This is Volume 2 of the Series: Annals of the International Society of Dynamic Games
The goal of the book is more normative than descriptive. All papers include careful modelling of the dynamics of the main variables involved in the game between nature and economic agents and among economic agents themselves, as well-described in Vrieze's introductory chapter. Furthermore, all papers use this careful modelling framework to provide policy prescriptions to the public agencies authorized to regulate emission dynamics. Several diverse problems are addressed: from global issues, such as the greenhouse effect or deforestation, to international ones, such as the management of fisheries, to local ones, for example, the control of effluent discharges. Moreover, pollution problems are not the only concern of this book. A correct, sustainable exploitation of renewable natural resources is also the objective of some analyses and policy recommendations (see, for example, the papers by Yeung and Kaitala-Munro). A common theme can be found throughout the book. There is recognition that an environmental problem and its interrelationships with economic activity and the dynamics of eco-systems are very complex and cannot be resolved with simple policy tools. Instead, it is necessary to use properly designed policy-mixtures in which several policy instruments are set at their "optimal" levels. Hence, policymakers both at the national and international level should debate over policy interventions which account for the interdependence between several tools and objectives in a dynamic framework, in order to prevent the economic and natural systems from taking unsustainable development paths.
Notice the importance of a dynamic analysis of environmental issues. The concern for future generations (explored in Beltratti's paper), the role of the assimilative capacities of nature (see Cesar and de Zeeuw's paper), the importance of irreversibilities (as in Tahvonen's work) and of capital stock's accumulation (cf. Xepapadeas' and Moretto's articles) are some of the elements that make it impossible not to use a dynamic framework when studying environmental problems. Moreover, the dynamic framework is often coupled with a game-theoretic one. This is a consequence of the natural context in which regulators' and polluters' decisions are reciprocally interdependent. However, more subtle reasons are proposed in the book. For example, the interaction (game) among polluters may prevent traditional emission charges from being completely effective, thus calling for other policy tools (see, among others, Carraro-Topa's and Ligthart's papers). In a different way, interactions among governments at the international level may offset, through the so-called leakage effects, unilateral efforts to reduce greenhouse gas emissions, thus calling for internationally coordinated policies (see, for example, the papers by Haurie-Zaccour and Kaitala-Pohjola).
The book is divided into three parts. The first part is devoted to models of global change and sustainable development. It contains recent contributions in the field of dynamic modelling of global warming and global environmental management, including issues of sustainable development, international policy coordination and optimal growth with limited renewable natural resources.
More precisely, in the paper "Differential Game Models of Global Environmental Management," A. Haurie and G. Zaccour deal with the modelling of economy-environment interactions for several countries which are assumed to behave competitively for the control of their own economic processes, but have to achieve jointly a common environmental management goal. In the first part of their paper, Haurie and Zaccour treat the modelling of issues related to process dynamics and players' interactions respectively. They discuss the control theoretic approach for representing the economic and pollution processes in a model of environment management, and also give a short discussion of a possible representation of uncertainty and risk in these models. The second part of the paper proposes a dynamic game modelling approach which combines the N-person equilibrium model with coupled constraints and the differential game model with active and passive players. This approach enables the authors whose strategies are such to define a tax scheme which induces a set of equilibrium seeking players to achieve, in the long run, a global environmental goal.
The second paper of the first part, "Sustainability and the Greenhouse Effect: Robustness Analysis of the Assimilation Function" by H. Cesar and A. de Zeeuw, faces the issue of global environmental management and sustainable growth by focusing on the role played in dynamic environmental models by the assimilation function. In most existing optimal control models with an environmental stock it is generally assumed that the assimilation function of nature is linear. At the same time, however, there is quite some scientific uncertainty on the general form of this function outside a specific range of values. In their paper, Cesar and de Zeeuw consider different (non-linear) specifications of the assimilation function in the case of the greenhouse effect. The optimal trajectories and the steady states are analysed for the various functional forms. Slight variations in the assimilation function can result in a dramatic change in the steady state values. Besides, neither multiple equilibria nor the absence of non-zero production steady states can be excluded. Hence, this paper provides useful information on the sensitivity of dynamic environmental analyses on the specification of the assimilation function of nature.
A similar robustness analysis is carried out in "Consumption of Renewable Environmental Assets, International Coordination and Time Preference" by A. Beltratti, in which a two-country linear-quadratic model of depletion of a renewable resource is studied both in static and in dynamic terms. The model allows for negative consumption externalities through the action on the stock of the environmental good, which enters the utility function. The main result of the paper shows that the noncooperative solution of the dynamic model is characterized, in the steady state, by suboptimally low levels of environmental resources and consumption, thus providing incentives for international cooperation. The robustness of this conclusion is then checked with respect to several parameters defining the structure of the economy. In particular, attention is given to the rate of intertemporal time preference, a parameter which captures the preference for future generations' welfare of present governments. It is shown that the suboptimality of the non-cooperative solution increases with the rate of time preference in a nonlinear way which depends on the other parameters of the economy.
