Poiesis Prax (2004) 3: 123–139 DOI 10.1007/s10202-003-0059-9 ORIGINAL PAPER

Alfred Endres

Game theory and global environmental policy

Published online: 4 March 2004 Ó Springer-Verlag 2004

Abstract Economists interpret global environmental quality to be a pure public good. Each country should contribute to its provision. However, this is hard to achieve because each government is tempted to take a free ride on the other governments’ efforts. Not only has this dilemma been analysed with game theoretical methods but game theory has also been used to think about how to make amends. This paper reviews the game theoretical discussion on how international policy frameworks may be designed to improve the chances for international cooperation. It is also shown that the evaluation of alternative environmental policy instruments deviates from the standard environmental economics model if applied to the international arena. For the benefit of an interdisciplinary readership, the evolution of the debate on global environmental policy is related to the recent history of economic thought. This history is taken to be materialised in the writings of economics’ Nobel Prize laureates. Zusammenfassung Aus o¨konomischer Sicht ist die globale Umweltqualita¨t ein reines o¨ffentliches Gut. Fu¨r eine global optimale Versorgung sollte jeder Staat einen Beitrag leisten. Tatsa¨chlich ist aber jeder einzelne Staat versucht, eine Trittbrettfahrerposition einzunehmen und von den Anstrengungen der anderen zu profitieren. Die Spieltheorie hat diese Probleme analysiert und Lo¨sungsansa¨tze vorgetragen. Der vorliegende Beitrag gibt einen U¨berblick u¨ber die Entwicklung der ju¨ngeren Literatur. Dabei stehen die Bemu¨hungen im Vordergrund, Rahmenbedingungen fu¨r das politische Handeln zu konzipieren, unter denen kooperatives Verhalten der Staaten wahrscheinlicher wird als im urspru¨nglichen Gefangenendilemma. Bei der Analyse zeigt sich auch, dass umweltpolitische Instrumente im internationalen Kontext anders zu bewerten sind als dies in der traditionellen umwelto¨konomischen Analyse geschieht. Fu¨r eine interdisziplina¨re Leserschaft zeigt der Beitrag, wie das Denken einiger mit A. Endres University of Hagen and University of Witten/Herdecke, Profilstraße 8, 58084 Hagen, Germany E-mail: [email protected]

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dem Nobelpreis ausgezeichneter Autoren die spieltheoretische Diskussion zur O¨konomie globaler Umweltprobleme gepra¨gt hat. Re´sume´ Les e´conomistes conside`rent la qualite´ mondiale de l’environnement comme un bien public. Chaque pays devait y contribuer. Cependant, chaque E´tat est tente´ de se de´solidariser et de profiter des efforts des autres gouvernements. Ce dilemme a non seulement e´te´ analyse´ suivant les me´thodes de la the´orie du jeu, mais la the´orie du jeu a e´galement e´te´ utilise´e pour re´fle´chir aux moyens d’y reme´dier. Cet article passe en revue la discussion actuelle utilisant la the´orie du jeu qui cherche a` concevoir des cadres politiques internationaux pour ame´liorer les chances de la coope´ration internationale. L’analyse fait e´galement apparaıˆ tre que les instruments de politique environnementale diffe`rent, quand ils sont applique´s dans le contexte international, de ceux qui sont utilise´s dans le mode`le e´conomique environnemental traditionnel. S’adressant a` un lectorat international, l’article fait le rapport entre l’e´volution du de´bat sur les politiques internationales de l’environnement et l’histoire re´cente de la pense´e e´conomique, et montre comment certains laure´ats du prix Nobel d’e´conomie ont fait entrer la the´orie du jeu dans leurs e´crits.

1 Introduction Game theory deals with how individuals behave in interdependent decision situations. If individual A makes a certain move, the consequences of this decision for his/her own welfare may not only depend on this move but also on what kind of a move B makes. Vice versa, the same holds for B. This kind of an interdependency is ubiquitous in economic and social life. There are ample examples ranging from the decisions made by rivalling political parties regarding their campaign programs, decisions made by oligopolistic firms regarding product prices, or the manifold interactions among members of a family. The prime economic questions is how the agent will decide given that he/she is aware of the interdependency and supposes that his/her opponent (partner) first is also aware of the interdependency and second will also take it into consideration when making his/her decision. Moreover, it has been of some concern to economists how the constraints under which individual agents operate can be defined such that individual equilibrium decisions lead to socially optimal results.1 Game theory and its applications are among the most thriving methods and fields in economics. A very high proportion of the contributions to leading economic journals is a variant of this theme. In 1994, J. Nash, J. Harsanyi and R. Selten were awarded the Nobel Prize in economics for their path breaking contributions to game theory.2 1 A result is ‘‘socially optimal’’ if it maximises the welfare of a society under the given constraints. Of course, it is difficult to say what the welfare of a society is conceptually, not to speak of the difficulties of measuring it. Theoretical economists like their life simple and assume these problems away. A critical assessment of social welfare measurement is in Dasgupta (2001). 2 An exposition of this field, which is particularly well accessible for the non specialist, is in Dixit and Skeath (1999).

