Aspects of Coalitions for Environmental Protection Under Co-utility

Abstract

The game theoretic modeling of coalitions for environmental protection within the framework of a new concept of co-utility [8] is analysed. The co-utility concept can be described by two elements. Firstly, agents can improve their payoffs by collaborating with each other. Secondly, the outcome of collaboration is stable. The similarity of co-utility with common concepts of coalition stability for environmental protection is shown. But the co-utility concept is more extensive and can serve as an umbrella in all applications where agents have room for simultaneous improvements of payoffs. The development from a myopically stable outcome to a farsightedly stable outcome is discussed.

Appendix. The FUND Model

This paper uses version 2.8 of the Climate Framework for Uncertainty, Negotiation and Distribution (FUND). Version 2.8 of FUND corresponds to version 1.6, described and applied by [28,29,30, 33], except for the impact module, which is described by [31, 32] and updated by [15]. A further difference is that the current version of the model distinguishes 16 instead of 9 regions. Finally, the model considers emission reduction of methane and nitrous oxide as well as carbon dioxide, as described by [34].

Essentially, FUND consists of a set of exogenous scenarios and endogenous perturbations. The model distinguishes 16 major regions of the world, viz. the United States of America (USA), Canada (CAN), Western Europe (WEU), Japan and South Korea (JPK), Australia and New Zealand (ANZ), Central and Eastern Europe (EEU), the former Soviet Union (FSU), the Middle East (MDE), Central America (CAM), South America (LAM), South Asia (SAS), Southeast Asia (SEA), China (CHI), North Africa (NAF), Sub-Saharan Africa (SSA), and Small Island States (SIS). The model runs from 1950 to 2300 in time steps of 1 year. The primary reason for starting in 1950 is to initialize the climate change impact module. In FUND, the impacts of climate change are assumed to depend on the impact in the previous year, in this way reflecting the process of adjustment to climate change. Because the initial values to be used for the year 1950 cannot be approximated very well, both physical and monetized impacts of climate change tend to be poorly represented in the first few decades of the model runs. The period of 1950–1990 is used for the calibration of the model, which is based on the IMAGE 100-year database [3]. The period 1990–2000 is based on observations of the World Resources Databases [35]. The climate scenarios for the period 2010–2100 are based on the EMF14 Standardized Scenario, which lies somewhere in between IS92a and IS92f [14]. The 2000–2010 period is interpolated from the immediate past, and the period 2100–2300 extrapolated.

The scenarios are defined by the rates of population growth, economic growth, autonomous energy efficiency improvements as well as the rate of decarbonization of the energy use (autonomous carbon efficiency improvements), and emissions of carbon dioxide from land use change, methane and nitrous oxide. The scenarios of economic and population growth are perturbed by the impact of climatic change. Population decreases with increasing climate change related deaths that result from changes in heat stress, cold stress, malaria, and tropical cyclones. Heat and cold stress are assumed to have an effect only on the elderly, non-reproductive population. In contrast, the other sources of mortality also affect the number of births. Heat stress only affects the urban population. The share of the urban population among the total population is based on the World Resources Databases [35]. It is extrapolated based on the statistical relationship between urbanization and per-capita income, which are estimated from a cross-section of countries in 1995. Climate-induced migration between the regions of the world also causes the population sizes to change. Immigrants are assumed to assimilate immediately and completely with the respective host population.

The market impacts are dead-weight losses to the economy. Consumption and investment are reduced without changing the savings rate. As a result, climate change reduces long-term economic growth, although consumption is particularly affected in the short-term. Economic growth is also reduced by carbon dioxide abatement measures. The energy intensity of the economy and the carbon intensity of the energy supply autonomously decrease over time. This process can be accelerated by abatement policies, an option not considered in this paper.

The endogenous parts of FUND consist of the atmospheric concentrations of carbon dioxide, methane and nitrous oxide, the global mean surface temperature, the impact of carbon dioxide emission reductions on the economy and on emissions, and the impact of the damages to the economy and the population caused by climate change. Methane and nitrous oxide are taken up in the atmosphere, and then geometrically depleted. The atmospheric concentration of carbon dioxide, measured in parts per million, is represented by the five-box model of [16]. Its parameters are taken from [12]. The model also contains sulphur emissions [34].

The radiative forcing of carbon dioxide, methane, nitrous oxide and sulphur aerosols is determined based on [25]. The global mean temperature T is governed by a geometric build-up to its equilibrium (determined by the radiative forcing RF), with a half-life of 50 years. In the base case, the global mean temperature rises in equilibrium by $2.5^{\circ }$C for a doubling of carbon dioxide equivalents. Regional temperature follows from multiplying the global mean temperature by a fixed factor, which corresponds to the spatial climate change pattern averaged over 14 GCMs [18]. The global mean sea level is also governed by a geometric build-up, with its equilibrium level determined by the temperature and a half-life of 50 years. Both temperature and sea level are calibrated to correspond to the best guess temperature and sea level for the IS92a scenario of [13].

