Decision Making in the Field of Renewble Energy

Table of Contents

Executive Summary

Table of Contents

List of Figures

List of Abbreviations

1 Introduction
1.1 Background
1.2 Problem Description
1.3 Objectives
1.4 Methodology

2 Making Decisions at a Glance
2.1 Introduction to Decision Theory
2.2 Decision Making Process
2.3 Game Theory
2.3.1 Classification Criteria
2.3.2 Prisoners’ Dilemma
2.4 Business Transfer of the Game Theory
2.5 Chapter Summary

3 The Energy Market
3.1 Available Energy Sources
3.2 Energy Requirement
3.3 Renewable Energy
3.3.1 An Overview about Renewable Energy
3.3.2 Solar Energy
3.3.3 Wind Energy
3.3.4 Geothermal Energy
3.3.5 Financial Aspects
3.4 Chapter Summary

4 Prisoners’ Dilemma within the Renewables
4.1 Applying the Decision Making Process
4.1.1 Managerial Issues
4.1.2 Macro-Environment
4.1.3 Industry- and Competitive-Environment
4.2 Structure of the Dilemma
4.3 The Utility for Utilities
4.3.1 Strategic Approach within the field of Renewable Energies
4.3.2 Joint Venture as an Outcome
4.3.3 Keep the actual Product Portfolio
4.4 Outcome
4.5 Practical Examples
4.5.1 DESERTEC Industrial Initiative
4.5.2 Offshore in the Irish Sea
4.6 Chapter Summary

5 Conclusion and Outlook

Appendix

Bibliography

Internet Sources

List of Figures

Figure 1 – Decision theory

Figure 2 – Decision making process

Figure 3 – Normal form of a game matrix

Figure 4 – Classification criteria of the different game types

Figure 5 – Nash equilibrium

Figure 6 – The prisoners’ dilemma matrix

Figure 7 – Interaction between market players

Figure 8 – Energy conversion chain

Figure 9 – World total primary energy requirements 1980 -

Figure 10 – An overview about renewable energies

Figure 11 – Natural resources of renewable energy

Figure 12 – Newly installed photovoltaic energy in megawatt

Figure 13 – Offshore is more than onshore in the water

Figure 14 – Wind turbine capacity – Development from 1980 -

Figure 15 – Composition of the electricity price in Germany

Figure 16 – Development of the German electricity price from 2002 -

Figure 17 – The components of a company´s macro-environment

Figure 18 – Questionnaire including weighted pay-off values (first version)

Figure 19 – Finished questionnaire (shortened version)

Figure 20 – Matrix structure for the decision making within the renewables industry

Figure 21 – Strategic approach of one player

Figure 22 – Pay-offs of the strategic approach of one player

Figure 23 – Pay-offs for the cooperation alternatives

Figure 24 – Complete matrix for the renewable energy dilemma including the Nash equilibrium

Figure 25 – DESERTEC project

Figure 26 – E.ON´s offshore portfolio and projects

List of Abbreviations

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Executive Summary

Renewable energies became a crucial factor within the energy industry. They developed from a fringe area to a competitive and sustainable alternative for nuclear power as well as for other energy types. The increasing importance of the use of renewables is also the result of an effective support policy for example by the German government. The focus of this master thesis lays on the electricity usage of renewable energies because nowadays electricity becomes a vital drug without alternative; otherwise the 24:7 rhythms of the today´s information society would not be possible and this yields to needs which have to be fulfilled by the utility companies.

This thesis analyses how decisions could be made by handling these situations. Special emphasis is given to the interaction on the markets of the renewable sector and the resulting impacts on different players. The task creates new challenges to the analysis of decision making. In order to deal with this, a questionnaire is developed which is made for the concept of the prisoners’ dilemma which is an example out of the game theory. Game theory as special approach of the overall decision making theory helps to understand how market players interact in different alternatives. The main challenge involved is the level of detailed information to predict in a certain kind the moves of the market´s player. The outcome of the developed questionnaire is used to fill the pay-offs within the game matrix without no real equilibrium, which is necessary for a certain validation of the decision, can be found. The analysis part puts all information together and develops such a tool for an easier and more structured way to make a decision based on the game theory and the decision making process.

The quintessence is that the game theory allows analyzing the interaction in the renewables energy market to find out if a strategic approach, a joint venture or the do nothing alternative is the best way to play the game within the renewables market. Two practical examples finally verify the results.