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Traditionally, game theory did not have a significant role in environmental economics. The reason is as follows: the theoretical basis of traditional environmental economics is the idea of an unregulated market economy. It has been shown that under some (rather restrictive) conditions the equilibria of this economy are socially optimal.3 This fundamental theorem of welfare economics is, among others, due to the work of K. Arrow and G. Debreu who were awarded the Nobel Prize in 1972 and 1983, respectively. If externalities are introduced into this setting, market failure results, i.e., equilibria are no longer socially optimal even if the economy is perfectly competitive. In economics, environmental problems are considered to be an application of market failure due to externalities. Following the traditional line of thought of welfare economics, it is the role of the state (government) to diagnose market failure and to make amends. The state is supposed to act as the keeper of the common good and, as such, must design instruments which are able to restore the social optimality property of private market equilibria. These instruments are called strategies to internalise externalities. The most well-known internalisation strategy is the Pigouvian Tax which would make each externality generator pay a per unit levy equal to the marginal external cost generated by his/her activity in the socially optimal situation.4 It is crucial in the context of the lacking role for game theory that there is a very clear cut hierarchy between the policy maker (the state) and the polluters, i.e., the government rules and the polluters obey. In this strict regulatory setting there is not much room for interactions between the state and those who are regulated, and interactions are all that game theory is about. There is no doubt that on the basis of these ideas, which are completely in line with traditional welfare economic thinking, a lot of progress has been made in environmental economics.5 Nevertheless, it must be observed that this simple regulatory approach is not suitable for the analysis of many important aspects of environmental problems and policies.


Public choice theory has doubted the relevance of the welfare economic idea of the state for quite a while. As a counterpoint, public choice theory models the state as an institution which is operated by decision makers who pursue their own private interests. These decision makers are politicians and bureaucrats. They are influenced by economic and social interest groups and supervised by (imperfect) democratic institutions. Compared to the traditional welfare economic approach, public choice sheds a completely different light on environmental policy (and any other policy). Here, environmental policy is no longer the materialisation of a higher wisdom at the service of the common goal but the result of interactions between organised social interests in the corridors of power (Dijkstra 1999). If we change from the traditional welfare economic view (ideal) of the state to the public choice interpretation, 3

Social optimality is defined here following the Pareto-criterion. On these issues, see any intermediate or advanced microeconomics text book, e.g., Varian (2003). 4 The idea dates back to the work of A.C. Pigou in 1920. Today it is part of the folklore of environmental economics. 5 Today most environmental economics’ contributions use this kind of approach, even though modern texts also include game theoretic methodology. (Endres 2000; Hanley et al. 2001; Hussen 2000; Kolstad 2000; Russell 2001).

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then there is an obvious role for game theory. Social interest groups are interactive agents in the political arena and their behaviour may be explained by game theoretical analysis.
Contrary to the simple regulatory model sketched above, compliance of polluters to governmental regulations may be incomplete. The reason is that the degree of compliance cannot be perfectly observed, i.e., there is asymmetric information between regulator and regulatees. The decisions of a firm to comply to regulations as well as to disclose private information and the decision of the regulatory agency to perform costly monitoring activities are interdependent. They may be modelled and explained by game theoretical analysis.
Many environmental problems are transboundary or even global. For these problems there is no supranational agency which would be able to take on the task assigned to the state according to the traditional welfare economic approach. International environmental problems are typically generated by many sources in many different countries and have to be taken care of by voluntary agreements between sovereign decision makers. To make things even more complicated, there is no international judicial system powerful enough to guarantee compliance to international environmental agreements. The welfares of the involved states are dependent upon each other just like it has been sketched above in our description of game theory’s object. Of course, what an individual government decides to concede in an international convention depends on what the other signatories concede and who these signatories are. Also the decision on whether or not to comply with a given treaty depends on the extent of the other parties compliance.6 Of the three areas introduced above the following analysis concentrates on the third one. We further concentrate on the polar case of transboundary environmental problems, i.e., global environmental problems. It is considered to be particularly relevant for present and future environmental policy and is also the most active area of research regarding the application of game theory to environmental problems.7

6 Since supranational jurisdiction is too weak to enforce, international environmental treaties are non-binding in an economic sense. The part of game theory dealing with non-binding contracts is called non-cooperative game theory. So even if it may sound somewhat inconsistent to readers from other disciplines (than economics), we try to explain cooperation using noncooperative theory. 7 There is an enormous and rapidly increasing amount of literature in this field. To mention a few among the many, see Bo¨hringer, Finus and Vogt (2002), Finus (2001), Schmidt (2000), and Schulze and Ursprung (2001). These references relate to books only. Journal articles are so numerous that this author’s confidence is too weak to allow for a selection and recommendation. (Also, there is a limit to the number of self-citations!) Among the most influential journals to be consulted, specialised journals include the Journal of Environmental Economics and Management, Environmental and Resource Economics as well as Environmental Economics and Policy Studies. Among the more general journals in which game theoretical analyses of environmental problems may be found are the Journal of Public Economics and Public Choice. However, most of the articles therein are relativley hard to access for readers from other disciplines.

