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Strategic aspects of climate policy

What are the prospects for devising global agreements to  mitigate climate change?  I provide an analysis of policies involving developed and developing nations which accounts for external benefits and carbon leakages.  Situations where mitigation effort should be concentrated in particular countries and where efficient outcomes can be fostered by international trade in emission permits are discussed.  The possibility for using auxiliary policies to transform intractable incentive problems to more tractable strategic problems is explored.  The role of commitments and the strategic implications of pursuing ‘no regrets’ and ‘adaptation’ policies are analysed.  Dynamic and repeated game formulations are examined.

 1. Introduction. An international treaty is the main way global climate change can be successfully mitigated. Greenhouse gas emissions (GGEs) are a global ‘public bad’ which must be addressed by a global mitigation response.  

A few large countries do have a significant impact on aggregate global GGEs (e.g. US, China, India) but for emerging economies per capita emissions are low because of their low energy intensities. In addition, the aggregate emissions of developing countries such as China and India have only been large for a historically brief period (Marland et al., 2007).   Moreover, while the US and China provide 50 per cent of the world’s GGEs, 15 countries provide in aggregate 80 per cent leaving another 158 countries providing about 20 per cent of emissions (Baumert et al., 2005).  The sources of GGEs thus comprise both distinct major emitters and a competitive ‘fringe’ of minor emitters who have a significant aggregate impact on global emissions.   Managing global GGEs is a ‘large group collective action’ problem (Olson, 1965).

An international agreement is essential since individual countries have sovereignty over their economic and environmental activities and there is no world government.  Countries are concerned in part with their individual self-interest but, pursuing this objective alone, may lead to unsatisfactory global GGE reduction outcomes.  Yet all countries generally do seek emissions reductions since they understand that their societies will be damaged by climate change. Thus countries hope to be able to negotiate a mutually satisfactory constraint that limits their individual autonomy in a way that leaves them individually better-off.

Countries find it easy to negotiate an agreement that limits their GGEs but self-interest may limit their propensity to sign or their willingness to abide by it.  They might also sign such an agreement and abide by it because they would anyway have acted in accord with the intentions of the agreement even had it never existed.

A treaty must be designed so countries have incentives to stick to its rules. Agreements must be self-enforcing (Barrett, 2003).  They must be individually rational so that no country can gain by withdrawing individually from them. They must be coalition proof – so it should not be possible for all or a coalition of nations to gain by renegotiation. Thus treaties should be both Nash optimal and collectively rational or Pareto efficient.  Finally, a treaty must be fair in the sense that parties see it as ‘legitimate’.  A treaty is a strategic instrument of policy restructuring incentives to alter behaviour so it becomes self-enforcing.

Here I develop non-cooperative game theory models to analyse the climate change policy design issue in a strategic setting: for a survey see Carraro (2007).  Section 2 starts with a static framework where a single developing country (‘China’) designs its climate change policies along with a single developed country (the ‘US’) by adopting ‘all-or-nothing’ policies of ‘mitigating’ or ‘not mitigating’ GGEs. This model highlights the split between policy perspectives of developed and emerging countries. The country labels here are partly generic: ‘China’ only partially captures the plausible policy positions of China just as ‘United States’ only partially captures the US position.  The labels are intended to generically model the strategic stance of emerging and developed countries respectively.

Clearly, however, contrasting the strategies for a single developed country with those of a single developing country is restrictive because different countries face particular circumstances with respect to their climate change prospects.  For example, while the US is often portrayed as facing limited local incentives to address climate change issues, other developed countries, such as those in Europe, face stronger incentives to act.  For analytical purposes the extension to include further countries is important.  This is done in Section 3.  The key issue is the extent to which having an extra country commit to mitigation affects the mitigation incentives of current non-mitigating countries.

 Section 4 returns to the two country framework but allows countries to employ ‘no regrets’ and ‘adaptation’ responses to climate change. All-or-nothing mitigation responses are not the only policy options. Policies can target local pollution concerns using ‘no regrets’ principles and there is also an option of adapting to climate change.

This discussion is mainly static or descriptive of steady state equilibria. Section 5 makes comments about repeated and dynamic game issues again in a developed-developing country policy setting.   Developing countries have higher discount rates and face an imperative to grow but they typically suffer the most longer-term from the impact of climate change. In addition, a core issue is the extent to which commitments to mitigate alter the mitigation responses of other countries.

Section 6 summarises the arguments and sets out conclusions in terms of a taxonomy of possible global policy options that may assist policy design post-Kyoto.  

2. Two country model. Consider two countries nominally designated ‘China’ (C) and the ‘US’ (U). Suppose these countries have only two options with respect to their GGEs, either to mitigate them (M) or not (DM).  If China mitigates then the gross local benefits it receives are Bc while spill-over benefits to the US are Bcu. The costs of mitigation are Cc.  If the US mitigates it gets local gross benefits Bu and provides benefits to China of Buc with mitigation costs being Cu.  Define the respective net national benefits from mitigation as πu = Bu-Cu and πc= Bc-Cc. The benefits and costs experienced are the environmental benefits and costs experienced by the countries and exclude benefits and costs related to a country’s perceived international image in terms of its mitigation stance. Countries are sensitive to international perceptions but such costs and benefits are complex and depend on the policy stance of the given country relative to that of others. For example, a country will presumably experience most national embarrassment if it is an isolated or sole non-mitigator.  

No carbon leakage effects. Suppose initially that the economies considered are closed to foreign trade and investment. Initially then spill-over benefits Bcu and Buc and locally incurred policy costs Cc and Cu are assumed independent of the mitigation response of the other country.  Thus spill-over benefits accruing to China from US mitigation do not increase when China does not mitigate rather than mitigate because (perhaps) of carbon leakages.

The payoff matrix for the two countries is set out as Figure 1. Each country has dominant strategies to mitigate (or not mitigate) if and only if the local benefits they receive from mitigation exceed (fall short of) country-specific costs.  Thus if πc > 0 China will mitigate while if, in addition, πu > 0 both will mitigate. In this limiting case – and only in this case – the climate change issue has none of the character of a global ‘public bad’ issue and can be interpreted as a set of purely local pollution issues that can be satisfactorily resolved by relying on each country to sensibly use nationalistically-oriented cost-benefit studies.  Apart from this extreme situation at least one country must consider strategic interdependencies when devising a mitigation response.