The issue of policy coordination is also the object of the subsequent paper, "Sustainable International Agreements on Greenhouse Warming: A Game Theory Study" written by V. Kaitala and M. Pohjola. It is clear, and is well-described in O. Vrieze's introductory paper, that reducing damages caused by climatic changes requires major international efforts. Many countries bear the view that the joint efforts should be undertaken under international agreements. The paper by Kaitala and Pohjola presents a dynamic game theory model for an international environmental negotiation problem that may arise in the context of global climate change. The basic assumption is that countries differ in their vulnerability to global warming and that two coalitions will possibly be formed. One coalition may include countries that do not suffer from global warming, or where the damages are minor, and the other coalition may be joined by countries that will suffer as a result of global warming. The greenhouse problem is then modelled as an economic infinite-horizon differential game. Countries negotiate an agreement among Pareto-efficient programs by allowing for transfer payments which account for the existing international asymmetric effects of global warming. Transfer payment programs are designed in such a way that it is possible at any stage of the agreement to punish violations against cooperation and to discourage the other player from selfishly polluting the atmosphere. In this context, it is shown that the incentives for international cooperative control of global warming will become stronger and will occur with an increasing frequency.
The last paper of Part 1 of the book, "The Environmental Costs of Greenhouse Gas Emissions" by M. Hoel and I. Isaksen, deals with a crucial issue in environmental negotiations, namely the evaluation of the costs of global warming. An efficient, comprehensive climate policy should balance the cost of reducing emissions of each greenhouse gas against the environmental costs of the emissions of the gas. However, the assessment of these costs is generally a difficult task. In their paper, Hoel and Isaksen show how these environmental costs may be calculated using an optimal control dynamic model. This is first done for the traditional case in which, at any time, one is only concerned about the state of the climate. Then, a more general environmental cost function is considered, for which it is assumed that the rate of climate change is more important for the environment and the economy than the state of the climate. Besides providing a clear presentation of the methodology, the paper also shows, through a numerical example, how the marginal costs of greenhouse gas emissions for both types of environmental cost function can be calculated.
The second part of the volume is devoted to the analysis of the interactions between technical progress, economic growth and environmental protection. The papers included in this second part are characterised by solid micro-foundations, and rely upon recent developments of industrial organisation theory. In particular, the robustness of traditional environmental policy prescriptions to imperfect competition is assessed in several papers. Therefore, this part of the book provides new insight into the optimal environmental policy-mix by showing how several tools may be activated in order to control polluting emissions without excessively damaging economic growth.
In the first paper, "Taxation and Environmental Innovation," C. Carraro and G. Topa propose an industrial organisation dynamic model to analyse the effects of environmental taxation on firms, innovation activity. A regulator is assumed to introduce an environmental tax. Firms may react both by changing output and by adopting a new, environmentally friendly technology. Conditions under which innovation is a firm's optimal choice are provided. The paper shows that firms innovation decisions are not simultaneous even when firms are identical (there exists diffusion). Moreover, firms have an incentive to delay the time of innovation, because the new technology can only be achieved through costly R&D. Hence, there exists room for incentives that move firms to the socially optimal timing of innovation. These incentives have to account for the presence of asymmetric information (the regulator is assumed not to observe firms, innovation costs). In this context, Carraro and Topa show that there exists a family of contracts defined by a pair (time of innovation, innovation subsidy) as to induce firms to behave optimally. The proposed policy-mix (environmental tax and innovation subsidy) is shown to reduce emissions more, and to reduce output less, than environmental policies based on a single policy instrument.
A similar multiple instrument approach to emission control is proposed, within an endogenous growth model, by J. Ligthart in her "Environmental Quality, Public Finance and Sustainable Growth." This paper extends theories of endogenous growth in order to deal with the optimal trade-off between economic growth and environmental quality in a meaningful fashion. Environmental quality is modelled in two different ways: (i) as a given stock which is damaged by a flow of pollution; and (ii) as a renewable resource which is used as an input in production. After a brief discussion of pollution, taxation and the cost of funds, attention is focused on renewable resources in order to come to grips with the concept of sustainable growth. The government reduces the use of natural resources and improves environmental quality by imposing a levy on firms. Economic growth is boosted by productive government spending, but is hampered by distortionary taxes on income or capital. The first-best outcome can be sustained in a competitive market economy only if lump-sum taxes and subsidies are available. In general this is not the case, so the paper focuses on the setting of government policies in a second-best context, showing how different policy instruments have to be combined in order achieve an adequate control of environmental resources.
