The impact of global warming on the global economy has been widely discussed in literature oﬀering a broad variety of estimates. Some papers have examined global impacts of climate change, whereas some studies have focused on regional or local consequences. Taking into account various diﬀerent publications, the ﬁrst part of this master’s thesis proposes individual functions at a country level that illustrate the impact of global warming. These functions are further used to simulate the countries’ behaviour over time using dynamic programming. We provide an analysis of the interaction between the abatement costs, the ecological impact caused by a certain temperature increase and the abatement eﬀorts made by the countries. A detailed analysis of their behaviour including the formation of coalitions rounds out the ﬁrst part of the thesis.
The second part considers recent proposals from the academic and political world. The 21st session of the Conference of Parties (COP21) in December 2015 was described as a fundamental breakthrough in climate negotiations by many commentators. However, several issues such as the establishment of binding quotas for the Parties being linked to the 2◦C global mitigation target remain unsolved. We simulate the eﬀorts of the Parties to reduce their emissions based on individual abatement targets.
To the best of our knowledge, our approach is the ﬁrst one to analyze the behaviour of countries in a climate change context using dynamic programming. All components of the Matlab program providing the results are ﬂexible and can be changed according to the assumptions.
1 Introduction.. 1
2 Model without policy intervention.. 4
2.1 Methodology of dynamic programming.. 4
2.1.1 Backward programming.. 6
2.1.2 Forward programming.. 8
2.2 Elements of the total cost function.. 9
2.2.1 The abatement cost curve.. 9
2.2.2 The temperature impact.. 11
2.2.3 The ecological impact.. 13
2.2.4 Considering the Parties’ expectations.. 20
2.3 Evaluation of results.. 22
3 Model with policy intervention.. 29
3.1 Academic and political background.. 29
3.2 Elements of the total cost function.. 31
3.2.1 The abatement cost curve.. 32
3.2.2 Assigning individual requirements.. 33
3.2.3 Determining a penalty for not meeting the requirements.. 36
3.2.4 Adding randomness.. 39
3.2.5 Accounting for the emissions of developing countries.. 40
3.2.6 Considering the Parties’ expectations.. 43
3.3 Evaluation of results.. 44
4 Comparison of both models.. 50
5 Conclusion.. 54
Global warming is a serious issue and continues to present challenges in the 21st century. Researchers from diﬀerent ﬁelds have published studies describing the eﬀects of increasing temperatures. Crop failures  or spreading diseases  are only two of many causes that create environmental refugees  and show the vulnerability  of the Earth. Policy leaders have been trying to tackle these problems, but although the 21st Conference of Parties (COP21) in December 2015 is described as historic by many commentators, numerous issues remain unsolved. The recently promoted system of Intended Nationally Determined Contributions (INDCs) to limit global warming to below 2◦ C relative to preindustrial levels shows several ﬂaws  and binding quotas are yet to be implemented.
Nevertheless, ﬁnding a global solution is of extraordinary importance. Academia oﬀers a broad variety of models to predict and quantify the eﬀects of global warming. As countries usually try to maximize their own beneﬁts, scientists have used game theory to predict their willingness to cooperate. Nonetheless, due to the enormous computational complexity, most approaches only model one single time period [7, 8] and do not use real-world data.
The currently most cited Dynamic Integrated Climate-Economy model (DICE) [9, 10], developed by Nordhaus, provides an optimal time-dependent global emissions trajectory and corresponding carbon taxes on a global level. In various adaptions, the behaviour of diﬀerent regions has been included  or a stochastic component has been added ; yet, to the best of our knowledge, none of the versions acknowledge the behaviour of all countries as individuals. That means that countries within one region are assumed to collaborate and act as one big player, which is already a political challenge for the European Union, but even more for larger regions such as South America or Africa.
Developing a realistic model, the distinct interests of every single Party should be considered and individual requirements should be set. Additionally, a global market should be created to enable trading of emissions permits. Another challenge lies in designing a functioning compliance mechanism. All of these key issues have been extensively discussed in literature.
In order to determine the Parties’ individual requirements, criteria such as equity, action, justice, responsibility, capability, integrity and eﬃciency [13, 14] should be met. In the following we show diﬀerent approaches to distribute the requirements among the Parties and demonstrate that the formula presented in  performs best measured by convergence and standard deviation. The requirements are calculated in a dynamic way using the current per capita emissions of each Party.
Emissions trading is possible at regional and national levels in wide parts of the world. However, many of these markets are poorly designed. Despite occasional successes , the Clean Development Mechanism (CDM) deﬁned in the Kyoto Protocol reveals a number of weaknesses  that need to be eliminated. Similarly, the European Union Emissions Trading System (EU ETS) is often criticized and requires improvements such as described in . Based on Weitzman’s famous paper “Prices vs. quantities” , Taschini  describes the challenges of ﬁnding suitable pricing mechanisms taking into account banking and borrowing opportunities, pollution abatement measures, strategic trading interactions and the presence of asymmetric information. As political enforcement mechanisms are hard to establish in a global market, the concept of “buyer liability” suggests to set economic incentives instead. In such a setting, buyers of permits are liable for those emissions where the permits prove not to be valid. Sellers, on the other hand, have an incentive to meet their requirements in order to signal that their permits are reliable. Keohane shows that this system is indeed self-enforcing .
When designing a compliance mechanism it is also crucial to consider the Parties’ individual costs and beneﬁts. Depending on these factors a Party might either decide to abate or to buy permits on the market. A third option can be oﬀered based on the prevailing compliance mechanism. This could be a simple penalty that has to be paid every period in case the requirements cannot be met. Another way of modeling incentives to abate emissions is to capture geographical characteristics by using country-speciﬁc data. Tol  describes that poorer countries tend to be aﬀected more strongly by global warming than richer countries. Likewise, hotter countries suﬀer more from increasing temperatures than cooler ones. Hence, it is possible to quantify the Parties’ incentives to abate, and thus to simulate their behaviour.
In Chapter 2, we use state of the art literature in order to simulate the behaviour of all countries worldwide in the absence of policy intervention by only taking into account ecological damages and beneﬁts caused by global warming. Having introduced the concept of dynamic programming, we describe individual abatement cost curves of countries, the implications of increasing emissions on the temperature and the ecological impact of this temperature change. We conclude this chapter by analyzing the countries’ behaviour considering diﬀerent expectations in global emissions.
As many commentators described the recent Conference of Parties (COP21) as a historic step in the battle against global warming, the resulting Paris Agreement is evaluated in Chapter 3. Furthermore, we propose three formulas for a top-down mechanism to distribute the requirements that are necessary to limit climate change. These formulas are then applied using dynamic programming and benchmarked against each other.
Summing up our ﬁndings, Chapter 4 compares the models with and without policy intervention. We conclude by describing the limitations of both models and give an outlook on both policy and further research possibilities, in Chapter 5.
2 Model without policy intervention
In the absence of a global planner, countries try to adjust their emissions in order to achieve the best possible economic outcome for themselves. In our model, this can be calculated by considering two factors. One of them concerns the abatement cost curves, that describe how much countries have to pay in order to reduce their emissions below their ‘business as usual’ (BAU) growth line. The second factor refers to the ecological impact caused by global warming. In an extensive literature review, Tol  provides numbers to describe the magnitude of this impact by aggregating results from a variety of diﬀerent studies. Based on these, we are able to create individual impact functions for all countries. Finally, we use dynamic programming in order to simulate the countries’ behaviour over time.