 

Two Country Game

US

M

DM

 

China

M

πc +Buc, πu +Bcu

πc, Bcu

DM

Buc, πu

0,0

Figure 1: Payoff Matrix for General Two-Country Game

Note here that apart from the case where local benefits exactly equal local costs, each country always has a dominant strategy of either mitigating or not mitigating.

It is not immediately obvious that the situation where local benefits do indeed exceed local costs is irrelevant particularly if net benefits are computed at steady state equilibrium values.  It might be that a developed country such as the US can achieve reduced GGEs  at relatively low cost even if local benefits of doing so are less than those of countries such as China which, for example, currently enjoys much lower per capita energy consumption.  Moreover, while China has development objectives that involve vastly increasing carbon-based energy consumption by its citizenry – the opportunity costs of undertaking mitigation efforts are therefore high – it is also the case that the benefits of forestalling the impacts of climate change are proportionately large in any society with a strong agricultural production bias[3]. Thus there can conceivably be an immediate case for a mitigation response by both rich and poor countries purely on the basis of individual self-interest.

If this is the case then this paper can almost end here.  The only task is to demonstrate to the respective governments that costs and benefits are what they are[4].  

Carbon leakage effects. Carbon leakage occurs when either (i) the mitigation response of one country raises local costs thereby giving countries that do not mitigate a trade advantage with consumers substituting goods not subject to GGE restrictions for local products subject to restrictions and with production moving offshore to the country not imposing GGE restrictions, or; (ii) taxes in one country add a premium to exported good prices reducing demand for them in countries not taxing these goods.

These leakages can arise if there is no uniform global emissions tax or, equivalently, if there is not free international trade in emissions permits that would equalise mitigation costs. If carbon leakages are important, and are accounted for, then the strategic analysis becomes more complex.  The empirical extent of likely carbon leakages are a matter of considerable current debate[5]. The Stern Review (Stern, 2007) argued such effects were likely to be small and evidence from the European Union’s experiences with its internal emissions trading scheme tends to confirm this (Convery et al., 2008). 

In addition, carbon leakage of industries from countries which mitigate to countries which do not mitigate can, in principle, be dealt with by taxing the carbon emissions associated with consumption rather than production and by taxing imports of goods originating from non-mitigating countries so that these goods do effectively bear a carbon tax prior to local consumption.  This is destination accounting of GGEs.   Suppose the US produce a manufactured item that emits CO2 during its production. Further suppose the good is consumed in the US and also exported to China. The carbon emissions in the US should then be taxed to reflect global damages imposed with a lump sum rebate provided on some base level of output exported to China.  If China produced the same goods and exported them to the US, but did not impose a sufficiently large carbon charge, the US could impose duties on import equal to the additional duty that should have been applied.  In either case there is no incentive for a firm to relocate to a country not taxing carbon emissions.  Indeed there is then an incentive to tax emissions locally so revenues accrue locally not to destination countries[6].

Unfortunately there are many difficulties with this proposal mostly associated with levying duties on untaxed imports.  If this is not done then local consumers have incentives to switch towards untaxed imports while local firms have incentives to relocate to evade the tax.  In a practical sense there are enormous difficulties in assessing the carbon content of goods with numerous inputs that are produced using a range of production technologies with differing carbon intensities.  At best this objection might be met by estimating average carbon content and by ignoring all those goods and inputs with relatively low implied carbon content.   Another practical difficulty is that such duties seem to be inconsistent with the World Trade Organisation’s Article I (General Most Favoured Nation Treatment) which requires nations which do levy tariffs on imports to do so uniformly and without discrimination on the basis of their country of origin[7]. 

If leakage effects do arise then the local benefits and costs one country gains from a mitigation response depend on the mitigation responses of other countries.  Suppose if the US mitigates but that China does not, that the US experiences extra costs Luu and China receives benefits Luc from this unilateral action compared to the situation where both mitigate. Similarly define Lcc and Lcu as the extra costs and benefits to China and the US respectively when only China mitigates.  Figure 2 outlines the relevant payoff matrix for the countries.

 

Two Country Game with Carbon Leakages

US

M

DM

 

China

M

πc +Buc,  πu +Bcu

πc -Lcc, Bcu+Lcu

DM

Buc +Luc, πu -Luu

0,0

Figure 2: General Payoff Matrix for General Two-Country Game with Carbon Leakage

Each country now faces more stringent conditions for their dominant strategy to be to mitigate on the basis of a local cost benefit analysis.  For the US to have a dominant strategy to mitigate πu > max(Lcu , Luu). Thus the net local benefits the US must derive from mitigation must now exceed the extra costs the US will impose on itself by mitigating unilaterally and the extra benefits that it would receive if China unilaterally mitigated.

Prisoners’ dilemmas.  The most widely discussed way game theorists see the global strategic implications of climate change is as a Prisoners’ Dilemma (PD) where all countries are better off cooperating but where each country has a dominant strategy not to.

With carbon leakage effects conditions for the payoff matrix in Figure 2 to be a Prisoners dilemma are πc < min (Luc , Lcc) and πu < (Lcu , Luu) so net benefits to each country must not exceed (i) carbon leakage benefits it would get were the other country to mitigate alone and (ii) carbon leakage costs it would incur were it to unilaterally mitigate.  Also, each country must derive positive benefits when they jointly mitigate so πc + Buc > 0 and πu + Bcu > 0.   The existence of carbon leakages and favourable mitigation spill-overs therefore increase the likelihood of PD’s by making it more likely each country will have a dominant strategy of not mitigating – each can now sometimes derive extra advantage if the other country alone mitigates and worse of if the other does not mitigate but they do. On balance carbon leakages make it more difficult to secure a global agreement to mitigate.  