1 Introduction

Renewable energies are discussed globally and more often than in the past. Renewable energies become more and more an important topic within political discussions. Renewable energies are one of a handful of possible solutions for the future supply of energy.^[2] Renewable energies are a topic where necessary decisions have to be taken.

Decisions have to be made globally and in almost the same manner as in the past. Decisions are made within the renewable energy industry but also in all other areas. Decisions are not based on perfect rational decision makers.^[3] Decisions could be theoretical explained with the help of decision theories. Decision theories are multifarious and often based on mathematics.^[4]

How both parts could be combined to give assistance in the decision process within the renewable energy industry is described in the present master thesis.

1.1 Background

Energy plays a crucial and important role in today’s modern world. As a matter of fact, it would be unimaginable without energy as houses would stay cold and rooms dark, Computers would cease to function, production plants would come to a halt and the world would be a very different place. All of which makes it abundantly clear why energy supply is one of the foremost concerns of the future. Therefore the issues of climate policy and security of supply are the main driving factors in the current debate on the electricity sector. An important aspect in these discussions is the kind of energy production. The rising gap within the electricity supply which appears if for example nuclear power plants have to shut down within the next few decades and coal fired plants are for example to pollutive, could be solved by the decision to support renewable energies. Renewable energy sources thus represent important pillars for the long-term development of the electricity sector in the given context. Thereby this thesis focuses only on the electricity production due to the fact that it is beside the heat generation and energy supply for transportation the biggest part of the energy generation using renewable sources.^[5] Nevertheless, some charts and information are given for the total energy market to get an impression about the overall sizes. In addition electric energy was in the past the key for the industrialization due to the fact that the industry was no longer bounded to the change of day and night and therefore to stop for example production facilities. In advance, nowadays electricity becomes a vital drug without alternative; otherwise the 24:7 rhythms of the today´s information society would not be possible.

1.2 Problem Description

With regard to the given information the question arises how the companies invest into the increasing market of renewable energies. Is a first-mover strategy more suitable than the cooperation with another market player for the development of a new renewables project or should a utility do not invest in the field of renewable energy at all? The decision process has to be prepared by providing detailed information about the own company as well as the market and the market players. Deciding about investment projects within the energy sector is somehow complicated because many different things have to be considered. A general decision making process is nothing new for the decision makers but this master thesis applies the game theories on the renewable energy sector. Both are brought together to get a validate basis for a sound decision, whereby one of the main problems within the game theory approach is the determination of the game matrix´s pay-offs.

Furthermore, the findings from the theoretical approach are revised in two practical examples. Both samples handling a different outcome of the matrix and dealing with different kinds of the renewables in order to find out if there is a homogeneous structure or not.

1.3 Objectives

The first aim of this master thesis is to provide the reader with a better understanding about the energy market itself and especially about the renewable energy industry. The scope is here set on the electricity generation. Secondly, the study performs an exploration into the general decision making theory with a clear focus on the game theory and its prisoners’ dilemma example. Astray from the original set up, this example will be adapted to explain the players and their possible actions in the renewable energy sector. To solve the described problem of filling the game matrix’s pay-offs a questionnaire is developed which could be used as a framework for the calculation. Therefore, the model development itself becomes a further objective of this thesis.

In general this work does not focus on the company’s strategy but act on the assumption of growth, market penetration, diversification, etc. The general request is the investment into renewables and how this decision process could be supported to assure the decision in an optimal way. It will be checked if the decisions in the European electricity industry with regards to the renewable energies are explainable by using the game theory approaches or not.

1.4 Methodology

An introduction, the problem description respectively the objective and the methodology of the work are given in chapter 1. In order to achieve these objectives and to work on the problem description, a literature study is the main research method. In advance, there are several internet pages as well as magazine reports and actual newspaper articles used to expand the information sources. Consequently, in a first step all available information with a focus on decision finding, game theory, the energy market, and renewable energies are gathered, analyzed and concentrated to draw up an actual picture of the current status in the mentioned fields in chapter 2 and 3.

Based on relevant findings, chapter 4 describes the development of a decision making concept through a deduction of the theoretical parts to a practically utilizable questionnaire. By means of the already mentioned prisoners’ dilemma, a well known game theory approach, is supported by the questionnaires’ outcomes to support the decision finding within the renewable energy industry. The practical examples at the end of chapter 4 are chosen from current ongoing discussions to show how the developed process can be transposed. At the end, in chapter 5 the conclusion and an outlook are given.