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2 Global environmental problems as a prisoners’ dilemma The simplest way to game theoretically deal with global environmental problems is to model them as a static prisoners’ dilemma. The idea of a global pollutant is defined by the assumption that it diffuses uniformly around the world. Therefore the adverse impact that it has at any point on the earth does not depend upon the location from which it was emitted. Due to these properties, the global pollutant is an example of a pure public good. Since it creates a disutility, it is a ‘‘good with a negative sign’’, which is sometimes called a ‘‘bad’’ in the economics literature. Of course, the good (‘‘with a positive sign’’) creating a global benefit is the reduction of the aforementioned pollutant. The economic theory of voluntary (decentral) provision of a pure public good predicts market failure: global environmental quality will not be sufficiently provided by the countries of this world decentrally. To keep things simple, consider only two states (groups of states) and observe the dismal incentives of the prisoners’ dilemma in global environmental protection. Following the joint interests of all countries (the ‘‘one world’’-approach), each country has to contribute to improve global environmental quality. Behaviour of a country which is in accordance with this goal is called cooperation ( C ). However, each individual state is subject to the incentive to act as a free rider on the other states’ contributions, i.e., to refrain from cooperation. This behaviour is called defection ( D ) in the literature.8 Putting these problems into a somewhat more formal language, the first important property of a prisoners’ dilemma situation is that the aggregate welfare of the involved states is maximised for a constellation of activities CC. The second property is that, for the welfare of each individual state, the ranking WDC > WCC > WDD > WCD

ð1Þ

9

holds. The dilemma is characterised by defection being the dominant strategy for each state, i.e., whatever one player does, the best response for the other player is to defect. Since this dismal incentive is valid for both players, they end up in an equilibrium of bilateral defection (DD). In this equilibrium, welfare (and global environmental quality) is suboptimal. If the two states are unable to make

8

In this simple exposition the choice of an individual state is between ‘‘cooperation’’ and ‘‘defection’’ only. Of course, the situation can be modelled as choosing the level of a continuous emission variable. Also, the globally optimal situation is not necessarily defined by each country simply ‘‘cooperating’’, as assumed above. Socially optimal levels of emissions reductions can be modelled as continuous variables in the more sophisticated exposition. The dichotomous choice model is chosen above for simplicity only. The fundamental results are not changed by this simplification. 9 The symbol W stands for the welfare of the country under consideration. The first letter in the subscript, denoting the activity combination of the two states, indicates what the state does whose preference ordering is shown here. Thus, DC denotes a combination with the first state defecting and the second cooperating. The first state prefers this constellation to one where both states cooperate. Accordingly, WDC denotes the welfare of the first country if it defects while the other country cooperates. Of course, this interpretation analogously holds for the other state.

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a binding agreement, they cannot escape this suboptimal situation even though they know that they both would benefit from bilateral cooperation (CC). The dilemma situation briefly sketched above has been extremely influential in the game theoretical literature. It defines the pattern whereby economists have understood the problems of decentral provision of public goods in general, and of global environmental quality in particular. Even though the prisoners’ dilemma is still a powerful idea in the economics of public issues, economists did not completely stick to it for the following reasons.


Contrary to what certain bad-mouths say, economists are not exclusively concerned with their theoretical models. Sometimes they venture to look at the real world. There (again, sometimes) they observe cooperative behaviour in the private production of public goods. This is also true in the area of global environmental problems. Some members of the international community struggle for cooperation and there is some success in global environmental policy. Even if these cooperative efforts are considered to be exceptions to the rule, economists feel uneasy that their standard model is unable to give an economic explanation for this behaviour. Economics loses some competitive edge in the noble rivalry among different social sciences concerning who has the most powerful model to explain the world if cooperation in the decentralised provision of public goods cannot be explained by economics.
In those wide areas (including most global environmental problems) where international cooperation is insufficient, economists want to help to make amends. They are eager to give advice to political decision makers regarding the design of institutional frameworks under which the chances for cooperation improve. There is also some competition for the role of political advisor between different social sciences (and within each individual social science).10 Looking at these two reasons for economists venturing into the field beyond the prisoners dilemma, one is reminded of a famous dictum by K. Marx and tempted to conclude: ‘‘Economists do not understand interpreting the world and changing it to be an alternative. They want to do both!’’ 3 Generalisations of the game structure 3.1 Introduction Any model must be ‘‘unrealistic’’ in the sense that it fails to cover many aspects which are important in the real world. The fine art of model building concerns the prudent choice of which aspects of the real world to include in the model and which ones to leave out. Given that, an optimal degree of abstraction has to be chosen. Of course, what is to be considered ‘‘prudent’’ and ‘‘optimal’’ depends upon the context within which the model is used and upon what the model is 10 We emphasise competition among different social sciences above. Following a modern understanding of this concept, it does not contradict cooperation between these different schools of thought. (‘‘Co-petition’’). To the contrary, interdisciplinary cooperation is one of the most promising (but also winding) roads to scientific progress and better policy advice regarding environmental and sustainability issues.