If there are ‘embarrassment’ costs associated with being a sole non-mitigator or if cost reductions arise with the carbon trading that can occur when both countries mitigate then rewards to each country rise when both mitigate. It is easy to see that in this case the prospects for cooperation improve. Suppose rewards increase to π’c > πc and π’u  > πu with joint mitigation. Then for a PD to arise Luc+Buc > π’c +Buc > 0 and Lcu+Bcu > π’u +Bcu > 0 so Luc > π’c and Lcu > π’u. Thus larger spill-over benefits to each country must occur when the other country alone mitigates.  This is a more stringent requirement than without ‘embarrassment’ or cost savings effects for given spill-over and carbon leakages.  With large enough ‘embarrassment’ or cost saving effects the game becomes a more tractable Assurance Game with two Nash equilibria (both mitigate, both don’t mitigate) but where each prefer the equilibrium where each mitigates.  Now each country has incentives to commit to mitigation when it knows the other country will follow suit so prospects for co-operation improve.

Even without embarrassment or cost-saving effects different game structures can arise depending on payoffs and costs.  For example, in a PD structure, unilateral or joint policy responses can be the efficient cooperative response depending on relative costs and benefits.

Initially imagine symmetrical benefits, costs and spill-overs. For example, suppose Bc=Bu=5, Cc=Cu=6 and Bcg=Bug = 4 and ignore carbon leakages. This is then a standard PD as illustrated in Figure 3. Local pollution issues alone are insufficiently costly to justify individually rational policy efforts. Indeed the dominant strategy for each country is to not mitigate. However accounting for spill-over benefits were each to agree to mitigate, active mitigation by both is appropriate so the optimal cooperative outcome is for both to mitigate. 

 

Two Country Game

US

M

DM

 

China

M

3,3

-1, 4

DM

4, -1

0, 0

Figure 3: Prisoner’s Dilemma where it is collectively rational for all to mitigate

Suppose alternatively asymmetric costs and benefits. Assume, for example, that πc=-0.5, πu =-4 and Bcu=10, Buc = 1 and ignore carbon leakages, as in Figure 4. Again local pollution issues alone are insufficiently costly to justify policy effort. The dominant strategy again is for each country to not mitigate. However accounting for spill-over benefits to both countries active mitigation by exactly one country provides the efficient international agreement.  An instance might be investment in mitigation effort by one nation in a geo-engineering solution to climate change. In this case if both nations were to mitigate then welfare in each increases but by less in total than obtained were it to be done in one country (here ‘China’) alone.  Some cost, benefit or spill-over asymmetry across countries is necessary to establish this case the optimality of unilateral action. Thus for the game described in Figure 1 to be a PD, πc < 0 and πu < 0 while πc +Bcu > 0. For unilateral action to yield higher global benefits πu + Buc < 0, a contradiction if payoffs are symmetric.

Clearly the move from the situation where the dominant strategy of each country is to not mitigate to that where China alone mitigates is not a Pareto improvement since China is worse-off with this move. It does however improve global welfare in the sense that aggregate benefits to both increase. Then both countries can be made better off if one (here the US) compensates the other (here China). For example, consider compensation of $ε with 10 > ε > 0.5.  This achieves the Nash equilibrium where China alone mitigates provided that the US makes a side-payment of ε to China. This is shown in Figure 5.

 

Two Country Game

US

M

DM

 

China

M

0.5,6

-0.5, 10

DM

1, -4

0,0

 Figure 4: Prisoner’s Dilemma – collectively optimal for one country to mitigate

 

Two Country Game

US

M

DM

 

China

M

0.5+ε, 6-ε

ε, 10-ε

DM

1,-4

0,0

Figure 5: Prisoner’s Dilemma – One country should mitigate once a side-payment made

The prospect of one party making side-payments to induce a globally optimal pattern of GGE controls is one means of achieving cooperative globally optimal GGE reductions.  The approach offers advantages if one country has relatively low cost GGE clean up options but the other has high willingness-to-pay for cleanup.

This idea can be made clear by considering continuously variable GGE mitigation options and in a more complete version of this paper we do just that.  As is well known PD problems of non-participation in global agreements to reduce emissions can also be resolved by establishing regulatory machinery so that if a country fails to mitigate it is subject to penalties. For example, with the payoffs of Figure 4, if any single country which fails to mitigate is penalised $5 if it fails to mitigate the game is transformed to the Assurance Game of Figure 7 where the Nash equilibria involve each country either mitigating or not mitigating but where both will choose to mitigate if either country assures the other it will mitigate.  If all countries not mitigating are subject to penalty $5 then the game described by Figure 4 is transformed to the game in Figure 8 where all countries have dominant strategies to mitigate.

The motivation to form such agreements and the penalties for non-compliance is that all countries are better off if they jointly mitigate.  But there remain PD motivations for not finally agreeing to being bound by such penalties. 

 

Two Country Game

US

M

DM

 

China

M

0.5,6

-0.5, 5

DM

-4, -4

0,0

Figure 7: An Assurance Game

 

Two Country Game

US

M

DM

 

China

M

0.5, 6

-0.5, 5

DM

-4, -4

-5, -5

Figure 8: A Game with Dominant Strategies to Mitigate

One institutional arrangement that resembles this proposal is to design retaliatory tariffs directed towards the imports of countries which do not mitigate (compare Stiglitz, 2008).  This proposal differs somewhat from the notion of a unilateral penalty imposed on a non-mitigating country that was just discussed since restricting the ‘gains-from-trade’ accruing to a non-mitigating exporting country also restricts gains to a mitigating importing countries.  Indeed it is difficult to design institutions to support such arrangements without this unattractive feature[8].

A more satisfactory resolution, due to Gersbach (2008), sees industrialised countries contributing initial amounts to establish a fund, a Global Refunding System (GRS), and then receiving refund payments in accord with their emissions reductions.  Each nation is free to choose tax rates to reduce their emissions but all tax revenues are paid into the GRS.  Refunds are then provided to each nation in proportion to that nation’s emission reductions relative to the prior year divided by the sum of all reductions.  Initially only a fraction of funds held would be redistributed and the fund would grow due to interest earned and retained tax revenues.  Eventually, however, the GRS would achieve its steady state size where refunds would equal revenues inclusive of interest.  The resulting global agreement is individually self-enforcing.  Countries have incentives to set higher carbon taxes than they would without the GRS to achieve high rates of mitigation that would lead to high refunds.  An individual country can get returns that exceed contributions when other countries set low tax rates by mitigating intensively and imposing high taxes.  Emerging economies would not be required to contribute initially to the fund but could benefit from the fund by eventually imposing high taxes and mitigating.  Indeed for a period they might not need to make contributions to the fund at all but simply draw on rewards from the fund as a reward for their emission cutbacks.