2 Making Decisions at a Glance

As announced in the introductory part in chapter 1, this part is now dealing with the theory of decision making. It will provide the reader with a short introduction in the versatile area of making decisions. However, out of the multitude different approaches, this one is chosen which is linkable to the general topic of this thesis, so which is also of interest for the decision making procedure within the field of renewable energies.

The techniques in this section help to make the best decisions possible with the available information at hand. With these tools it is possible to map out the likely consequences of decisions, work out the importance of individual factors and choose the best course of action to take. Which course this is, depends on the problem arose as well who tries to solve it. Companies do have other goals than e.g. the government.

Then, the last subchapter will focus on the game theory which was developed by the mathematicians John von Neumann and Oskar Morgenstern in the nineteen-forties and furthermore enhanced by John Nash in the nineteen-fifties.^[6] These explanations provide a basis for the deeper analysis in chapter 4.

It can be stated that the decision theory is strongly linked to mathematic models. This thesis does not want to claim to be a mathematical thesis; therefore the theories are broken down to a minimum of technical formulas to secure a better understanding of this delicate matter.

2.1 Introduction to Decision Theory

The literature describes two different approaches within the decision theory: the prescriptive/normative and the descriptive one. Figure 1 gives an overview about them:^[7]

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On the one hand the prescriptive approach – literature describes it also as normative approach – is searching for decision rules and standards for rational action. These rules should regulate and prescribe the decision makers´ decision.^[9] But it is very difficult to describe human behavior with economical descriptions. The whole approach tries to identify the best decision to take, assuming an ideal decision maker, who is fully informed, able to compute with perfect accuracy, and fully rational. Furthermore, the decision models – like the game theory – have their basis in this approach.^[10]

On the other hand, the descriptive decision theory rather describes how people, who are in the decision phase are attempting to act and why they are acting in this certain way. In general, people do not behave in optimal ways as they do not have a perfect information level. Descriptive methods are used to create empirical based hypotheses about the behavior of the decision makers. These hypotheses are used to make for example predictions about further decision situations. Due to the fact that within the normative decision theory hypotheses are prepared for testing against actual behavior, these two approaches are closely linked.^[11]

Decisions are made every day by each single individual, as well as by organizational decision making groups.^[12] Some are made knowingly or unconsciously, e.g. within a family, in the circle of friends, alone at home or at work.^[13] Others are more important and affecting financial issues. Basically, it is necessary to have a goal which has to be achieved and there has to be at least two action alternatives which could lead to different outcomes.^[14] Due to the fact that decisions are made in different ways, it is also necessary to know some more details about the problem itself for which someone is searching a decision. Furthermore, it is important to know the actors which are involved as well as their objectives and policies and how their acting could influence the whole picture. In addition to that, facts like the time frame, possible scenarios and constraints are of interest. For smaller decisions it is not necessary to write them down each time, but doing so for bigger or more important ones, yields to the fact that they are at hand.^[15]

One of the main tasks is to characterize the decision problem throughout alternatives. As mentioned, there has to be a minimum of two different alternatives otherwise no decision is needed. Those alternatives have to differ and have to be mutually exclusive, but in the end yield to the same result to fulfill the goal. One requirement is that they have to be achievable. This could be limited for instance by laws, funds, available capacity and other factors. The reasons for deciding for the one or the other alternative have to be balanced; risks have to be calculated and the best fitting alternative has to be chosen.^[16] Furthermore, there could be interdependences between the ultimate goal and those alternatives. The maximization of one alternative could for example the yield to an interference with the goal system. This could require a reformulation of the goal with a higher focus on possible risks.^[17]

2.2 Decision Making Process

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The whole decision making theory can also be seen as a kind of life cycle, process or phase model which is described at full length in literature: Analyze a problem, think about alternatives, and realize one of the alternatives.^[19] Figure 2 gives an overview of such a decision making process.

The first step of the decision making process is the problem definition itself. In general, some symptoms result in an unsatisfied situation, which needs to be improved and analyzed and afterwards carefully defined as the problem.^[20] For all further phases, an intensive information search is necessary although that this is the really first step in the whole process. The more detailed it is known and understood, the better is the assessment of the alternatives as well as the choice of the optimum alternative at the end. Knowledge is powerful but it has also to be kept in mind, how to apply it to the whole process.^[21]

The second step addresses the specification of the target system. The alternatives which will be defined in the third step will be evaluated according to that system. A concretion of the system will also guide the evaluation of the action alternatives.^[22]