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supposed to explain. The design of the model also depends upon the scientific state of the art at the time of its construction. The static prisoners’ dilemma is still useful today since it is able to explain the fundamental incentives of dilemma situations in a didactically efficient manner. However, a cost benefit analysis of possible extensions of this fundamental model leads to promising results; using recent developments in game theory the model can be extended with little effort. Thereby a considerable increase in the model’s explanatory power is gained. There are two specific properties of the standard prisoners’ dilemma which call for improvement by generalisation, namely, the model is static, and the model assumes that payoffs are given and known to the players. Regarding both properties, the model has been generalised in the literature. Allowing for dynamics and risky payoffs makes the structure of the model more similar to the situations in which actors of the real world make their decisions. It has been shown that these generalisations have strong impacts on the equilibria produced by the players in the game.11 3.2 Dynamic games Moving from the static prisoners’ dilemma to its dynamic version, it must be decided upon whether the planning horizon of the actors is considered to be finite or infinite. It has been shown that there is not much change regarding the equilibria of the game if the planning horizon is finite and the actors know in which period the game will end. Changes from the static to the dynamic prisoners’ dilemma are more significant if the planning horizon is supposed to be infinite. In this setting, cooperation in the voluntary and decentralised production of a public good, e.g. the reduction of global pollutants, is an equilibrium strategy under certain conditions. One of these conditions is that future effects of the decision on whether to cooperate on the welfare of the decision maker are not discounted ‘‘too strongly’’. Another important condition is that cooperating countries are willing (and able) to ‘‘punish’’ defecting countries. The punishment strategy which most simply explains the fundamental idea is the trigger strategy. Using this strategy, cooperating states turn a defecting state into an ‘‘outcast’’ in that they decide to refrain from cooperating with this state for all times. Given that, the ‘‘cost benefit analysis of defection’’ for any given state can be briefly explained using the terminology introduced above. Beneficial to the defecting country is the surplus of national welfare that the strategy combination DC yields for this country compared to the constellation CC in the period of defection. The price that the defecting country pays for reaping this benefit is that the other country refuses to cooperate, for all future periods, starting with the period after defection. That is, defection in the first period leads to the result that in the following periods the activity constellation DD occurs instead of CC. The cost of defection is the aggregate welfare forsaken by attaining DD instead of CC calculated for all future periods. 11 If complications of the model do not change the results, these complications should not be introduced into the model. Otherwise the model would be inefficient.

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Obviously the rate with which future effects of present actions are discounted by the decision maker is crucial to whether the country decides to defect. If the discount rate is not too high, then the infinite stream of future welfare reductions caused by present defection overcompensates the benefits of defection gained in the first period. In this case the country will decide to cooperate. Of course, these reasonings analogously hold for any country. The problem with this didactical explanation is that punishment according to the trigger strategy may be considered irrational since the punishing states do not only punish the defecting country but also themselves. This is so because by using the trigger strategy the punishing countries forego their own benefits of cooperating with the country rendered an outcast. However, even though the trigger strategy may be frowned upon, the results of the model using this strategy are quite robust. In recent literature, punishment strategies have been designed which are rational for everyone involved and lead to the result that has been sketched above using the trigger strategy. With a sufficiently low discount rate and an infinite time horizon cooperation, a dynamic game with a prisoners’ dilemma incentives structure is an equilibrium (Finus 2001). 3.3 Risky payoffs In the traditional prisoners’ dilemma setting, payoffs are certain and known to the players. We now deviate from this assumption and suppose that the involved countries know the probability distribution of the payoffs.12 Thereby we move from the simple static prisoners’ dilemma to a game which has the payoff structure of this game in terms of the expected values of these payoffs. It turns out that the risk preferences of the involved countries are crucial for the equilibria in this game. Given that the decision makers are risk neutral, there is no change compared to the traditional setting. However, using risk averse agents has tremendous impact (Endres and Ohl 2000, 2002). To analyse the welfare effects of risk averse countries, means and spreads of payoffs resulting from different strategy combinations must be observed. The most simple way to deal with this problem is to assume that countries strive to maximise a risk welfare function of which means and spreads are elements. The question of how means depend upon strategy combinations is answered by the assumption that we are dealing with an expected prisoners’ dilemma. Putting it a little more formally, this comes down to transforming Eq. 1 above into lDC > lCC > lDD > lCD :

ð2Þ

Regarding the question of how spreads depend on strategy combinations, there is no easy answer. However, it is suggestive (even if not imperative) to assume that uncertainty decreases with the degree of cooperation. Applied to the 12 It should be noted that introducing the second complication into our model (i.e., uncertainty), we relinquish the first complication introduced in the section above, i.e., dynamisation. For matters of simplicity, each complication is dealt with as the only complication within a model which is the standard one in all other respects. Of course, in a more sophisticated exposition model complications may be combined.