This scheme elaborates the idea of imposing a penalty on any non-mitigating country.  A non-mitigator will lose either lose claim to the resources it initially contributes to the fund and subsequent contributed tax revenues or, for a developing country, forgo the possible financial rewards it can enjoy by mitigating. 

Non-Prisoner Dilemma Games. Finally, problems of countries refusing to mitigate are resolved if other countries secure large enough gains by living with the defection and maintaining or even increasing the intensity of their own mitigation responses. These are Leadership Games where one player – suppose the US – bears relatively large losses if it does not mitigate even if the other country – suppose China – does not mitigate.  This is not a PD. China in this case can force the US to carry the burden of the mitigation response.

This last possibility is illustrated in Figure 9 where we take πu = 12, Buc = 7, πc = -2, Bcu = 6.  The Nash equilibrium strategies here are for the US to mitigate even though China will not.

This may be an important practical possibility. Emerging countries face development imperatives that call for increased energy consumption while developed countries such as the US face relatively low costs of complying.   It may make sense for developed countries to pursue a leadership role at least for an interim period as occurred under the Kyoto Protocol.   

 

Two Country Game

US

M

DM

 

China

M

5, 18

-2, 6

DM

7, 18

   0, 0

Figure 9: A Leadership Game

Policy games can only take the form of a Chicken Game in the presence of carbon leakages. This can be seen by referring to payoff matrix Figure 2.  Here China must not want to mitigate if the US mitigates but to mitigate if the US fails to.  Thus Buc +Luc > πc +Buc ↔ Luc > πc and πc >Lcc so Luc > πc  >Lcc. Similarly the US must not want to mitigate if China does but to mitigate if the US fails to. Hence Lcu > πu >Luu. In addition each country must prefer mitigating to not mitigating so πc +Buc > 0, πu +Bcu > 0.  If all carbon leakage effects are zero then all cells are Nash equilibrium and the game degenerates to the point where choice of strategy by either country is irrelevant.  With carbon leakages Lcu = Luc = 10, Lcc= Luu = 6, spill-overs Buc = Bcu = 0 and local benefits πc = πu = 8 one obtains the Chicken game described in Figure 10 with two Nash equilibria where exactly one country does not mitigate.  Each country prefers the distinctive Nash equilibrium where it alone does not mitigate but the other country does.  Moreover, both countries prefer joint mitigation to jointly not mitigating. A joint-mitigation strategy maximises aggregate policy gains.

Finally, it would be useful information to know that in some situations the strategic policy game being examined is an Assurance Game with two Nash equilibria ((mitigate, mitigate) and (don’t mitigate, don’t mitigate)) but where both countries prefer the first equilibrium to the second.  Then an effective agreement to deal with climate change can easily be negotiated once one of the two countries commits to mitigate. The other country will then follow suit. 

 

Two Country Game

US

M

DM

 

China

M

8, 8

2, 10

DM

10,2

0,0

 Figure 10: A Chicken Game

However such simple agreements are ruled out at least in the absence of punishments such as retaliatory tariffs or embarrassment costs.  This is demonstrated using Figure 1.  For China to prefer the mitigation strategy to that of not mitigating when the US mitigates we require:

πc + Bug > Bug so πc > 0.

But simultaneously for China to prefer not mitigating when the US does not mitigate it must be the case that πc < 0 a contradiction that applies symmetrically to the case of the US.  Thus simple Assurance Game structures do not arise in climate change games.  As shown however, using Figure 7, an Assurance Game can arise if any country that does not mitigate is subject to a hefty tax although there remains the difficult task of negotiating and implementing the penalty scheme.   It is also worth noting that assurance games do arise naturally in situations where there are significant carbon leakages. From Figure 2 necessary conditions for an Assurance Game with leakages are Lcc > πc > Luc and Luu > πu > Lcu.  Such a game arises when, for example, Lcc = Luu = 6, Luc = Lcu = 4 and πu= πc = 5.

3. Multi-Country Models. A game theoretic analysis of climate change issues is worth carrying out in settings with more than two countries because of asymmetrical mitigation incentives among countries, particularly developed countries. A common observation, for example, is that European countries have stronger incentives to mitigate climate change than the US.

The simplest extension is to consider the case of exactly three countries. Parts of the earlier analysis are now extended to do this.  Consider China (c), the US (u) and Europe (e) with respective local net benefits πc, πu and πe and respective spill-overs Bcu, Bce, Buc, Bue, Bec, Beu defined as before. Thus Bcu is the spill-over benefit provided to the US when China mitigates.  

With respect to carbon leakages suppose that if the US alone mitigates it incurs extra costs Luu and China receives extra benefits Luc while Europe gains extra benefits Lue. Similarly if Europe alone mitigates then it incurs extra costs Lee and China receives extra benefits Lec while the US gains Leu. If China alone mitigates the cost to China is Lcc and the benefits to the US and Europe are Lcu and Lce respectively.  

If both the US and Europe mitigate but China does not then they incur net losses L’uu and L’ee respectively and provide gains to China of L’uec.  If both China and Europe mitigate but the US does not they incur losses L’’cc and L’’ee respectively while the US gains L’’ceu.  Finally if both the US and China mitigate but Europe does not they experience losses L’’’uu and L’’’cc respectively while Europe gains L’’’uce. Initially focus on the decision to mitigate in China.

If China mitigates it faces payoffs in Figure 10. If it doesn’t mitigate Figure 11 payoffs obtain.

What are the conditions for there to be dominant strategies for countries to mitigate? Consider the US.   If there are no carbon leakages the earlier condition that local net benefits must be positive to motivate mitigation prevails so, for the US, πu > 0.   With carbon leakages the analysis is more complex. For the US to have a dominant strategy to mitigate the payoff from doing this must exceed that obtained if it defected from a cooperative agreement involving all countries to mitigate, so:

πu +Beu + Bcu > Beu +Bcu + L’’ceu  so πu > L’’ceu.                      