The third step deals with the identification of possible alternatives, which will also include the restrictions, which are a kind of prevention to choose too much alternatives. A first measurement is that no alternatives should be looked at which cannot be realized at all due to financial issues, laws etc. Thereby, the whole process will be much easier and also speed up. Furthermore, it has to be thought about further alternatives.^[23] To find them out or develop new ones is a question of creativity. Innovative ideas depend on the level of knowledge of the decision maker whereby the described problems are often beyond the total sum of one´s experience. In general it is well advised to incorporate other persons in the readjustment process to get new ideas and different perceptions in order to improve the overall quality.^[24]

At the end of this step, the alternatives will be checked by a prognosis of their potential to solve the recent problem. It is a kind of consequence estimation because all real decisions are made at an imperfect level of information. Every time it is a decision which is done with a certain kind of risk and uncertainty.^[25]

Step 4 is then the actual decision making, which means that someone has to choose one of the alternatives. In general, the decision maker takes this alternative which first of all will solve his target system but secondly, gives the best – or at least better than some of the others – result in reaching his goals.^[26] Does the decision maker feel unsatisfied with the provided alternatives it is also usual to go back to the previous steps to adjust some things.

The last step then includes the realization phase. This means the chosen alternative will be implemented. This includes further decisions about for example the time frame of the whole process, people who needs to be informed, action lists, etc. Like in the steps before the whole decision making process comprised a multitude of “small” decisions and lives from solving these smaller problems to reach the target system.^[27]

Going through such a process it is like other processes more a tool to systemize a topic in different phases, which should be finished one after another. Regarding this special decision making process, it should be kept in mind that there are high interdependencies between all the phases. And in general it should not be seen as sequential and independent completion of one phase after the other it is more an interaction between them. It is much more convenient to check the rough interconnections and/or relations when choosing the alternatives then to refuse them at the end. In total this will help to reduce or simplify the complexity of the planning process. If there is no reasonable alternative left at the end it is also necessary to jump back to the beginning or to one of the firsts.^[28]

2.3 Game Theory

Subsequent to the description of the decision making process, this subchapter deals with the more relevant theory for this thesis: the game theory. Nevertheless, it is quite important to get an overview about the decision making in general to understand the more detailed game theory more easily. This chapter describes the different theoretical models of the game theory and focuses on the “prisoners’ dilemma” which will then be used in chapter 4 to describe a decision making process within the renewable energy market.

Game theory is a decision finding tool that can be used to analyze strategic problems like competitive situations, which could be setup with a multitude of variables.^[29] It is not the recommended way to get the right strategy, but it gives a bundle of techniques for analyzing mathematical problems.^[30] One of the main reasons for applying the game theories is that they can be used for cases in the field of decision finding where the later result is not only dependent on the decision of oneself but also on the actions of a second (or more) player.^[31] It can be defined as the study of how people interact and make decisions under certain conditions. This broad definition applies to most of the social sciences, but game theory in addition applies mathematical models to this interaction under the assumption that each person's behavior impacts the well-being of all other participants in the game. These models are often quite simplified abstractions of real-world interactions. Furthermore, it is not an appropriate tool when the decision makers ignore the reactions or actions of the takers or use this information as impersonal market condition.^[32] This principle is well known in the field of strategic games like chess therefore the name “Game Theory” established itself. The noun game shouldn´t be understood literally, as it is only used as a synonym for a situation where a minimum of two players interact and can affect the opponents results, so the game is an abstract representation of many serious situations and has a serious purpose.^[33]

A major issue within game theory is the necessity to make assumptions. Any model of the real world must make assumptions to simplify the reality for a reduction of complexity. Even if it is possible to create a model which pictures reality it is not possible to calculate it because there are too many variables. The usual assumptions are rationality and common knowledge. In general everybody tries to take whatever actions are necessary to achieve an advantage. Furthermore, everyone is trying this as perfect as possible in some extent also at others expense. Finding assumptions for the actions of two different companies in a real market are even harder.^[34]

The game theory is mainly based on the mathematicians John von Neumann and economist Oskar Morgenstern. They published the “Theory of Games and Economic Behavior” in 1944.^[35] The idea historically dates back to the Talmud and Sun Tzu's writings. However, in the early 1950s, John Nash generalized their results and provided the basis of the modern field of Game Theory. In 1994, he along with John C. Harsany and Reinhard Selten received the Nobel Prize for economics for their further work in the field of game theories concepts.^[36]

