Working Paper – Climate Change and Game Theory: a Mathematical Survey

I have recently written a working paper, available from the Environmental Economics Research Hub website.

Wood, P. J., 2010, ‘Climate Change and Game Theory: a Mathematical Survey‘, Environmental Economics Research Hub Research Report No.62.

The abstract is as follows:

This survey paper examines the problem of achieving global cooperation to reduce greenhouse gas emissions. Contributions to this problem are reviewed from non-cooperative game theory, cooperative game theory, and implementation theory.

Solutions to games where players have a continuous choice about how much to pollute, games where players make decisions about treaty participation, and games where players make decisions about treaty ratification, are examined. The implications of linking cooperation on climate change with cooperation on other issues, such as trade, is examined. Cooperative and non-cooperative approaches to coalition formation are investigated in order to examine the behaviour of coalitions cooperating on climate change.

One way to achieve cooperation is to design a game, known as a mechanism, whose equilibrium corresponds to an optimal outcome. This paper examines some mechanisms that are based on conditional commitments, and could lead to substantial cooperation.

 

Accountability During COP 15

In climate negotiations, issues of accountability and transparency are very important. If the leader of a country pledges to reduce their emissions by a certain amount by a certain year, then they should be held accountable to that pledge, and judged accordingly. If a country pledges to increase their emission reduction if other countries emission reductions add up to a certain amount, then they should be accountable for that, and there needs to be a transparant mechanism for tallying and adding up different countries emission reduction commitments.

But accountability and transparency are not just about emission reduction commitments. These issues are also important for the negotiations themselves. If in negotiations, a country waters down the strength of the agreement, or obstructs progress, then the rest of the world will judge that country, and arrive at their own conclusions about whether they were negotiating in good faith or not. The fact that the plenaries are televised online, and some contact groups are open to observers, helps to facilitate transparency on this issue.

In the interests of transparency, I will list below some of the things that happened during the negotiations that countries perhaps should be held accountable for. These include:

• Russia’s on-again off-again emission reduction target;
• Saudi Arabia, China, India, Venezuela, Algeria, Kuwait, Oman, Nigeria, and Ecuador blocking discussion on proposals for a legally binding agreement from Tuvalu, Australia, Japan, the United States and Costa-Rica.
• Japan (supported by Russia and Canada) putting into question whether there would be a second commitment period to the Kyoto Protocol;
• the talks being suspended for 5-6 hours on Monday Dec 14 (when there was a lot of work to do);
• the United States watering down the nature of commitments from developed countries at the final AWG-LCA plenary;
• in the COP plenary that occured after the final AWG-LCA plenary, India proposed to delete collective emission reduction commitments by 2050 from the LCA text, as well as proposals to periodically review progress;
• the (admittedly weak) Copenhagen Accord could only be ‘noted’ by the Conference of Parties, for the COP to do anything stronger (like adopt it) was blocked by Sudan, Venezuela, Bolivia, Cuba, and Nicaragua – this was a highly acrimonius meeting;
• a proposal from Tuvalu to discuss a legally binding treaty at COP 16 next year was blocked by China, India, and Saudi Arabia.

 

Public Interest in Climate Change is at an All Time High

According to Google Trends. I guess it might have something to do with COP 15.

 

White Paper released, Kevin Rudd announces target.

The Carbon Pollution Reduction Scheme White Paper has been released. Australia’s Prime Minister Kevin Rudd has announced an emissions reduction target of 5-15% in 2020 compared to 2000 levels.

The target of 5-15% by 2020 sends a signal to the rest of the world that Australia is not willing to play its part in an international agreement that stabilises at 450 ppm or less. It does not even signal that Australia is willing to stabilise at 500 ppm or less. It obstructs a good agreement on climate change. This means that it says that we don’t care about the Great Barrier Reef, we will not make a serious attempt to stop it from being destroyed or seriously degraded. Curiously, Kevin Rudd states that 450 ppm should remain a core part of international negotiations.