Thus for mitigation to be a dominant strategy a necessary requirement is that net local US gains from mitigation must exceed the carbon leakage benefits it derives if all other countries mitigate but the US does not. 

In addition, the US must achieve greater gains from mitigating when China mitigates but Europe does not than when the US joins Europe in not mitigating:

πu + Bcu –L’’’uu > Bcu + Lcu so  πu > L’’’uu + Lcu.

Thus net local US gains must exceed the carbon leakage losses they would avoid by joining Europe in not mitigating plus the carbon leakage benefits that would accrue to the US if China alone mitigated.

 

Three Country Game: China Mitigates

Europe

 

M

 

DM

 

 

 

US

 

M

πu +Beu + Bcu,

πe +Bue + Bce,

πc + Buc +Bec

πu + Bcu –L’’’uu,

πe + Bue + Bce + L’’’uce,

πc + Buc –L’’’cc

 

DM

Beu +Bcu + L’’ceu,

Bce – L’’ee,

πc + Beu + Bcu –L’’cc

Bcu + Lcu,

Bce + Lce,

πc -Lcc

 Figure 10: Payoff Matrix with China Mitigating

In addition, the US would need to be a net gainer when Europe mitigates but China does not compared to the gains it would enjoy in joining China in not mitigating:  

πu +Beu –L’uu > Beu + Leu so  πu  > L’uu. + Leu

Thus the net gains to the US must exceed the carbon leakage losses incurred by joining Europe in mitigating even though China did not mitigate plus the carbon leakage gains that accrue to the US if Europe alone mitigates.

 

 

 

 

 Three Country Game: China Does Not Mitigate

Europe

 

M

 

DM

 

 

 

US

 

M

πu +Beu –L’uu,

πe +Bue – L’ee,

Bec +Bec + L’uee

πu – Luu,

Bue + Lue,

Buc + Luc

 

DM

Beu + Leu,

Πe -Lee,

Bec + Lec

0,

0,

0

 

 Figure 11: Payoff Matrix with China Not mitigating

Finally, the US must gain from mitigation even if the other countries did not mitigate πu > Luu. So gains to the US must exceed carbon leakage losses sustained from unilaterally mitigating.

These conditions can be summarised.  Any country will have a dominant strategy of mitigating if (i) the local gains it derives are greater than the carbon leakage benefits it derives if both other countries mitigate but it did not, (ii) the carbon leakage losses it sustains when it unilaterally mitigates are greater than not mitigating and (iii) in the case where one other country does mitigate but the other does not, when the gains from mitigating exceed the losses they will incur in joining the other country in mitigating plus the carbon leakage losses they would gain by joining the non-mitigating country in not mitigating.

If one country commits to mitigating irrespective of the intentions of the other countries the strategy problem for the remaining countries simplifies to the 2-player game of Figure 12.

 The conditions for mitigation to be a dominant strategy for the US are then πu > max(L’’ceu, L’’’uu + Lcu.)

There is some improvement in the prospects for extra countries mitigating when one country commits to mitigation so that there are reasons to suppose that forces equivalent in effect to ‘moral suasion’ works in driving further countries to mitigate.   But the local gains from mitigation must still exceed the presumably large gains a country would receive when it alone does not mitigate but gets carbon leakage benefits from all the countries which do (these are L’’ceu here for the stylised situation involving the US).  But, for the dominant strategy to involve mitigation, local gains now do not need to exceed the presumably huge costs of going it alone in mitigating (Luu) since the pool of potential carbon leakage losses has fallen as other countries commit to mitigating.

 

Two Country Game with Carbon Leakage when China Mitigates

Europe

 

M

 

DM

 

 

 

US

 

M

πu +Beu + Bcu,

πe +Bue + Bce,

πu + Bcu –L’’’uu,

πe + Bue + Bce + L’’’uce,

 

DM

Beu +Bcu + L’’ceu,

Bce – L’’ee,

Bcu + Lcu,

Bce + Lce,

Figure 12:  Mitigation Payoffs for the US when China Mitigates

These improvements in the prospects for avoiding PD issues improve the greater the potential reduction in carbon leakage losses. So if a developing country like China were to commit to mitigation and to thereby rule out carbon leakage losses for developed countries if they mitigated, a substantial improvement in the prospects for cooperation obtains. If a small country or an already developed country mitigated then the case for other developed countries to mitigate is weaker.

The ambiguous prospects for enhanced global cooperation can be re-examined in repeated or dynamic game settings and this is done in Section 5 below.  This work can be adapted to account for asymmetries in national interests and for the possibility of repeated negotiations.

Alternative approaches draw on the behavioural economics literature which examines the conditions under which agents cooperate even though it is not in their individual self-interest to do so (Brekke et al. 2008).  Laboratory experiments suggest that people are willing to cooperate if they see others doing so. Moreover, field evidence suggests people’s willingness to contribute to good social causes increases with their perception of the contribution of others. These are instances of conditional cooperation.  There is also much laboratory evidence consistent with reciprocity – this is a social norm that motivates people to reward kind and to punish unkind actions towards them.  This reciprocity is not conditional on gaining some long-term reward and can even occur in one-shot interactions. Intentions of kindness or unkindness can matter as well as consequences of actions.

These observations relate to individuals rather than countries interacting strategically in a multi-country setting.  The issue is whether or not agents become more or less cooperative in a group situation and the experimental evidence here, unfortunately, goes both ways. 

In addition behavioural economics also provides evidence of self-serving biases.  When facts and principles are ambiguous we tend to choose those which favour our self-interest.  Even if people are motivated by ‘fairness’ their world view as to what delivers fairness is likely to converge toward views that serve their self-interest.  For example policy-makers in rich countries may simply seek to avoid ethical discussions involving the needs of energy poor developing countries and climate change because entering into this discussion might induce discomfit.  Cognitive dissonance may also be a factor. Countries which release large volumes of GGEs may change their beliefs to fit their behaviour by coming to believe that the damages of GGEs are overstated.