Like decision making itself, game theory is also balancing different alternatives to find a solution for a problem. All these possible “games” – better to say strategies – could be mapped in a game matrix. Figure 3 shows the normal form of such a matrix. The whole matrix should simplify the problem to solve it in an easier way. Therefore, it includes only two players and – in this case – three different strategies for each player (A1 to A3 and B1 to B3).^[37] The numbers within the matrix define the possible results if player 1 and 2 decide for a special combination. These results are called pay-offs. The pay-off could be money or several pieces of chocolate it is just a matter of what is important and what the goal which the players want to achieve is. Therefore, the pay-off is often measured in a kind of utility which afterwards can be transferred into money etc.^[38] For example, if player 1 chooses strategy A2 and player 2 strategy B3 out of the game matrix in figure 3, there will be an utility of 4 for player 1 and a utility of 1 for player 2. The whole outcome of these theories are resulting out of the described pay-offs. Therefore, it is sometimes the main task to find the right or better to say the true values which could be implemented.

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There are several different possibilities how to use the game theory they so called game rules. For example it has to do with the information level both players do have. Furthermore, it is of interest how many times the game should be played, if there is an equilibrium or not, if the players are playing simultaneous or in a sequence, if they do want to cooperate or not, and if it is a cooperative or a non-cooperative game.^[40] Figure 4 gives a rough overview about the main application fields which will be described in more detail in the following subchapters.

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Before describing them in further detail, one fact should be clarified which is important for all decisions especially those within the game theory. It should be assumed, that in a rational game, each player is choosing the best available action which results in an optimum (or maximum) pay-off. But the best action for each depends on the other players’ strategy. Choosing the best alternative for one does not implies that the opponent is doing something to support this. A kind of belief about the opponents’ actions has to be formed by each player.^[42]

The response with the best pay-off to all players by choosing a combination of players’ strategies is the so called Nash equilibrium. It is named to the above mentioned Nobel Prize winner John Nash. However, the Nash equilibrium may be not the best response for each single player but if all players are handling their thoughts regarding this strategy none will lose.^[43]

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Coming back to the example from figure 3, the Nash equilibrium is obtained, when both players choose strategy 1 (=A1 and B1). It is also marked in figure 5 with the blue rectangle behind the pay-offs. The colored ellipses show the best utility for every strategy of each player. As it is also marked, player 1 could achieve a better pay-off if he chooses strategy A3 instead of A1 but this implements that player 2 has to stay with strategy B1 whereby B3 brings him the same result. There are also further exemptions and different other theories to explain and analysis such an example but they are not of further importance for this thesis.^[45]

2.3.1 Classification Criteria

As shown in figure 4, the game theory can be classified into different criteria. Whereby all these classifications are more or less self explaining this subchapter is explaining them in a short way.

On the one hand, game theory literature distinguishes between cooperative and non-cooperative games. Whether a game is cooperative or not is decided by the players themselves. In a cooperative game it is allowed to communicate and also to make special agreements as well as assumptions. This means all players are adjusting the rules whereby this is done with the agreement of all. The most games in reality are non-cooperative ones due to the fact that players only act in their own self interest. That does not imply that no agreements can be achieved within non-cooperative games but those are more or less agreed on mutually beneficial outcomes for the players and then they will jump back to the selfish strategy.^[46]

On the other hand games could be played simultaneously or sequentially. Simultaneous games are draw down by using matrices like the one in figure 3 or 5. Such matrices give a good overview about what happens after the players made their move.^[47] For sequential or dynamic games it is better to use a game tree to explain all possible alternatives which could be appear during the – most several – sequenced moves.^[48]

The third criterion is the number of how often the game is played. If a game is only played once it is called ‘one-shot game’. If a game is played several times with the same players it is called repeated, multi-stage or n-stage game. It is quite important to know how often a game is played to choose the right strategy. A single game can end up totally different than if the same game with the same players is played five times which is often also much more complicated.^[49]

Furthermore, the sum of the players’ pay-off in a game classifies two different kinds of game. On the one hand, a zero-sum game is a game where the total pay-off is constant at zero. This indicates that one player´s gain is the loss of the other one. Those games normally cause pure conflicts.^[50] On the other hand, there are also situations where the losses of one player are not equal to the gain of a second player. Those games are called non-zero sum games.^[51]

Perfect information games are such games, where all players know the entire history of decision taking. It means that the players have the same information level like an observer who is standing outside of the game.^[52] While in an imperfect information game players do not know the full history of the next move. The player has to decide under less information which mainly causes uncertainty. This is more or less the case in real life.

In total all these criteria could be mixed up to have different approaches for different decision problems. These basics are the central rules within the game theory.