A careful comparison of environmental policy instruments in microfounded endogenous growth models is also the objective of T. Verdier's paper "Environmental Pollution and Endogenous Growth: A Comparison Between Emission Taxes and Technological Standards." This paper develops a model of endogenous growth with environmental pollution. Firms create, through R&D, new products and also design the environmental features of these products by choosing their output-emission ratios. Cleaner products are assumed to be more costly to develop than dirty products. Using an extension of the expanding variety product of Helpman and Grossman, this paper investigates and compares the effects of emission taxes and technological standards. In particular, in the second best context where R&D subsidies are not possible, Verdier provides a welfare comparison of two instruments, emission taxes and technological standards, for a given pollution target that the policymaker wants to implement in the economy. Under certain conditions, it is shown that an emission tax, acting as an implicit R&D subsidy, may induce too much growth of the polluting industry compared to what is socially optimal. This effect can then reverse the usual cost effectiveness superiority of taxes over technological standards.
The problem of excessive growth induced by environmental policy is also analysed by A. Xepapadeas in his "Rate of Return Regulation, Emission Charges and Behaviour of Monopoly." The well-known Averch-Johnson thesis indicates that the main result of rate-of-return regulation is overcapitalisation. By extending the model to include environmental externalities, this paper assumes that a regulated monopoly can adhere to environmental policy by undertaking investment in pollution abatement equipment, along with investment in output production. In this context, over- (or under-) capitalization effects have a direct influence on the monopoly's emissions. Hence, it becomes crucial to verify whether optimal policy still induces overcapitalisation. Therefore, this paper analyses two related issues. The first is the direction and distribution of the effects of introducing rate-of-return regulation under a given environmental policy on investment in productive and pollution abatement equipment. The second is whether the regulated firm responds in the same manner as the unregulated firm to the introduction of the above environmental policy.
Xepapadeas' paper analyses the impact of environmental policy on the level of the capital stock. By contrast, M. Moretto's paper "Polluter's Capital Quality Standards and Subsidy-Tax Programs for the Environmental Externalities: A Competitive Equilibrium Analysis" focuses on the quality of the capital stock. More precisely, the paper concentrates on the role of the physical features of the fixed assets in determining the extent of discharges. It considers the case where firms have access to a technology which allows them to regulate the quality of capital instantaneously, through a lump-sum maintenance expenditure which applies only when the state variable achieves a predetermined minimum quality standard. In a partial equilibrium framework (single firm and a long-run competitive industry), the paper investigates the relationship between the optimal firm's barrier policy comprising the capital's minimum quality standard and the use of a subsidy/tax program for decreasing pollution emissions by those who generate externalities. Again, the main message is that the complexity of dynamic interactions between economic and environmental phenomena call for "sophisticated" policy measures in which several policy instruments are implemented.
The third part of the book contains several dynamic analyses of issues related to pollution activities in the presence of renewable resources and the stability of the economic and/or ecological system. The stability of a biological system facing damages induced by economic activity is indeed the object of T. Vincent's analysis in his "The ESS Maximum Principle as a Tool for Modelling and Managing Biological Systems." Ever since the advent of DDT and the discovery of mutant strains of mosquitoes immune to DDT, it has been public knowledge that ecosystems can and will evolve in response to human beings' efforts at control. While differential equations have been in common use as management models, it is uncommon to find any such models that attempt to capture the evolutionary game approach to modelling which should provide more realistic application. In order to include evolution into management models, and point out some areas of possible application, we are faced with two fundamental questions: what is evolving? And where is it evolving to? In the evolutionary game theory presented in Vincent's paper, the "what" are parameters in the differential game model associated with characteristics of the species that are clearly adaptive (such as sunlight conversion efficiency for plants or body length in animals). The "where" are the evolutionary stable strategies (ESS) to which these parameters can evolve. These strategies can be determined using the ESS maximum principle. This principle is extended here to include a wider class of models. The ESS maximum principle, when used with appropriate models, has the capacity to predict the evolutionary response of biological systems in response to human inputs. These inputs can include physiographic changes, harvesting, and the introduction or removal of new species and/or resources.
The stability of the ecosystem in the presence of irreversible pollution damages is also discussed in 0. Tahvonen's paper "Pollution, Renewable Resources and Irreversibility." This study shows that irreversible pollution damage leads to nonconvexities in dynamic models. There may exist two locally optimal solutions: an optimal infinite horizon solution (sustainable) and an optimal finite horizon solution. In general, the choice between these optimality candidates must be made by comparing the present values of both policies. However, the study shows that there are special cases where the choice can be made on a priori grounds. In particular, it is shown that including the pollution problems in the renewable resource model changes the ordinary "optimal extinction" results.