Brekke and Johansson-Stenman (2008) summarise what we can learn from this literature:

‘Taken together, what can we learn from the BE literature on cooperation for climate negotiations? First, people, and also countries, are able to make decisions that are not in their own material interest if they have other sufficiently strong reasons for doing so, such as obtaining a situation that is overall socially desirable and if this can be obtained in a way that is perceived as reasonably fair. Second, when individual parties analyse what a fair outcome should look like they are typically influenced by self-serving bias, and this makes it more difficult to reach agreements. Third, negotiating parties are likely to avoid looking at information that would force them to reflect over ethical issues. A potential policy implication is therefore to emphasise such information to the point where it is impossible for the negotiators to ignore it…. Fourth, the possibility to use sanctions and punishments seems essential for the longer term effectiveness of a climate agreement. The Kyoto protocol and the forecasts for the next agreement currently lack this opportunity. …see also Stiglitz (2006) for a suggestion of linking the climate and trade negotiations, leading to countries that fail to act responsibly in the climate area being punished by tolls’.

4. Intermediate Policies – No Regrets Options.  Return now to a two country world but now admit as candidate policies for each country ‘intermediate’ or ‘no regrets’ policy options that address local pollution concerns on the basis of high local benefits but which have a much lower impact on global environmental concerns than the ‘mitigation’ responses analysed in Section 2 offered.  The payoff matrix now considered distinguishes the original local benefits, international benefits and policy costs associated with a full mitigation option but now defines new notation (the original notation with an ‘I’) that describe these same variables when intermediate policies (denoted IM) address only a more limited range of local environmental and energy concerns.  The intent is to rationalise a case for pursuing intermediate rather than ultimate policy targets.

The extent of carbon leakage effects depends on the exactly policy response of countries.

Let Luu be the extra carbon leakage costs imposed on the US if it mitigates but China does not at all. Suppose Luc are the associated benefits to China.

Let Luu’ be the extra carbon leakage costs imposed on the US if it mitigates but China pursues ‘no regrets’ options. Let the extra benefits to China be Luc’.

Let Luu’’ be the extra carbon leakage costs imposed on the US if it pursues no regrets options but China does not. Suppose the extra benefits to China are Luc’’.

Suppose that if both countries either mitigate or mitigate using no regrets policies that there are no carbon leakage effects.

Evidently here Luc > Luu’ or  Luu’’ and that Luc > Luc’ or Luc’’. Whether Luu’ >  Luu’’ and whether Luc’ > Luc’’ depends on the scale of the costs and benefits of non regrets policies relative to comprehensive mitigation.  Define similar variables (Lcc, Lcu, Lcc’, Lcu’, Lcc’’, Lcu’’) when China is the more active mitigator and the US is less active and define πic=BIc-CIc, πiu=BIu-CIu.  The payoff matrix Figure 2 can now be expanded to Figure 13 below.

Suppose BIc < Bc, BIcg < Bcg, CIc < Cc, BIu < Bu, BIug < Bug, CIu < Cu so there are smaller spill-overs and mitigation costs with ‘no regrets’ policies.

 

General Two Country Game

 

US

M

IM

DM

 

China

M

πc +Buc,

πu +Bcu

πc +BIuc –Lcc’,

πic +Bcu + Lcu

πc -Lcc,

Bcu + Lcu

IM

πic +Buc +Luc’,

πu +BIcu-Luu

πic +BIuc,

πiu +BIcu

πic -Lcu’’,

BIcu +Lcc’’

DM

Buc +Luc,

πu -Luu

BIuc +Luc’’,

πiu –Luu’’

0,0

 Figure 13: Payoff Matrix for General Two-Country Game with Intermediate Policies

Inspection shows that the intermediate policy of addressing local needs only with a GGE policy is a dominant strategy for China if and only if πc < πic >0 so the intermediate policy must yield positive net benefits which exceed those derived from completely mitigating.  By symmetry the same condition holds for the US.   

Much has been made of the fact that China is committed presently to a ‘no regrets’ climate change policy rather than to comprehensive GGE controls.  In the stylised setting described in Figure 13 the US would then choose full mitigation (M) over no regrets policies which in turn would be preferred to no mitigation if:

πu +BIcu-Luu’ > πiu+BIcu > BIcu +Lcc’’

or if:

πu -Luu’ > πiu > Lcc’’

which requires that the local benefits from full mitigation net of consequent carbon leakage losses must exceed the local benefits from joint partial mitigation which must in turn exceed the carbon leakage gains that would accrue to the US if it continued not to mitigate.  It is somewhat interesting that this choice is independent of spill-over effects of mitigation – it only depends on local benefits from policies less their associated carbon leakage costs.

5. Repeated Games and dynamics

Repeated games. Standard results suggest enhanced prospects for cooperation in repeated PD contexts (Dixit and Skeath, (1999, chapter 8)). Countries may have a preference for mitigating now if failure to mitigate will bring about persisting non-mitigation by other participants.  This can be true if countries adopt contingent strategies that depend on the prior mitigation responses of other countries.

In repeated games countries can adopt strategies that depend on behaviour in previous periods.  Attention has focused particularly on when countries might play ‘tit-for-tat’ (TFT) trigger strategies.  In the present setting this means playing the mitigate strategy if other countries have played the mitigate strategy.  This view of policy can resolve Prisoner’s Dilemma problems without countries adhering to a policy of never mitigating.  Countries tend to pursue a mitigate option if they have relatively low discount rates so that they place relatively high value on longer-term environmental benefits.  In addition, countries will have increased incentives to mitigate now if they expect future economic conditions to remain good in the presence of an active mitigation policy. If mitigation costs or the net benefits from mitigating were expected to decline in the future they would have a propensity to defer mitigation effort.  Likewise if the benefits from mitigation in the future were expected to increase there would be increased prospects for mitigation.

Much policy attention has focused on the possibility of countries cheating on global mitigation efforts.  This is a profitable strategy if the immediate gains from doing it are large and if the probability of their cheating being quickly detected is low.  The gains from cheating are reduced if emissions in individual countries are being monitored to check that cheating is not occurring and cheating is somehow punished.  Examining trends in global GGEs will be less satisfactory if large numbers of countries are involved. 

This argument for taking a longer-term view backed up by monitoring is bolstered by experimental which provides evidence that agent behaviour in repeated games tends to become less cooperative through time, and to converge toward the conventional non-cooperative Nash equilibrium, unless free riders are punished (Fehr and Gächter, 2000a, 2000b).

