be of growing importance. Even among those who propose different schemes to the Kyoto scheme, some seem to agree to retaining the CDM as a device to keep developing countries in the framework. In this regard, CDM reform continues to be an important agenda.

In view of bargaining theory, the CDM could be part of the "status quo" if the Kyoto scheme is supposed to last. By contrast, if the Kyoto scheme is discontinued, the value of CDM credits may depreciate significantly. Hence, the status quo payoff for non-Annex B countries would decrease too. In other words, non-Annex B countries have a stake in the current scheme and so, to gain their support, something at least as attractive as their current expected payoff must be assured. At the same time, they have something to lose if the negotiation of the Kyoto scheme breaks down completely.

In addition, the detailed decision of the COP (UNFCCC) and CMP (KP) on the coverage of the CDM project matters. In fact, there is a chance that the type of "project" eligible as a CDM project may be widened by the CMP. Programmable CDM is one such example. Notable are policy CDMs that are not admitted currently, which would widen the category of eligible projects substantially and hence raise the future value of countries retaining non-Annex B status while reducing the value of CDM credits (compared with the case if a policy CDM were not admitted, other things being equal) because of an increase in the supply of credits.

This suggests that, in the end, a CDM treating emission reduction by one developing country as a whole can be constructed. If this is the case, non-Annex B countries are effectively given a one-sided incentive to cut their emissions relative to the "business as usual" (BAU) level. There is no penalty for excessive emissions but, by reducing emissions, they obtain benefit in the form of credits, provided that there is a market that values the credits. This seems to be a politically viable option to get non-Annex B countries involved and, indeed, guarantees participation incentives, on the one hand. On the other hand, making their current expected growth paths equal to its future quota on emissions would increases the prospective payoff for non-Annex B countries greatly, which would make their incentives to change their status very low. The restraint posed by such a CDM with respect to BAU could be too lenient and potential emissions could be so large that mitigation cannot be achieved. Moreover, administration of the CDM becomes too much of a political problem and exceeds the capacity of the CDM-EB.

The San Paulo proposal (a report prepared under the Basic project (http://www.basicproject.net/data/.nal/Paper17Sao%¥20Paulo%20Agreement%20 on%20Future%20International%20Climate%85.pdf) contains a mechanism to get non-Annex B countries to choose to enjoy such nationwide CDMs while, at the same time, making them declare the amount of total credits they produce under this proposal so that, if the amount of credits they produce exceeds that level, they must change their status into Annex B. This is one example of an innovative scheme that accounts for incentives well.

For the evaluation of the schemes involving CDM in this post-Kyoto context, one could repeat the arguments made for smaller CDM projects, including baseline methods. Furthermore, the impact of the CDM defined for one nation as a whole may not be small compared with the size of the market, and thus a broader scope of analysis may be required. (One relevant point would be that raised in Imai and Akita (2003) that a juxtaposition of the cap on the one hand and a CDM with an ex post baseline scheme on the other hand may skew the distribution of risk bearing with respect to environmental risk in the world community.)

Another possibility, as mentioned above, is a replacement of the Kyoto-type scheme with another scheme without a quota on emissions (including the case of ending up with no scheme at all), and so the value of CDM projects falls substantially. If no alternative compensation scheme for CDMs is instituted at the same time, this would imply scraping constructed machineries such as DOEs

(designated operational entities) and DNAs (designated national authorities) and possibly damage the adaptation fund. Thus, this possibility works as a threat to non-Annex B countries but there seems to be enormous costs and vested interests on the rest of the world as well.

All these suggest the importance of CDMs in this negotiation and it seems that an improvement in the organization to handle CDMs is quite important. At the same time, it should be kept in mind that any decision on the CDM would have some effect on the current negotiation over the post-2012 scheme, and game theoretical thinking can help evaluate such an effect.

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