Another ecosystem is analysed by V. Kaitala and G. Munro who focus on "The Economic Management of High Seas Fishery Resources." This paper deals with the economic analysis of both "shared" and "straddling" fishery stock management. There are at least two important differences between the analysis of "shared" and "straddling" stocks. The paper designates these differences as: 1) the problem of new entrants; 2) the number of participants or "players." In "shared" stock fisheries management, the number of coastal states, as joint owners of the resource, is fixed. In the case of straddling stocks, on the other hand, the existing Law of the Sea Convention allows, to some extent at least, hitherto non-participatory distant water fishing nations to enter the high seas portion of a straddling stock fishery. If unimpeded access is granted to new entrants, any attempt at cooperative management of a straddling stock may be undermined from the start. With respect to the number of participants or players, most models of economic management of "shared" fishery resources involve but two coastal states or "players." The assumption of bilateral exploitation of the relevant fishery resources proves to be a reasonable one in many real world cases of "shared" fishery resource management.
By contrast, in analysing the management of "straddling stocks," one cannot be content with the assumption that the resource is exploited by one coastal state and by only one distant water fishing nation. The typical "straddling" stock case is one in which a coastal state confronts two or more distant water fishing nations operating in the adjacent high seas. Moreover, the relevant set of distant water fishing nations may change through time. These facts greatly complicate matters and result in the analysis of "straddling" stock management being far more complex than the analysis of "shared" stock management. Given these differences between "shared" and "straddling" stock management, the paper by Kaitala and Munro first reviews briefly the economist's standard model of a fishery. Then it provides a detailed analysis of the case of "straddling" stock in which the coastal state does in fact confront but one distant water fishing nation and in which new entrants are effectively barred forever. This is the "straddling" stock case which most closely corresponds to the typical case of "shared" stock management applies with little or no modification. Next the paper relaxes the assumption of bilateral exploitation of the "straddling" stock, and allows for a situation in which the coastal state confronts three or more distant water fishing nations in the adjacent high seas. However, when the issue of new entrants is addressed, the paper does not even attempt to provide a full analysis. Rather, it provides an initial exploration of this issue, and lays out an agenda for future research.
Pollution management in the industrial sector is the objective of D. Yeung's analysis in the paper "Pollution-Induced Business Cycles: A Game Theoretic Analysis." In this paper, the industrial sector chooses the level of investment to maximise net revenue and the government imposes a tax and uses the tax proceeds for pollution abatement operations. The feedback of pollution on capital accumulation and the effect of the level of pollution on the natural rate of decay are incorporated in the model. The author solves for the (subgame perfect) feedback Nash equilibrium solution of the resulting differential game, and obtains explicitly the game equilibrium accumulation dynamics of capital and pollution. Various properties of the equilibrium follow from this closed form solution. It is found that the game equilibrium output path exhibits continual oscillation about a long run equilibrium level. Moreover, when a constant rate of decay is introduced into the model, damped output cycles appear.
The dynamics of pollution resulting from the solution of a dynamic game between government and polluters are also the outcome of J. Krawczyk's analysis of the management of effluents dumped into a stream by identifiable polluters. In his paper "Management of Effluent Discharges: A Dynamic Model," Krawczyk analyses the game between a Regional Council and some polluting firms, where the Regional Council imposes environmental levies on the polluters whose economic activity, otherwise beneficial for the region, results in pollution of the stream. The game is "played" in discrete time. In the game, polluters are the "followers," whereas the Council is the "leader." This formulation leads naturally to a Stackelberg solution concept for the game at hand. However, because of the obvious difficulties implied by this solution concept, in the paper an equilibrium is sought through the use of an applicable Decision Support Tool, wherever an analytical solution appears intractable. The polluters are supposed to be myopic and small; the Regional Council is interested in promoting production, collecting taxes, and in the clean environment. Moreover, the model of spread of the pollution within the stream allows for biodegradation. The results suggest the possibility that adequate policy instruments can be found to manage effluent discharges in an optimal way.
This brief introduction to the papers contained in this volume is not meant to cover all issues analysed in the volume. Furthermore, this collection of papers should be viewed as one of the first attempts to demonstrate that control and game theoretic techniques can be effectively applied to analyse important environmental problems. As such, we hope that the book will stimulate the reader to raise new questions, to discover new problems and methods, and to ask for more precise policy prescriptions. Of course, the entire subject of quantitative modelling of environmental problems is still in its infancy. Nonetheless it is a subject that will have profound impact on science, economy, society and ultimately on the environment in which we live. The chapters of this book demonstrate the complexity of the underlying problems; however, they also provide some answers, tools, and recommendations. They will certainly show the advances recently achieved by the theory of dynamic environmental games. Many of the papers will also prove to be useful for applied economists and policymakers. Finally, we believe that directions for future research are also clearly indicated, thus providing new stimuli for further advances in the understanding of the environment.
Carlo Carraro ----------- Jerzy A. Filar
Introduction: The Environmental Game
O.J. Vrieze ..... (p. xvii )
Part 1: Models of Global Change and Sustainable Development