Dynamics.  The repeated game setting is static and excludes any dynamic resource effects of current policies.  There are numerous ways these interactions might be dynamized. We consider only one.  Return to a two-country setting with China and the United States considering their mitigation responses in a two-period setting (‘now’ and the ‘future’) where, for simplicity, carbon leakage effects are ignored.  Suppose the environment is a luxury good that is strongly demanded at developed country income levels but less keenly sought at emerging country income levels.

Countries such as China face development imperatives now that, in themselves, provide strong incentives to forego mitigation.  Some positive mitigation response however is called for in part because future expected income is much higher and greater weight will then be placed on the environment if it is a luxury good for its citizens.  In addition China will face relatively severe impacts from unmitigated climate change and high adjustment costs of reorienting its energy consumption plans entirely in the future towards less polluting sources.  Developed countries such as the US may place relatively higher weight on having a quality environment now and retaining that environmental quality into the future but may face lower future impacts from unmitigated climate change. In a game setting there will be US recognition of the dynamic incentives that China faces to under-supply current mitigation effort but to more fully mitigate in the future.  There will also be recognition by the US that China will face more severe economic costs of adaptation in the future to climate change which will temper somewhat this pressure to shift mitigation responses forward.  China for its part will recognise increased current and future incentives for the US to mitigate more than it otherwise would in response to a diminished Chinese effort.  China will recognise too that that this increased commitment to mitigate will be tempered by an increased US capacity to adapt to unmitigated climate change.

It is a relatively straightforward task to write down a formal two period model of these strategic interactions although the rewards from doing so may not be great given the ambivalent incentives that face different nations. 

 6. Conclusions

It is important to make the simple point that unless nations put themselves ‘in the shoes of other nations’ that a satisfactory resolution of the climate change issue will not result. ‘There will be no agreement unless each country’s leaders and policymakers put in the necessary effort to understand each other’s perspectives. If countries push forth only with their own assessment of what would be best for themselves, independently of the effects of that position on the international discussion, no agreement will be reached.’ (Garnaut, (2008, 13) ).

Strategic models of climate change have been developed which account for externalities associated with the common property character of GGEs and for possible carbon leakages.  While the PD structure of the strategic task posed was taken as central the assumptions underlying this view were considered.  The situation where current local benefits from mitigation exceed mitigation costs cannot be ruled out even for developing countries where the objective of increasing current energy consumption levels is taken seriously. A unilateral case for mitigation might still prevail if account is taken of the future costs of dealing with severe climate change in a society with a dominant climate-exposed agricultural sector.

This case for unilateral action in developing countries is strengthened if developed countries resist joining in co-operative GGE mitigation efforts unless major developing countries do so also.

Developed countries such as the US face relatively lower costs of adapting to the effects of climate change and have argued strongly that they will not do so unless developed countries also do so because of feared carbon leakage effects.  Some evidence was provided suggesting that such leakage effects may have been exaggerated.  In addition a proposal to tax consumption by imposing carbon charges only on the locally-consumed portion of outputs with compensatory border taxes on untaxed imports was examined. This proposal is complex to implement and inconsistent with pre-existing WTO trade rules. If leakages do occur then the conditions for mitigation to be a dominant strategy for countries become more stringent and the prospects for PD inefficiencies enhanced.

One approach to addressing these difficulties is to impose penalties on countries which do not mitigate or to reward countries which do mitigate.  It might, for example, be the case that some countries can bribe other countries with sufficiently large rewards to induce them to mitigate.  This can be understood in terms of standard public goods modelling in the situation where one group of countries have a strong preference for reducing GGEs but mitigation efforts are most cheaply carried out in other countries.  We showed how this outcome could be realised by an appropriate allocation of GGE quotas and how trade in quotas could minimise the global costs of meeting prescribed emission targets.

We also examined Leadership Games where smaller countries could end up being capable of forcing larger countries to bear the burden of mitigation and Chicken Games where there are multiple Nash equilibria with each preferred by a single country where, not unnaturally, that country does not mitigate but where countries jointly prefer mitigating to not mitigating at all.

Situations where strategic situations resolve into Assurance Games are of interest to uncover since then a cooperative agreement to deal with climate change can be engineered once some countries commit to mitigate.  Without carbon leakage effects we show that such a decomposition never obtains unless countries are subject to a hefty tax should they not mitigate.  An Assurance Game outcome can however obtain if carbon leakages are strong enough even without punitive taxes.

An examination of three country models with carbon leakage effects accounted for enabled us to account for the impact of extra countries committing to mitigate on the incentive of remaining non-mitigating countries to commit to mitigation.  While there is some reason for believing that something equivalent in effects to a ‘moral suasion’ force operates here to encourage extra countries to mitigate – the costs of ‘going it alone’ in terms of carbon leakage losses are reduced as more countries mitigate – it remains the case that local gains from mitigating must still exceed the potentially large carbon leakage benefits that accrue to a country which ‘holds out’ on mitigating thereby gaining the carbon leakage benefits on countries that do.  The possibility of deriving enhanced prospects for cooperation as more countries comply on the basis of social norms reflecting ‘reciprocity’ was also examined.  Self-serving biases and the desire to avoid dealing with moral issues that force nations to reflect over ethical issues obstruct such enhanced cooperativeness although emphasising the global advantage from cooperation is likely to be a powerful counterargument.  Sanctions and punishments seem vital to ensure cooperativeness.

We also examined the implications of certain countries committing to pursuing ‘no regrets’ options for the policies of other countries.

Finally the analysis considered the potential for enhanced prospects for cooperation in repeated and dynamic game settings.  The prospects for cooperation in a modified repeated games setting where payoffs evolve are undermined without monitoring of emissions efforts to ensure mitigation, by high discount rates, by reducing costs of mitigation effort and reduced future benefits from mitigation.