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problem of global warming this would be the assumption that the standard deviation of the effects of different temperatures decreases if the efforts to stabilise the climate are successful. Given that and using r as a symbol for the spread rDD > rCD ¼ rDC > rCC ð3Þ follows.13 It should be noted that the size of the spread is negatively correlated with national welfare for risk averse countries. Since the spread increases with the degree of defection, risk aversion puts a break on the incentive to defect compared to the unconstrained attractiveness of defection in the static prisoners’ dilemma with certain payoffs. Therefore, in the model of the expected prisoners’ dilemma with risk averse agents there are two countervailing tendencies at work. On the one hand, each country is tempted to defect because the expected value of its own national welfare is increased by defection. On the other hand, it is attractive to cooperate since cooperation decreases the standard deviation of national welfare. It is intuitively clear (and confirmed by formally deriving the equilibria of the game) that the incentive to cooperate increases with the degree of risk aversion in the countries’ preferences. It can be shown that cooperation is an equilibrium in an expected prisoners’ dilemma game if risk aversion exceeds a certain threshold. For certain degrees of risk aversion the incentives of the expected prisoners’ dilemma game are transformed into the incentives of a chicken game, which exhibits a unilateral incentive to cooperate, or a no conflict game (providing a bilateral incentive to cooperate). 3.4 Consequences It follows that the extremely pessimistic assessment regarding the possibility of cooperative equilibria under the prisoners’ dilemma framework is at least in part due to the quite restrictive assumptions of the traditional model. If this model is generalised in that the factors time and uncertainty are integrated, the horizons for cooperation brighten to a certain extent. This statement, however, is not to be confused with a statement saying that cooperation in the prisoners’ dilemma is no problem if the model is specified correctly. To the contrary, even in its modern formulation cooperation is an equilibrium only if certain requirements are met. As previously stated, in the dynamic case an efficient punishment system must be installed and discount rates must not be too high. In the model allowing for uncertainty, agents with a sufficiently high degree of risk aversion as well as a certain correlation between cooperation and the spread of the risk involved, have been shown to be requirements for cooperation. There has been considerable discussion in the literature on how incentives for cooperation may be enhanced.

13

rCD=rDC means that countries are assumed to be symmetric.

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4 How to increase the propensity to cooperate 4.1 Internal incentives for participation and stabilisation Above we have used the trigger strategy as an example for the method to punish defection. There are other means to increase the attractiveness of cooperation which are designed to induce countries into entering agreements for cooperative behaviour and to comply with these agreements.14 These internal mechanisms for participation and stabilisation share the idea to make cooperative behaviour of any country contingent upon cooperative behaviour of any other country. If one country infringes upon an agreement to cooperate the agreement is no longer binding for the other countries. The different variants of the idea of internal incentives for cooperation differ from each other by the assumptions on how the involved countries use this leeway. In addition to the trigger strategy (supposing that the other states cease to cooperate for all times with the contract breaching country), the following options are discussed in the literature. 4.1.1 Re-optimisation If countries decide to join their efforts to reduce global pollution they must decide upon how much each state contributes in terms of its own emission reductions. The equilibrium reduction quantity (the quantity a welfare maximising state endorses) depends on how many states cooperate. For each given size of a ‘‘coalition’’ a different equilibrium emission reduction for each cooperating state exists. Therefore, if one country switches from cooperation to defection the emission reduction quantities of the remaining states are no longer optimal for the smaller coalition. The re-optimising strategy says that states are not obliged to their emission reductions that have been equilibria before the defecting state left. Under conditions which are not very restrictive, the result will be that the members of the now smaller coalition expand their equilibrium emission levels (Finus 2001). This can be regarded as a punishment for the exiting coalition member since it is now suffering from increasing global pollution. This sanction is credible since it is a result of the welfare maximising behaviour of the states remaining in the coalition. However, closer inspection reveals that the effects of this strategy to stabilise coalitions are limited. Unfortunately, in cases where joint effort is particularly desirable only coalitions with small membership can be stabilised (Barrett 1994a). 4.1.2 Expanded tit-for-tat-strategy To begin with, this strategy is the same as the re-optimisation strategy sketched above. However, the defecting state is admitted back into the coalition after having shown sufficient ‘‘remorse’’. Sufficient remorse may be demonstrated by accepting a fine or an excessive emission reduction obligation. 14

The incentive to participate in an agreement is called the individual rationality of the agreement. The incentive to comply is called the stability of the agreement.