2.3.2 Prisoners’ Dilemma

The most widely known example of game theory is probably the “Prisoners’ Dilemma”. It got its name from the following hypothetical situation:^[53]

Two criminals arrested under the suspicion of having committed a crime together. However, the police do not have sufficient evidences to have them adjudge. The two prisoners are being isolated from each other and the police officers offer each of them a deal: “The person that offers evidence against the other one will be freed.” If none accepts the offer, it has to be presumed that both are cooperating against the police, and both of them will get a small punishment (1 year jail) because of lack of proof. They will both win. However, if one person betrays the other, by confessing to the police, he will gain more, since the first one is freed (no jail). The one who remained silent, on the other hand, will receive the full punishment (6 years jail), since he did not help the police, and there is sufficient proof. If both betray, both will be punished, but less strict than if they had refused to talk (3 years jail for both).^[54]

Figure 6 illustrates this dilemma in a decision matrix, whereby the pay-offs are the (negative) years which the two players have to go to jail.

[...]

^[1] Pnas.org (2009).

^[2] Cf. Eisenbeiss (2009), p. 84.

^[3] Cf. Blake (2009), p. 38.

^[4] Cf. Stein (2009), p. 10.

^[5] Cf. Schiffer (2005), p. 240.

^[6] Cf. Carmichael (2005), p. 3.

^[7] Cf. Dörsam (2007), p. 7.

^[8] Graphic by author’s own, based on Dörsam (2007), p. 7; Laux (2007), p. 2; Meyer (2000), p. 2.

^[9] Cf. Meyer (2000), p. 2 f.

^[10] Cf. Becker (1993), p. 15.

^[11] Cf. Davis (2005), p. 15.

^[12] Cf. Campbell et al. (2009), p. 60.

^[13] Cf. Laux (2007), p. 1.

^[14] Cf. Kirkwood (1997), p. 2.

^[15] Cf. Saaty (2001), p. 208 f.

^[16] Cf. Laux (2007), p. 4 f.

^[17] Cf. Laux (2007), p. 5.

^[18] Graphic by author’s own, based on Ullmann (2006), p. 32 and Laux (2007), p. 8.

^[19] Cf. among other literature Abts/Mülder (2009), p. 301.

^[20] Cf. Edmund (2006), p. 6.

^[21] Cf. Laux (2007), p. 9.

^[22] Cf. Laux (2007), p. 10.

^[23] Cf. Edmund (2006), p. 14.

^[24] Cf. Bhushan/Rai (2004), p. 4 f.

^[25] Cf. Edmund (2006), p. 21.

^[26] Cf. Laux (2007), p. 11.

^[27] Cf. Bhushan/Rai (2004), p. 4 f.

^[28] Cf. Laux (2007), p. 13.

^[29] Cf. Dixit/Nalebuff (2000), p. 1 f.

^[30] Cf. Thomas (2005), p. 17.

^[31] Cf. Ortmanns/Albert (2008), p. 71.

^[32] Cf. Rasmusen (2007), p. 11.

^[33] Cf. Wiese (2002), p. VII.

^[34] Cf. valuebasedmanagement.net (2009).

^[35] Cf. Davis (2005), p. 7.

^[36] Cf. Schlee (2004), p. 1.

^[37] Cf. Ortmanns/Albert (2008), p. 73.

^[38] Cf. Carmichael (2005), p. 6.

^[39] Graphic by author’s own, based on Ortmanns/Albert (2008), p. 73.

^[40] Cf. Carmichael (2005), p. 8 f.

^[41] Graphic by author’s own, based on Ortmanns/Albert (2008), p. 7 f / Carmichael (2005), p. 8 f.

^[42] Cf. Osborne (2002), p. 19.

^[43] Cf. Fundenberg et al. (1991), p. 11.

^[44] Graphic by author’s own, based on figure 3.

^[45] For further readings: Ortmanns/Albert (2008), p. 77 ff, Carmichael (2005), p. 36 ff and others.

^[46] Cf. Carmichael (2005), p. 16.

^[47] Cf. Osborne (2002), p. 205 f.

^[48] Cf. Carmichael (2005), p. 18.

^[49] Cf. Rasmusen (2007), p. 129.

^[50] Cf. Ison/Wall (2007), p. 157.

^[51] Cf. Ison/Wall (2007), p. 159.

^[52] Cf. Ritzberger (2002), p. 85 f.

^[53] Cf. Tucker (1980), p. 101.

^[54] Cf. Nisan et al. (2007), p. 3 f; Ortmanns/Albert (2008), p. 76 f and many others.