The climate impact module, based on [32, 33] includes the following categories: agriculture, forestry, sea level rise, cardiovascular and respiratory disorders related to cold and heat stress, malaria, dengue fever, schistosomiasis, diarrhoea, energy consumption, water resources, and unmanaged ecosystems. Climate change related damages can be attributed to either the rate of change (benchmarked at $0.04^{\circ }$C) or the level of change (benchmarked at $1.0^{\circ }$C). Damages from the rate of temperature change slowly fade, reflecting adaptation [33]. People can die prematurely due to temperature stress or vector-borne diseases, or they can migrate because of sea level rise. Like all impacts of climate change, these effects are monetized. The value of a statistical life is set to be 200 times the annual per capita income. The resulting value of a statistical life lies in the middle of the observed range of values in the literature [7]. The value of emigration is set to be 3 times the per capita income [26, 27], the value of immigration is 40% of the per capita income in the host region [7]. Losses of dryland and wetlands due to sea level rise are modelled explicitly. The monetary value of a loss of one square kilometre of dryland was on average $4 million in OECD countries in 1990 [10]. Dryland value is assumed to be proportional to GDP per square kilometre. Wetland losses are valued at $2 million per square kilometre on average in the OECD in 1990 [10]. The wetland value is assumed to have a logistic relation to per capita income. Coastal protection is based on cost-benefit analysis, including the value of additional wetland lost due to the construction of dikes and subsequent coastal squeeze.

Other impact categories, such as agriculture, forestry, energy, water, and ecosystems, are directly expressed in monetary values without an intermediate layer of impacts measured in their ‘natural’ units [32]. Impacts of climate change on energy consumption, agriculture, and cardiovascular and respiratory diseases explicitly recognize that there is a climatic optimum, which is determined by a variety of factors, including plant physiology and the behaviour of farmers. Impacts are positive or negative depending on whether the actual climate conditions are moving closer to or away from that optimum climate. Impacts are larger if the initial climate conditions are further away from the optimum climate. The optimum climate is of importance with regard to the potential impacts. The actual impacts lag behind the potential impacts, depending on the speed of adaptation. The impacts of not being fully adapted to new climate conditions are always negative [33]. The impacts of climate change on coastal zones, forestry, unmanaged ecosystems, water resources, diarrhoea, malaria, dengue fever, and schistosomiasis are modelled as simple power functions. Impacts are either negative or positive, and they do not change sign [33]. Vulnerability to climate change changes with population growth, economic growth, and technological progress. Some systems are expected to become more vulnerable, such as water resources (with population growth), heat-related disorders (with urbanization), and ecosystems and health (with higher per capita incomes). Other systems are projected to become less vulnerable, such as energy consumption (with technological progress), agriculture (with economic growth) and vector- and water-borne diseases (with improved health care) [33].

Note that we make use of data only for the year 2005. This is sufficient as static game theory is used but with a sophisticated stability concept.

Table 1 Our data from the year 2005, where $\alpha$ is the abatement cost parameter (unitless), $\beta$ the marginal damage costs of carbon dioxide emissions (in dollars per tonne of carbon), E the carbon dioxide emissions (in billion metric tonnes of carbon) and Y the gross domestic product, in billions US dollars. Source FUND

1.1 The Welfare Function of the FUND Model

We approximate the FUND model with a linear benefit/quadratic cost structure for the analysis of coalition formation. Specifically, the abatement cost function is represented as:

$$\begin{aligned} C_i = \alpha _i R^{2}_{i} Y_i, \end{aligned}$$

(1)

where C denotes abatement cost, R relative emission reduction, Y gross domestic product, index i denotes regions and $\alpha$ is the cost parameter. The benefit function is approximated as:

$$\begin{aligned} B_i = \beta _i \sum _j^n R_j E_j \end{aligned}$$

(2)

where B denotes benefit, $\beta$ the marginal damage costs of carbon dioxide emissions and E unabated emissions. Table 1 gives the parameters of Eqs. (1) and (2) as estimated by FUND. Moreover, the profit $\pi _i$ of a country i is given as:

$$\begin{aligned} \pi _i = B_i - C_i = \beta _i \sum _j^n R_j E_j - \alpha _i R^{2}_{i} Y_i. \end{aligned}$$

(3)

The second derivative of $d ^2\pi _i/dR_i^2 = - 2 \alpha _i < 0$ as $\alpha _i > 0$. It follows that the profit function of every country i is strictly concave, and as a consequence has a unique maximum. Hence, the non-cooperative optimal emission reduction is found from the first-order optimal condition:

$$\begin{aligned} d\pi _i/dR_i = \beta _i E_i - 2 \alpha _i R_i Y_i = 0 \Rightarrow R_i = \beta _i E_i / (2 \alpha _i Y_i). \end{aligned}$$

(4)

If a region i is in a coalition with a region j, the optimal emission reduction is given by:

$$\begin{aligned} d\pi _{i+j}/dR_i = 0 \Rightarrow E_i (\beta _i + \beta _j) - 2 \alpha _i R_i Y_i = 0 \Rightarrow R_i = (\beta _i + \beta _j)E_i / (2 \alpha _i Y_i). \end{aligned}$$

(5)

Thus, the price for entering a coalition is higher emission abatement at home. The return is that the coalition partners also raise their abatement efforts.

Note that our welfare functions are orthogonal. This indicates that the emissions change of a country does not affect the marginal benefits of other countries (that is the independence assumption). In our game, countries outside the coalition benefit from the reduction in emissions achieved by the cooperating countries, but they cannot affect the benefits derived by the members of the coalition. As our cost-benefit functions are orthogonal, our approach does not capture the effects of emissions leakage. Even so, our cost benefit functions are sufficiently realistic as they are an approximation of the complex model FUND and our procedure of dealing with farsighted stability is also general and appropriate for non-orthogonal functions.