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It can be shown that by using this strategy results are somewhat better than with pure re-optimisation, but success is still limited to stable coalitions with quite small membership (Finus and Rundshagen 1998).15 4.1.3 Ratification Using this mechanism an international contract is not effective before a certain number of signatories ratifies.16 This strategy is supposed to provide a double incentive to participate in cooperation, i.e., a cooperating state does not have to worry about being caught in a CD-situation. A CD-situation would be one in which this state engages in costly reduction activities which turn out to be in vain because the other states defect.17 On the other hand, any defecting country puts the whole agreement into jeopardy by missing the minimum requirement of the number of ratifying states. Unfortunately, an incentive to ratify is not the same as an incentive to comply.18 The link between ratification and compliance is closer when the obligations accepted as part of an international agreement are transferred into national law. Again, ratification strategies enhance incentives to cooperate, but they are not strong enough to provide a general solution to the prisoners’ dilemma. 4.2 External incentives for participation and stabilisation Economists have been aware that the above mentioned internal mechanisms are useful but insufficient. Therefore, additional means have been developed. 4.2.1 Transfers In economics the most popular instrument to harmonise the activities of agents (from individuals to whole countries) with diverging interests is money transfers. This instrument can be used to make individuals strive for the common goal. In terms of economics the common goal is the social optimum which is defined by the aggregate welfare of all involved parties being maximal. Of course, it is not true that every individual decision maker benefits by a move from a socially suboptimal to a socially optimal situation. There may be winners and losers. However, by definition of the social optimum the aggregate profit of the winners must be higher than the aggregate loss of the losers. Therefore, it is conceptually possible for the winners to use parts of their profits to at least compensate the losers. For any move from a socially suboptimal situation to a socially optimal one there exist schemes of transfer payments under which everyone benefits from 15

Strictly speaking, the expanded tit-for-tat-strategy is not a pure internal means of stabilisation. This is so because it uses fines. They are beyond the idea of making cooperative behaviour of any state contingent upon cooperative behaviour of any other state. 16 The most well-known practical example for this kind of a mechanism is the Kyoto-agreement. See Faure, Gupta and Nentjes (2003) on the (law and) economics of this protocol. 17 CD is in the last slot of Eq. 1, ordering alternative situations according to their attractiveness. 18 Indeed, compliance with many ratified environmental agreements seems to be poor in practice (Endres, Finus and Lobigs 2000). (This article is in German but contains an English summary and points to further readings on this subject which are written in English.)

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the move.19 Applied to the problem under consideration in this paper this means that countries benefiting from a globally optimal environmental agreement would have to, at least, compensate the losing countries. However, implementing this wonderful Coaseian idea turns out to be a Herculean task. For the countries benefiting from the optimal environmental agreement, the emissions reductions provided by the receivers of these payments are a public good. That is, given that receiving country A reduces global pollution by a certain amount, the benefit for a paying country B does not depend on how much B contributed to the aggregate payment. In this setting it is highly difficult for the paying states to agree upon a scheme according to which each individual state is obliged to contribute. As with any attempt to arrange the provision of a public good on a voluntary and decentralised basis, severe free-rider-problems are expected to arise (Barrett 1994b). It has been noted above that, unfortunately, there is no powerful supranational judicial system able to enforce environmental agreements. This is also true regarding agreements involving compensation payments of some countries for emissions reductions of other countries. It is far from being trivial that the involved countries will always comply to what has been agreed upon. Strictly speaking, transfer payments as a means to stabilise agreements on emissions reductions themselves need stabilisation. Game theoretical models with transfer payments suppose that each involved country can measure its own benefits and costs of emissions reductions. In most models it is also assumed that the government knows the benefits and costs of each country involved. With these assumptions it is no problem, in principle, to decide upon which state has to pay a (marginal) compensation payment to which other state to serve the goal of social optimisation.20 In real life, country specific cost and benefits are not known. Since these are the basis for calculation of transfer payments there are incentives for strategic behaviour of the individual government. The portfolio of opportunistic behaviour ranges from the dissemination of biased information in the international bargaining process to the choice of suboptimal reduction policies and reduction technologies. These measures might be chosen by a country in order to qualify for receiving transfer payments.21 Things get even more complicated if the behaviour of states cannot be described according to the economic understanding of social welfare maximisation. Using monetary costs and benefits in global environmental policy is plausible to most economists. It does not follow that politicians behave accordingly. Some of the problems mentioned above are due to the fact that transfers have been supposed to be in monetary terms. Accordingly, other forms of transfers have been discussed in the literature. The most popular issue is transfer of environmental technologies to developing countries. It is thought that the 19

In terms of economics these transfers turn a potential pareto improvement into an actual one. This is the essence of the famous Coase Theorem. Of course, the Coase Theorem requires that transaction costs are zero. Ronald Coase was awarded the Nobel Prize in economics in 1991. 20 In the model the only matter of dispute among the countries is how the rents generated by moving from the suboptimal starting point to the social optimum are distributed. 21 See Buchholz and Konrad (1994) on these strategic issues.