A comprehensive dynamic model was not provided only a suggestive qualitative account.  Developed countries will recognise the incentives developing countries face in the short-term to promote energy consumption and the trade-off between these objectives and the desire to anticipate higher future preferences for mitigation in newly-emerging countries once development objectives have been met.  There is also the prospect that agriculturally-based newly emerging countries might face relatively high costs of adapting to climate change.  Developing countries will likewise recognised the aversion developed countries now will display towards the risks of climate change both now and in the future and the fact that these risks are somewhat offset by low adaptation costs.  This suggests that accounting for strategic interactions developing countries will mitigate somewhat more than they otherwise would and that developed countries will mitigate somewhat less.

These are loose results that need to be fleshed out in a fully articulated growth model where the specific preferences, discount rates and production sectors of emerging and developed countries are precisely articulated.

References

V. Alexeeva-Talebi, A. Löschel & T. Mennel, Climate Policy and the Problem of Competitiveness: Border Tax Adjustments or Integrated Emission Trading, ZEW Discussion Paper No. 08-061, Centre for European Economic Research, 2008.

S. Barrett, Environment and Statecraft. The Strategy of Environmental Treaty-Making, Oxford University Press, Oxford, 2003.

K. Brekke & O. Johansson-Stenman, ‘The Behavioural Economics of Climate Change’, School of Economics and Law, University of Gothenberg, Working Papers, 305, May 2008.

K. A. Baumert, T. Herzog & J. Pershing, Navigating the Numbers: Greenhouse Gas Data and International Climate Policy, World Resources Institute, 2005.

W.R. Cline, Global Warming and Agriculture: Impact Estimates by Country, Peterson Institute for International Economics, Washington DC, 2007.

F. Convery, D. Ellerman & C. De Perthuis, The European Carbon Market in Action: Lessons from the First Trading Period.  Interim Report, by, MIT CEEPR and University College Dublin, March 2008.

 A. Dixit & S. Skeath, Games of Strategy, W.W. Norton, New York, 1999.

E. Fehr & S. Gächter, ‘Fairness and Retaliation: The Economics of Reciprocity’, Journal of Economic Perspectives, 14, 2000a, 159-181.

E. Fehr & S. Gächter, ‘Cooperation and Punishment in Public Goods Experiments’, American Economic Review, 90, 2000b, 980-994.

Garnaut Climate Change Review, Targets and Trajectories, Supplementary Draft Report, Commonwealth of Australia, 2008.

H. Gersbach, ‘A New Way to Address Climate Change: A Global Refunding System’, Economist’s Voice, July 2008, 1-4.

T. Houser, R. Bradley, B. Childs, J. Werksman & R. Heilmayr, Levelling the Carbon Playing Field: International Competition and US Climate Policy Design,  Peterson Institute for International Economics, Washington, 2008.

G. Marland, T.A. Boden & R. J. Andres, ‘Global, Regional, and National Fossil Fuel CO2 Emissions’. In Trends: A Compendium of Data on Global Change,  Carbon Dioxide Information Analysis Center, Oak Ridge National Laboratory, U.S. Department of Energy, Oak Ridge, 2007.

J. Stiglitz, ‘A New Agenda for Global Warming’, The Economist’s Voice, 3, 7, 2006, 1-4.

[1]  Our game models initially also abstract from reductions in global costs consequent on countries collectively agreeing to mitigate and then trading their GGEs.  These effects can be substantial. Australia could set 10 per cent GGE cutbacks to 2020 that would cost the same as 5 per cent cutbacks to this date if GGE entitlements were traded.  See Garnaut (2008). A non-game theoretic analysis of these issues is provided in Figure 6.

[2]   In a many-country setting some countries with high local benefits of mitigation will find it worthwhile to mitigate while others may not.

 

[3]  Agriculture is the ‘canary-in-the-mine of global warming’s economic impact’ according to Cline (2007).  Warming will hit poor people hardest since these people often have no alternative to being farmers. Their agriculture will become less productive and the undernourished will find food supplies even harder to obtain.

 

[4]   This is a non-trivial task in itself.  While for many infrastructure projects the costs of new projects are often underestimated in the environmental area the tendency has been (in such areas as SO2 control) to substantially overstate costs.   This might reflect the fact that cost estimates for infrastructure projects often rely on estimates of project promoters while cost estimates for environmental projects come from businesses who would prefer no regulation and who do not see the full opportunities for new cost-saving technologies.

[5]  It is unclear how important they are.  Houser et al. (2008) argue that the damages to developed countries from leakages would be small. Most manufacturers (let alone service industries) do not use much energy, the main source of emissions, and so would not suffer big costs. Energy makes up less than 1% of the cost of making cars, furniture or computers. Even some energy-intensive industries, such as power generation, should not be much affected. Since they have no foreign competition, they could pass on extra costs to their customers. See also ‘Emissions Suspicions’ The Economist June 19, 2008.

[6]  Alexeeva-Talebi et al (2008) also consider the possibility of an integrated emission trading (IET) regime where foreign producers in non-mitigating nations must purchase emission entitlements in the destination country.  They argue that border tax adjustments better protect local competitiveness while IET reduce foreign emissions to a greater extent.

[7] These are complex issues. There are ways of circumventing this GATT rule. Articles XX (b) and (g) of the GATT allow measures to protect the environment necessary to protect human or animal life and health and to conserve exhaustible resources.  A thorny issue is whether such measures can be based on production methods used. The Shrimp-Turtle dispute outcome suggests there may be the possibility for such measures (World Bank, 2008, 37-39).

[8] As mentioned earlier these retaliatory tariffs – such as the proposed European ‘Kyoto Tariff’ on non-carbon-taxed US exports – may be inconsistent with GATT articles governing free trade.  If this is so, the global benefits the World Trade Organisation has realised by promoting freer trade are being reduced by environmental losses that stem from the fact that retaliatory tariffs cannot be imposed on countries not mitigating GGEs.  This will undermine confidence in WTO processes.

[9] Specifically BIuc = BIcu =Lcc’’ = Luu’’ = Lcu’’ = Luc’’ = 0.

 

 

 

2 comments to Strategic aspects of climate policy

  • Very interesting post Harry. There does seem to be a problem with the links in the footnotes.

    The question of linking climate and trade is very interesting. One point that Barrett makes is that the issue of carbon leakage adds credibility to threats involving trade (p. 320). A multilateral approach to trade penalties would be much more preferable to unilateral approaches.

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