EU Energy Policy Blog

Climate negotiators recognize that, at root, the climate problem is a free-rider problem. Each country would prefer that the others do more. But the free-rider problem is not immutable, and that has been overlooked. The design of agreements can exacerbate it or alleviate it. Instead, the implicit assumption has been that it must be overcome by moral suasion and scientific argument, both of which are weak instruments when dealing with national self-interest. Because of this oversight, both Kyoto and Copenhagen negotiations followed a global cap-and-trade framework, which has proven ineffective. We find that adopting cap-and-trade rules polarizes the free-rider incentive and discourages cooperation.

Green House Gases (GHG, hereafter) emissions cause an externality—an effect that is not priced by private markets—and consequently GHG abatement is a global public good. Because each country is only a small part of the global economy, the resulting free-rider incentives dominant national strategies. Little abatement will be provided without an agreement on international cooperation.

Although this view is widely accepted, the problem of how to design an agreement to overcome free-rider problems has been largely ignored by negotiators, environmentalists and climate scientists. This is surprising in light of the cooperative failures observed starting with the Kyoto summit. Despite clear warnings from a number of prominent economists (for example, Schelling 2002; Barrett 2003; Stiglitz 2006; Nordhaus 2008, Barrett and Toman 2010), there appears to be little recognition that there is a science of cooperation and that changing the rules of a game can make the play of the game more—or less—cooperative. Without such understanding, the negotiating strategy of the major players has been to induce cooperation by invoking scientifically determined numbers with vehement and often moralistic insistence.

However, the behavior of Copenhagen negotiators was highly strategic in nature. Ignoring strategic interactions, negotiators have pursued a set of rules that degrade the limited tendencies toward cooperation found in the public-goods game. This is remarkable because the public-goods game is known for producing even less cooperative results than the two prisoners’-dilemma game.

In a recent paper we make three fundamental points. The design of the climate policy game plays a key role in determining whether countries cooperate. The cap-and-trade game induces the types of uncooperative strategies that have become ubiquitous. Some modifications of the public-goods game exhibit far more cooperative equilibrium behavior and hold much greater promise for an effective climate agreement.

To make these three fundament points, four games are investigated, starting with the standard public-goods game. In each case, countries choose the value of a single strategic variable, and a unique Nash equilibrium is discovered. The four games are:

In the first three games countries are identical except for size; in the Green-Fund game, countries also differ in their monetary valuation of climate benefits.

The public-goods game

In this game countries abate, without any international agreement, to the point where their marginal cost equals their marginal benefit. Since larger countries capture a higher proportion of the benefits of abatement, they abate to a higher level of marginal cost, also known as their domestic carbon price, Pj.

Since this price does not take into account the benefits to other countries of their abatement, this price falls below the optimal price: since the benefit functions are all assumed to be linear, marginal benefit does not change with abatement and the optimal price, which is the same everywhere, is Po = ∑Pj, where the sum is taken over all N countries; by contrast, the suboptimal price resulting from the public-goods games is Po/N, where N is the number of countries.

As a point of reference, suppose countries are identical except for size, and the cost functions are quadratic and the benefit functions linear. Then, in the Nash equilibrium, a country that is responsible for 20 percent of the emissions under business as usual will abate by one fifth the optimal amount, and smaller countries will abate proportionally less. If Europe is counted as one country total abatement under these standard but idealized assumptions, for the world’s Nash equilibrium, would be about 12 percent of optimal.

The outcome of the public-goods game is inefficient for two reasons. First, much too little abatement takes place, and second, the abatement that is undertaken is not undertaken efficiently. Abatement proceeds in each country until marginal costs equal marginal benefits. Since larger countries have higher marginal benefits they sustain higher marginal costs, which means they could achieve the same abatement more cheaply if they could pay small countries to abate.

Cap and trade game

Global cap and trade implements a global market for abatement that allows high-marginal-cost countries to purchase abatement from low-marginal-cost countries, thereby making efficient the abatement that is undertaken.

Note that the global cap-and-trade game is strategically dissimilar to the national cap-and-trade game because the global game lacks a government capable of allocating carbon allowances or permits. The global game focuses on national strategies for choosing targets, a country’s move consists of choosing a target, Tj, instead of a level of domestic abatement, Aj. A target can be met with either domestic abatement or with abatement purchased in the global cap-and-trade market at the global market-clearing price of abatement (price of carbon), P.

With identical countries, the equilibrium price is the same as the domestic carbon prices in the public-goods game (i.e., Po/N). But the outcome can easily be worse than the public-goods outcome as can be seen by considering a world with two countries one of which is 99 times larger than the other. The larger country, because it internalizes almost all the climate benefits will set its carbon price near Po, and this will cover almost all emissions, while the tiny country will set its price near zero. In the cap-and-trade game, both will face a world carbon market with a price of Po/2. This is much worse in 99 percent of the world and better in only one percent.

