Radio-Link Budget: Friis Equation [42]

successful because they give persistently a larger fraction of their endowment over the course of a period. In addition, the first contribution of the leader yields a high return concerning final earnings. The leader is slightly better off than an average subject in NOLEAD, but not significantly.

8.5.4.3 Examples of good and bad leadership

To illustrate the effect of good and bad leadership, we present some exem-plary groups in this section. The black line in the graphs represents the leader contributions, while the grey lines represents the follower contributions. Fig-ure8.8depicts two examples of bad leadership. In the left part we see that the leader stops contributing after three rounds, although the followers matched him before (at least partly). This results in a breakdown of cooperation and almost no further growth after round 3. In the right part we can observe a leader who started with a medium contribution in the first round. After this, the leader decreases his contribution in every subsequent round and the fol-lowers mimic this behavior, resulting in a low final average endowment.

Figure 8.8: Bad leadership

Figure 8.9 shows two examples of good leadership. In both cases the leader starts with a full contribution of 20 Taler in the beginning. In the left part we can see that the leader only deviates in the last round from full contribution.

The same is true in the graph on the right part, where the leader sticks to his plan of full contribution until round 6, although one group member is a free-rider who only matches the leader partly.

8.6 conclusion 145

Figure 8.9: Good leadership

8.6 c o n c l u s i o n

Is leading-by-example a suitable tool in improving cooperation in dynamic environments like research and development partnerships? In this chapter, we provided an experiment investigating the effect of leadership in a dy-namic public goods game with endowment carryover and, hence, endogenous growth and inequality. The analysis of our experiment shows that leadership indeed yields an improvement: We see larger contributions and consequently higher earnings if groups have a leader. The leaders, however, benefit less.

They contribute more to the group pot than the followers, but receive lower payouts. However, the average leader in LEAD is not worse off than an aver-age player in NOLEAD. From a welfare perspective, it can thus be argued that leading-by-example leads to a Pareto improvement. In addition, we observe a significantly lower inequality in groups with a leader compared to NOLEAD.

As a measurement for inequality we use the Gini Index which also refers to a utilitarian social welfare function that integrates individual inequity aversion (Schmidt and Wichardt2018). Assuming inequity averse agents, we can thus report a further welfare improvement through leadership.

We also find that the leader’s contribution in the first round has a large impact on the final results across all groups. For the groups, it pays off if the leader prefaces by setting a good example in the form of a large initial contribution. Based on a sequential prisoner’s dilemma, we elicited types for conditional cooperation in part I of the experiment. Our results indicate that groups work best when led by conditional cooperators. The mechanism is quite interesting: it is apparently their perseverance in setting a good ex-ample (contributing a high proportion of their income for a long time) that makes conditional cooperator types successful. By contrast, we discover signs of strategic leadership in the selfish types, with very high contributions in the first two rounds followed by a sharp crash. In a similar vein, we see that followers that are classified as conditional cooperators match a leader’s con-tribution to a higher degree than selfish types.

R É S U M É

This thesis has set out to further explore the role of pioneers in social dilemma situations both theoretically and empirically. High expectations have been placed on leadership, in particular when dealing with global problems such as the provision of global public goods. The question is: Does leadership meet these expectations?

The theoretical Part I that sticks to the standard assumption of narrow payoff-maximizing agents has shown that it depends on the kind of lead-ership considered whether an amelioration of a social dilemma situation is possible. Regarding pioneering behavior in coalition building, Chapter 1 has poured some cold water on optimistic expectations. We have seen that par-tial cooperation of one group reduces the likelihood that others are willing to form a coalition, in particular if it is a large coalition that cooperates. More-over, coalition building of a small group may even reduce the level of public good supply.

Another kind of pioneering behavior discussed in Chapter 2 seems more promising: the approach of technological innovation of a coalition and sub-sequent free transfer of the technology to other countries. While the coun-tries within the coalition cooperate at the innovation stage, they act non-cooperatively when choosing their public good contribution (which is in con-trast to Chapter 1). The prospects of such leadership are quite good: a costly innovation of the coalition may increase both the level of public good supply and the utilities of all countries involved given a sufficient scope of technolog-ical diffusion and automatic spillovers, e.g. through international trade. But there remains an incentive problem to adopt the innovation on behalf of the recipients if technological diffusion is endogenous.

In a similar vein, Chapter 3 has focused on technological innovation. In this chapter, an interesting effect materializes. Leadership expressed through the move structure, i.e. a leader-follower (Stackelberg) game instead of a simul-taneous (Nash) game is usually unfavorable for the level of public good pro-vided (Varian1994). Chapter 3, however, has shown that this needs no longer be true when the leading country has the option to adopt a better technology.