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probability of misuse is reduced, compared to monetary transfers. Still, it is not granted that environmental technology, even if provided free of charge, is actually used (and used as directed) in the receiving countries. This is particularly true if this technology is additive instead of being integrated into production technology. 4.2.2 Issue linkage Game theorists have found it intellectually very attractive not only to design a single contract incentive compatibly but to combine different contracts with each other. The idea is that each contract helps to stabilise its counterpart. However, contracts tied together must exhibit certain properties to make this idea work. Ideally, the country losing from joining a socially optimal environmental contract is the net winner from the other contract. However, it is easier to specify a pair of contracts which meets this requirement in a theoretical model than to find one in practice. This is particularly so if contracts are not only bilateral but multilateral. 4.2.3 Sanctions Sanctions have been briefly mentioned in the context of the extended tit-for-tatstrategy above. In practice the most common form is sanctions in international trade. Here, countries which do not join an environmental treaty or do not comply with what they have agreed upon are threatened with exclusion from international trade with the ‘‘coalition states’’. There are two problems with trade sanctions. First, the punishing states might also punish themselves by their action. If so, the threat to use trade sanctions suffers from low credibility. Moreover, it is difficult to distinguish trade sanctions against breach of international environmental contracts from pure protectionism. There is a danger that the former serves just as a pretext to practice the latter (Kirchga¨ssner and Mohr 1996).

5 Instruments of international environmental policy 5.1 Introduction Above we have modelled the decision problem of a country in the global environmental context as an issue of dychotomic choice. Countries choose between cooperation and defection. Of course, in reality the spectrum is much broader (see footnote 8). Countries might use alternative instruments of environmental policy (or combinations thereof) and decide upon the degree to which they apply these instruments. For simplicity we concentrate on two alternative instruments as objects of international environmental negotiations. The countries must decide whether to negotiate equal (percentage) emission reduction quotas or the rate of an internationally applied emissions charge. From the point of view of traditional environmental economics it is quite clear that the emission charge is the superior

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instrument. This is due to the fact that the charge is efficient and the quota is not.22 Surprising to some, this fundamental insight of traditional environmental economics does not always hold in the international arena. 5.2 Institutional constraints Consider the case where the countries negotiate using one of the two instruments. Assume further that no transfer payments, issue linkage and the like, are used. Then, it is plausible that the countries use the principle of ‘‘lowest common denominator’’ to decide upon the level of the tax rate or the size of the reduction quota.23 The equilibrium tax rate and equilibrium quota are defined by the state as having the lowest net benefit from applying these instruments. This state would not agree to a marginal extension of the tax rate or reduction quota. In order to assess whether it is better to use an emissions tax or an emission quota in terms of aggregate social welfare two criteria have to be considered. The first is efficiency, i.e., for any given aggregate emission reduction, what are the involved abatement costs using the effluent charge compared to using the quota? Second, how high is the aggregate emissions reduction quantity that results from an agreement in which emission taxes are used compared to one which is on emission quotas? Regarding the first criterion, the emission tax has a clear cut advantage. Generally, for any quantity of emissions reduction the involved abatement costs are lower using the tax rather than the quota. Things are ambiguous, however, regarding the second criterion. Under certain conditions the involved countries agree upon a higher aggregate emission reduction if they negotiate quotas rather than if they negotiate tax rates. If this is true, this ‘‘quantity effect’’ working in favour of the quotas may overcompensate the efficiency effect, working in favour of taxes, in terms of social welfare. Then, it is advisable for the international community to concentrate on quotas instead of taxes (Endres 1997; Endres and Finus 2002). The rationale for the result that conventional environmental economic wisdom does not necessarily hold in the international arena is as follows. Traditionally, environmental economists assume the existence of a government designing and enforcing environmental policy. In this setting it is consistent to assume that the government fine tunes the level at which the two instruments under consideration are applied such that the government’s predetermined goal of aggregate emissions reduction is achieved no matter whether taxes or quotas are used. Therefore the ‘‘quantity effect’’ achieved with these two instruments is the same. The only effect which distinguishes the two instruments is their efficiency where taxes are always superior to quotas. This leads to the conclusion of the overall superiority of taxes. This reasoning no longer holds if applied to the international arena. There is no supranational institution able to prefix the aggregate emissions reduction no 22

An instrument is efficient if it achieves the pre-specified goal of aggregate emissions reduction with minimum abatement cost. Only in the special case of all polluters exhibiting identical marginal abatement cost functions, the two alternative instruments are equally efficient. 23 Since negotiations are voluntary, no country can be forced to agree to a contract which reduces its welfare. If countries do not give up national sovereignty (like they did, in part, as members of the European Union), votes must be taken unanimously.