Rudd and the White Paper have argued that a 5% reduction would imply greater per-capita reductions than the EU’s 20% reduction by 2020 because of Australia’s greater projected population growth. This argument is irrelevant because Australia’s per-capita emissions are much higher than the EU’s. Any international agreement that does not have high per-capita emitters reducing emissions more than low per-capita emitters would never be accepted by the developing countries in the world. Rudd’s approach makes promising per-capita approaches to climate change, such as contraction and convergence, more difficult to achieve.

In short, there are four problems with the targets that Rudd has chosen:

1. They are too weak to correspond to the stabilisation targets that we need to avoid dangerous climate change. They effectively rule out Australian cooperation with global stabilisation targets that add up to 500 ppm or less.
2. They are based on a model where low per-capita emitters and developing countries bear a disproportionate amount of the burden of emissions reductions. They do not take into account Australia’s high per-capita emissions and are therefore inequitable.
3. This means that developing countries have less incentive to participate in a global agreement, making the mitigation task harder.
4. There is considerable evidence that Australia can afford much more mitigation — the expected cost of climate change will be greater than the expected cost of mitigation.

Now for some comments on specific aspects of the White Paper.

Assistance measures: Much money is being squandered on assistance to emissions intensive industries. The coverage of assistance to “emissions intensive trade exposed” industries has been expanded to include industries that made the most noise, such as liquefied natural gas. Rentseekers have been rewarded. There will also be $3.9 billion dollars (assuming a $25 carbon price) in free permits handed out to coal-fired electricity generators. This is money that could have been invested in low emission technologies, reducing emissions from deforestation or forest degradation, or assistance to low income households. Instead it does nothing more than line the pockets of shareholders.

The large amounts of assistance to polluting industries have meant that there much less funding available for compensating households. The distribution of assistance to households is strange, households with incomes of less than $20,000 are given less assistance than households with incomes between $20,000 and $120,000. Newstart recipients will recieve $14.20 more per fortnight; people on the minimum wage will recieve $14.95 more per fortnight. No money has yet been allocated to help households increase their energy efficiency.

Low price cap on permits: There will be a price cap on permits, so the emissions cap can be exceeded by firms buying more permits at a price of the level of the cap. According to the White Paper:

• The scheme will have a transitional price cap for the period 2010–11 to 2014–15.
• The level of the price cap will be set at $40 commencing in 2010-11.
• The level of the price cap will rise in real terms by 5% per year.

This price cap is less than recent estimates of the social cost of carbon from economists such as Richard Tol [Richard Tol disagrees, see comments]. It is much less than what Nicholas Stern has suggested is likely to be the social cost of carbon. Having a price cap does not make sense if it is less than the social cost of carbon.

No price floor: I have discussed why an emissions trading scheme needs a price floor here. Dr Richard Denniss, from the Australia Institute has recently pointed out a problem with purely cap-and-trade schemes, that in my opinion could be addressed by a price floor, if it was high enough. With cap-and-trade schemes, if a household decided that due to concerns about global warming, it wanted to reduce its electricity consumption, that will not necessarily reduce global warming. What it will mean is that the electricity generator would not sell as much electricity, would not need to buy as many permits, and another firm could buy the permits more cheaply. The total amount of permits will be the same. This is more of a problem when the cap is too weak.

A price floor, it it was high enough, would mean that the scheme would function more like a carbon tax, but still with an absolute cap on emissions. A price floor could be introduced by there being a reserve price when permits are auctioned, or by firms paying an extra fee when they exercise their permits.

Forestry: The White Paper proposes to cover reforestation, on a voluntary basis, and not cover deforestation. Forest entities will not be required to surrender more permits than have been issued for an individual forest stand. Only activities that are covered by the Kyoto Protocol will be included. Judith Ajani and I have shown that at carbon prices of significantly less than $20 per tonne, there will be more revenue from using plantation forests as carbon sinks that as sources of wood. Because native forest logging does not attract a carbon price, and is not properly regulated, there will be an increase in native forest logging. This is likely to lead to carbon leakage from the plantation forest sector to the native forests logging sector, and a net increase in emissions. We made some submissions to the Carbon Pollution Reduction Scheme green paper here and here.