In this case, advantageous leadership is feasible where public good supply and utilities of both countries increase compared to simultaneous play.

Technology thus appears to be an interesting sphere for leadership. To get an impression how such technological leadership and technology diffusion may look like, Part II has studied the example of Germany’s feed-in tariff for photovoltaic. It illustrates the magnitude of such pioneering efforts and outlines the technological progress through learning-by-doing.

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r é s u m é 147

Moving away from narrow payoff-maximizing agents, Part III and Part IV have pursued the questions of the existence and possible implications of reci-procity in a leader-follower relation. Both in the public discussion and the-oretical literature reciprocity is regarded as a key to successful cooperation.

Given that followers have reciprocal preferences (i.e. react to an increase in the leader’s contribution by increasing own contributions), the argument of crowding-out looses its importance. In a leader-follower (Stackelberg) game an increase in public good supply thus seems feasible compared to the bench-mark of simultaneous play (Nash-Game) given sufficiently reciprocal prefer-ences of the followers – even in the absence of reciprocal preferprefer-ences of the leader (see Buchholz and Sandler2017).

Does that mean that reciprocity is the secret of successful leadership? This thesis provided some evidence for this assertion. As a first step, Part III pur-sued the question whether it seems reasonable to assume reciprocal behavior.

In this regard, Chapter 5 has shown that there is indeed empirical evidence for reciprocity in the field of experimental economics as well as international rela-tions. Moreover, reciprocal preferences are quite stable across social dilemma games as the experimental investigation in Chapter 6 has pointed out. Con-sequently, a basic prerequisite for successful leadership is given. Does this materialize in an amelioration in public goods supply in experimental public goods games? The answer is yes for most of the experiments portrayed in the systematic literature review in Chapter 7 but also for the dynamic public goods game in Chapter 8 of Part IV.

However, there remains an interesting aspect of leadership - the question of “Why lead?”. In the classical world of narrow payoff-maximizing agents, this question is obvious: the first mover attains a first-mover advantage. In this world, the leader can commit himself to a low public good contribution while the followers will have to give more in equilibrium. This is, however, in contrast to the results in Chapter 7 and Chapter 8. What we can observe here is that a first-mover advantage is either only present in a reduced form or in many cases does not exist at all. On the contrary, in the voluntary contribu-tion mechanism (VCM) which has a zero contribucontribu-tion prediccontribu-tion for narrow payoff maximizing agents, leaders contribute distinctly more than followers.

Quite similarly, in a game with predicted interior equilibria and first-mover advantage given agents without reciprocal preferences, this first-mover advan-tage does not materialize. Why is this the case? This seems to be the flipside of reciprocal preferences.

Reciprocity apparently alters the balance of power in the leader-follower game. Without reciprocity, the leader is in a fortunate position and conse-quently contributes less than the follower(s). In anticipation of a reciprocal response of the follower(s) this game now turns. The first-mover position of the leader becomes unfavorable – some even speak of a “leader curse”. The leaders contribute more than the followers, the profits from cooperation are unevenly divided among leaders and followers. It is the followers that benefit most from sequential play. Followers’ reciprocity thus not only is a reliable remedy to stand one’s ground in a strategically unfavorable position but it also allows to exploit the leader to a certain extent.

r é s u m é 148

This impression gained from the empirical Part IV can also be illustrated by a short theoretical example in Appendix E. In this example, the leader would not contribute at all in the Stackelberg equilibrium if neither of the two play-ers had reciprocal preferences and public good supply in consequence would be the standalone allocation of the follower. Given a sufficiently reciprocal fol-lower in this example, however, the leader contributes more than the folfol-lower - even if he holds reciprocal preferences himself.

So, why lead? Why should one choose to be the leader? A first answer might be that the leader does not fare worse compared to simultaneous play, he only improves less. Consequently, it is better to swallow the bitter pill if no one else did. Still, the question is who should do it. Maybe, it takes some idealism to adopt this pioneering position, a sort of idealism that makes the cake bigger even though the own piece of cake may be smaller than that of the rest. The problem of leadership is ultimately not only a problem of finding reciprocal followers, it is also a problem of finding idealistic leaders willing to sacrifice relative gains for the common good.