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matter which instrument is used. On the contrary, the aggregate goal must be agreed upon by sovereign countries and it turns out that the level of this goal is contingent on environmental policy design. Therefore the assessment of alternative instruments of environmental policy is ambiguous in this context. 5.3 The role of risk preferences We have argued that an expected prisoners’ dilemma game may be transformed into different types of games if countries are risk averse and strive to maximise a risk welfare function. This has important consequences regarding the comparison between alternative policy instruments like emission taxes and emission quotas (Endres and Ohl 2000, 2002). The two instruments not only differ in terms of their efficiency, as mentioned above, but also in terms of their ecological accuracy. Using quotas, emission quantities are the direct object of regulation. Opposed to that, using effluent charges, the regulation determines the ‘‘price for pollution’’. The effect of a given tax rate in terms of emission quantities is a matter of how the polluters adjust to the tax rate.24 Therefore, the risk to miss a prespecified goal in terms of aggregate emissions reduction is much higher using charges compared to quotas. If countries are sufficiently risk averse the higher accuracy of quotas may overcompensate the higher efficiency of taxes in terms of aggregate welfare. Closer game theoretical analysis reveals that states may play different kinds of games using different policy instruments. It is possible that they play a prisoners’ dilemma game using the emissions tax and a game with a higher incentive to cooperate using quotas. This may be a chicken or even a no conflict game. It is plausible that it may be better to play an inefficient game where the optimal outcome of this game can be obtained, rather than playing an efficient game (which by definition has a higher optimal outcome) in which this optimal outcome cannot be achieved due to the dilemma structure of the game.

6 On methodology and future research It is sometimes appropriate to analyse environmental problems and policy with an emphasis on the interaction of different decision makers and groups of decision makers. This kind of analysis is at the heart of game theory. Applying game theoretical models to global environmental problems led to ‘‘an explosion’’ of environmental economic literature and opened up new horizons of understanding and policy advice. On the other hand, many problems remain to be solved as has been elaborated above. Let us briefly point to some of the roads that further developments might take:


Game theory requires that actors are highly rational. It is well known that people do not always behave in experiments (not to speak of real life?) as they are supposed to behave according to the game theoretical dogma.25 Therefore game theoretical analyses, generally, and particularly the ones applied to 24

How they do it is explained in any environmental economics textbook (see footnote 5). See the works of H. Simon, D. Kahneman and V. Smith who have been awarded the economics Nobel Prize in 1978, 2002 and 2002, respectively.

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global environmental policy must be extended to allow for bounded rationality. Of course this is easier said than done. Perfect rationality is certainly a restrictive concept. However, it is a clear one. This cannot (yet) be said about bounded rationality. There is no concept here that is generally superior to the traditional economic concept in terms of its ability to explain real world behaviour.26 Most game theoretical models suppose that countries behave as if they would want to maximise a national welfare function. Apart from the problems of the rationality assumption indicated above, it is notable that this approach ignores the influence of interest groups on policy. Integrating public choice analysis with the game theoretical approach is a promising line of research (Bo¨hringer, Finus and Vogt 2002). A third deviation from the assumption of the welfare maximising government would be to introduce additional elements into the objective function of the political decision maker. It has recently been argued that the acceptability of an agreement does not only depend on the agreement’s consequences for the contractor in terms of welfare. It may also be important whether the involved parties consider it to be just. It would be interesting to analyse the behaviour of decision makers with ‘‘preferences for fairness’’ as negotiators in the international environmental arena.27 International environmental coalitions have been mostly analysed using the simple concepts of external and internal stability, implied above. The consequences of different forms of membership rules and different decision mechanisms within the coalition must receive greater attention by game theoretical analysis.28 In game theoretical models countries interact in a setting which prevents agreements from being binding. This may be an admissible simplification to start with. However, it should not be ignored that in reality countries are tied up with each other in a multidimensional web of bounds with differing intensity and reliability. This ranges from completely non obligatory declarations to partially relinquishing national sovereignty. Sometimes the relationship between states develops over time by increasing commitments. (The evolution of the European Union is an example; see footnote 23). In this process, information is generated, reputations and trust are being built up (or destroyed) and preferences are changed. The analysis of these kinds of processes is among the most challenging and most attractive future tasks of game theory.

However, there is some progress in this respect. See e.g. Rubinstein (1998), Gigerenzer and Selten (2001). It is sometimes surprisingly difficult to draw the line between perfect rationality and bounded rationality. See Lipman (2002). 27 Among the first approaches using game theory to apply this idea to the economics of global environmental problems is Lange and Vogt (2003). 28 See Carraro (2003) and Finus, Altamirano-Cabrera and van Ierland (2004) on these issues.

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