Update: The Australian Governments’ climate change advisor, Ross Garnaut, has written an article criticising the White Paper for its conditional targets not being higher enough, the inclusion of a price cap, and the transfer of wealth to emissions intensive rent-seeking industries. This article was published in the Fairfax press, and at East Asia Forum (under the title oiling the squeaks)..

 

Is Australia stalling climate negotiations?

Climate Progress has reported from Poznan that

Dr. Harlon Watson, a political appointee by the Bush Administration and lead negotiator in Poznan, has continued to reject emissions targets with base years attached, and is working with U.S. allies (Australia, Canada, Japan, New Zealand) to stall negotiations. These actions actively jeopardize our future.

This is somewhat different to Bali in 2007 when it was reported in the Sydney Morning Herald that

THE Prime Minister, Kevin Rudd, signalled his support for developed countries, including Australia, agreeing to making deep cuts in their greenhouse gas emissions in the next 12 years.

In a significant move last night the Australian delegation to the UN climate talks stated it “fully supports” the proposal that developed countries need to cut their greenhouse gas emission by 25 to 40 per cent by 2020.

The world will have to wait until December 15 to find out about Australia’s targets when the Australian government releases its White Paper. If Treasury’s modeled scenario’s are any guide, then the most likely targets for Australia to announce will be between 5% and 15% reductions by 2020. The Australian government had announced that it would be releasing targets before the negotiations at Poznan. It is now waiting until afterwards.

The Australian government has also been criticised for taking a hypocritical position on forestry at these negotiations.

Update: John Hepburn, from Crikey’s Rooted blog, has reported that Australian delegates have hardly said a word – apart from suggesting time-wasting agenda changes, and have barely participated in negotiations (possibly spending more time at the bar).

Further Update: Submissions to the UNFCCC Ad Hoc Working Group on Long-Term Cooperative Action (AHG-LCA) from different countries are available from here.

Further Update: The Guardian reports that Australia, along with the US, New Zealand and Canada, have deleted a line about indigenous peoples’ rights from a draft agreement on protecting forests. The original confidential draft, seen by the Guardian, talked of “noting the rights and importance of engaging indigenous peoples and other local communities”. The amended version mentions only “recognising the need to promote the full and effective participation of indigenous and local communities”.

 

Why Environmentalism Needs Equity

On 16 September 2008, Ms Sunita Narain, Director of the Centre for Science & Environment and Director of the Society for Environmental Communications, delivered the 2008 K R Narayanan Oration on “Why Environmentalism Needs Equity” at the Australian National University. The podcast is now available from here, a video is available from here.

I would highly recommend this lecture to anyone interested in environmentalism, equity, or climate change issues.

 

A simple model of carbon leakage

Suppose that a carbon price reduced the production of a trade exposed emissions intensive good. Loss of production could increase the goods price, which could increase production elsewhere (where there is not a carbon price). Similarly, if we were to reduce exports of a fossil fuel (e.g. coal), there could also be a similar price effect.

Assuming market clearance and no non-linear (bubble like) price effects, some manipulation of partial derivatives leads to the following equation:

where:

• R is the ratio of the change in quantity supplied from overseas (from countries that do not apply a carbon price) to the change in quantity exported (from countries that do apply a carbon price) – this value will be negative;
• Qo is the quantity supplied from countries that do not apply a carbon price;
• Qe is the quantity exported from countries that do apply a carbon price;
• Qt is the total quantity supplied (Qt = Qe + Qo);
• εs is the price-elasticity of supply, for expanding supply;
• εd is the price-elasticity of demand, which will be negative.

Inelastic demand is associated with necessities, such as staple foods and so on. If there are substitutes, such as gas, then demand becomes more price-elastic. The price-elasticity of supply depends on factors such as spare-production capacity and bottlenecks.