Part V

A P P E N D I X

A

A P P E N D I X C H A P T E R 1 : D E R I VAT I O N O F T H E T H R E S H O L D L E V E L I N P R O P O S I T I O N 1 3

Proof. It directly follows from eq. (18) in Chapter 1 that

∂G^B_I

∂ξ = ^w−eK−ξe^K₂

1+ξe^K₁ +me₁^M (1)

which is positive since e₁^K > 0, e₁^M > 0, e^K₂ < 0 and 1−e^K is a member of K’s private consumption which is positive in the equilibrium E^B_I(k, m) by definition. Inserting (21) into

∂u^BK_I

∂ξ

= ^∂u(e(G^B_I, ξ), G^B_I)

∂ξ

=u₂((ξe₁^K+₁)^∂G

BI

∂ξ

+ξe^K₂) ₍₂₎

gives

∂u^BK_I

∂ξ = ^u2((ξe^K₁ +1)(w−e_K) +ξme^K₂e^M₁ )

1+ξe^K₁ +me₁^M . (3)

Then an upper bound

¯ χ >

¯

ξB(m) which has the properties required by Proposition 11 exist since at ξ =

ξ¯

B(m)we have w−e^K = 0. Hence, because of e^M₁ > 0 and e^K₂ < 0, the numerator is of (30) is negative there so that continuity implies that u^BK_I must also be falling for all ξ close to

¯k_B(m).

150

B

A P P E N D I X C H A P T E R 6 : I N S T R U C T I O N S F O R T H E E X P E R I M E N T

Basics

This online experiment will consist of two parts.

First, part 1 will be explained. After part 1 ends, you will receive instructions for part 2. Your decisions in part 1 do not influence your payoff in part 2 and vice versa.

In this study you will earn POINTS. Each POINT is worth 0.05 Dollar (20 POINTS = 1 DOLLAR). At the end of the study you receive your amount of POINTS cashed out in Dollar.

In this study, you must answer control questions to ensure that you have un-derstood the task correctly (there are five control questions in total). Only if you answer them correctly you can complete this survey. The control ques-tions require some small calculaques-tions. If you give a wrong answer to a control question, you can try multiple times until you find the correct solution.

Sequential Prisoner’s Dilemma (SPD)

You will be matched with one other random MTurker who also participates in this study. One of you has the role of “Player 1” and the other one has the role of “Player 2”. Each of you is endowed with 10 POINTS. You have to decide whether you want to KEEP your 10 POINTS or whether you want to SEND your 10 POINTS. If the POINTS are sent, they double for the other player. The other MTurker has to make the same decision.

This game is played sequentially – i.e., the players make their decisions sub-sequently (this is illustrated by the graph below).

First Player 1 (BLUE) makes a decision. Player 2 (RED) observes this decision and makes a decision as well. In this study, you make a decision for both roles, Player 1 and Player 2 (follow for this purpose simply the instructions on the screens). At the end of the study, a random device determines the role of you and the other MTurker. There are two possibilities: you are Player 1 and the other MTurker is Player 2 or you are Player 2 and the other MTurker is Player 1. The combination of the decisions of you and the other MTurker determines your payoff in this game, as shown in the graph below.

Conversion rate: 20 POINTS = 1 DOLLAR.

151

a p p e n d i x c h a p t e r 6: instructions for the experiment 152

Before starting with the actual decisions, you are asked to answer two short control questions to make sure that you have understood all rules of the game correctly.

Sequential Public Goods Game (FGF)

You will now be in a group of 4 MTurkers. Each MTurker must decide on the division of 20 POINTS. You can put these 20 POINTS in a private account or you can invest them fully or partially into a project. Any POINT that you do NOT invest into the project, will automatically be transferred to your private account.

Your income from the private account:

For each POINT you put in your private account you will earn exactly one POINT. Nobody except you earns something from your private account.

Your income from the project:

The amount of POINTS contributed to the project by ALL group members, will be increased by 60% and then equally split among all group members.

This means, each group member will receive the same income from the project.

Consequently, for each POINT invested in the project each group member (in-cluding yourself) receives 1.6/4 = 0.4 POINTS.

Hence, for each group member the income from the project will be deter-mined as follows:

Income from the project = sum of contributions to the project x 0.4.

For example, if the sum of all contributions to the project is 70 POINTS, then you and all group members will get a payoff of 70 x 0.4 = 28 POINTS each from the project. If the sum of contributions is 15 POINTS, then you and all group members will get a payoff of 15 x 0.4 = 6 POINTS each from the project.

a p p e n d i x c h a p t e r 6: instructions for the experiment 153

Your total income:

Your total income is the sum of your income from the private account and the project:

Income from the private account(= 20 - contribution to the project) +

Income from the project(= 0.4 x Sum of contributions of all four players to the project)