The key point is that the cap-and-trade framework exacerbates and monetizes polarization. Large and rich countries place a higher value on abatement, which means a higher price on carbon. Poor countries place a lower value on abatement. But cap and trade creates a global carbon market that presents all countries with the same carbon price. Rich countries see it as low and target more abatement under cap-and-trade. But poor countries see it as high and target less abatement. In fact the global market makes it rational and profitable for most of them to set an abatement target of less than zero and sell all “abatement” above that target level to the rich countries. Note that in practice that cap and trade game is rejected. The players simple choose not to play such a game: To rich countries, the equilibrium seems unfair. They reject the perfectly rational response of poor countries to the proposed international framework, and so the negotiations deadlock. The problem stems from the polarization it causes.

The simplest example of polarization has two countries, with one twice as large as the other. The two net-benefit equations are:
NB1 = 2A – (A1.A1) – P(T1-A1)
NB2 = A – 2 (A2.A2)- P(T2-A2)

The second country is smaller, with half the benefit and twice the cost per unit abatement. We know mathematically that the price will be the average marginal benefit or P* = 1.5. Setting marginal cost equal to price gives A1 = 0.75, and A2 = 0.375. Using some maths the target values can be calculated as shown in Table 2.

The example illustrates several points. First, changing the game from a simple public-goods game to a cap-and-trade game can reduce the total abatement of the Nash equilibrium. Second it can reduce total net benefit, even while making the abatement that does take place efficient. Third, it can increase polarization—that is, it can cause high abatement countries to target an even greater abatement level and low-abatement countries to target even less abatement. Fourth, the change of rules can be good for low-abatement countries and bad for high abatement countries.

The price-target game

The price-target game takes place in the same idealized world as the cap-and-trade game but depolarizes the negotiations and results in an optimal global carbon price instead of one N times too low.

In the basic price-target game, there is one global price target, PT, and all countries are required to price (not tax) carbon at that level. Such a system has been proposed by Cooper (2008) and by Cramton and Stoft (2009). In the latter proposal, countries that under-price can buy credits from countries that over-price in any given year, just as countries that under-achieve a quantity target can buy credits from those that over-achieve.

Because there is only one global target instead of many national targets, that target must be decided through a collective process, and that process is the price-target game. For simplicity we assume that each country names its preferred global price target, Pj, and that the lowest of all named targets is selected as the global price target. Selecting the lowest price means that no country is asked to sign a stronger treaty—with a higher price target—than it named. In practice, some countries, such as oil exporting countries, may name an unacceptably low price.

In the price-target game with counties that differ only in size, every country will favor the socially optimal value of the global price target.

The problem is that countries differ in ways other than size. This is also a problem for any similar scheme based on a single global quantity target. And it is also a problem for schemes based on national targets. But the advantage of a global price target is that the simplest possible formula for national targets already corrects for country size and emission levels. A country with twice the emissions must collect twice the carbon revenue. It also handles growth appropriately. If India were suddenly to become as rich as the United States, any effective cap would create impossible problems, but a global price target would create none.

Still, the price-target game just analyzed would fail because poor countries would vote for a low global target. One solution to this problem is to link Green-Fund payments to the level of the global price target. In this way poor countries can be given an incentive to choose a reasonably high target. The way such a green fund could be designed is described in detail in our paper.

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Our diagnosis provides a ray of hope. The Copenhagen summit failed, not because cooperation is beyond reach, but because the proposed agreement was reaching in the wrong direction. The agreement’s structure was adopted without any consideration for its impact on cooperation. Instead efficiency and certainty were the goals.

To enhance cooperation, the agreement should use a single global target instead of reproducing the free-rider problem with national targets. The target should be a global carbon price, because there is an agreed best relationship between national prices and the global target—they should be equal. There is no hint of such an agreed relationship for a global quantity target. The agreement should include equity transfers to compensate low-emitting poor countries for meeting the global target. These transfers should reinforce cooperation with the price target rather than make free-riding more profitable.

Such a design, in contrast to the cap-and-trade design, mitigates free-rider incentives and creates a game with an equilibrium that is highly cooperative. International cooperation is the only way to solve a global public goods problem, and the only way to achieve cooperation is to design for cooperation.

Peter Cramton and Steven Stoft Peter Cramton is professor of economics at the University of Maryland. Steven Stoft is director of the Global Energy Policy Center

This entry was posted on Saturday, August 21st, 2010 at 1:01 pm and is filed under Climate Change. You can follow any responses to this entry through the RSS 2.0 feed. You can leave a response, or trackback from your own site.