The above equation has the following implications:

• The magnitude of R will be less than 1, unless the elasticity of supply is infinite or the elasticity of demand is zero, in which case the magnitude of R will be equal to 1. This suggests that the common assertion from industry that “any loss in production will be offset by an increase in production elsewhere” is technically incorrect.
• As Qo approaches zero, R will approach zero. So the greater the coverage of the carbon price, the less that leakage is a problem, even if coverage is not complete. Because the above equation would affect the payoff matrix, when the coverage is greater, the prisoner’s dilemma will be marginally easier to resolve.

The above equation suggests that sectoral agreements to apply a carbon price in trade exposed sectors would be a useful approach. Even if the coverage of the sectoral agreement is not complete, the agreement would still be advantageous to resolving the prisoner’s dilemma. Because the mathematics of whether to apply a carbon price to fossil fuel exports is also governed by this equation, sectoral agreements among fossil fuel exporters, especially coal exporters, would be a useful mechanism for increasing the coverage of the carbon price.

Levies on exports may be a better alternative to border adjustments on imports or protectionism for emissions intensive industries. There is a precedent for this – in order for China to reduce the incentive for other countries to re-introduce levies on textile imports, it imposed a small levy on its textile exports. It has been suggested that this tactic could help unlock climate change negotiations. At present, a levy on Australia’s coal exports could significantly increase the coverage of a carbon price.

While reducing carbon leakage would affect global greenhouse gas emissions, the ultimate way that the carbon leakage problem will be solved will be for the successful resolution of international climate negotiations, and full coverage of a carbon price. Protection of emissions intensive industries will encourage, through reciprocity, the protection of these industries elsewhere, and more costs overall. It may be that the best approach to carbon leakage would be to ignore it. This would suggest that assistance to trade exposed emissions intensive industries could be reduced.

 

Game theory, long tails, and a per-capita approach to climate change

Addressing climate change requires the resolution of a prisoner’s dilemma, and preferably resolving it quickly. The prisoner’s dilemma can be thought of as a multiplayer repeated game, with communication between players, this makes it easier to resolve. In some ways present mitigation actions are more important in how they contribute to resolving the prisoners dilemma than their direct affect on emissions.

The most successful algorithms in experiments involving simulated multiplayer prisoner’s dilemmas have been ‘tit-for-tat’ strategies, this suggests that the issue of reciprocity is important. Weitzman’s recent work affects the cost of not cooperating, but does not effect the marginal benefit from free-riding. This affects the pay-off matrix in a way that increases the chance of resolving the prisoner’s dilemma (but also increases the cost of not resolving the prisoner’s dilemma). How much this affects the prisoner’s dilemma depends on how much different agents value Weitzman’s “VSL-like parameter”, and how much risk aversion they have. Other factors include the disaggregated climate change impacts, how much an agent values environmental goods, and what discount rate they use.

One approach that would encourage developing countries to participate in an international agreement is a pure per-capita approach (paywalled). All participating countries are allocated permits based on their population and average per-capita emissions. High per-capita emitters would buy permits from low per-capita emitters. According to the paper by Baer et al. on a per-capita approach:

The Kyoto Protocol assigned emissions caps to the industrialized countries based on their 1990 emissions levels (a “grandfather clause”). By basing future emissions caps on past levels, the protocol rewards historically high emitters and penalizes low emitters. A fair long-term agreement will require a transition to limits based on equal per capita emissions.
A per capita allocation can work because it is simple. Most of the alternatives under consideration blend past emissions with analysis of outcomes. They assume that the consequences of climate change for different nations, as well as their abilities to ameliorate or adapt, can be understood in advance.

A per-capita allocation is the same as the end point of a contraction and convergence approach. The question then becomes what is the amount of time taken to reach the end point. Equity arguments would suggest that this should take place quickly. It may be difficult to achieve this because high per-capita emitters could make it difficult. If Australia, a very high per-capita emitter, advocated a short convergence period, this outcome would be more achievable.