Dictator game experiments come in three flavors: plain vanilla with strictly dichotomous separation of dictator and recipient roles, an interactive alternative whereby every subject acts in both roles, and a variant thereof with role uncertainty. We add information regarding which of these three protocols was used to data from the leading meta-study by Engel (Exp Econ 14(4):583–610, 2011) and investigate how these variations matter. Our meta-regressions suggest that interactive protocols with role duality compared with standard protocols, in addition to being relevant as a control for other effects, render subjects’ giving less generous but more efficiency-oriented. Our results help organize existing findings in the field and indicate sources of confounds.

US power ‘elites’ are substantially less fair-minded than ‘non-elite’ general populations claims a study by Ray Fisman and coauthors [Science 349, 6254 (2015)]. This supposedly explains why US governments, run by people less fair than the citizens they represent, have been uninclined to tackle inequality. We critically replicated the study, because different experimental protocols for ‘elites’ (interactive variants) and ‘non-elites’ (standard dictator games) were used to measure preferences. We find that the protocol potpourri drove the conclusion: under standard protocols, we find no significant class differences, if any opposite ones. Our work highlights the risk of producing false positives when ex post results appear invitingly plausible.

We aim to estimate the power distribution in the Council of the European Union-both a priori and a posteriori. With respect to the latter, our analysis suggests that several previously used indices are ill-suited for this application. By introducing minimal modifications, we propose a new index and compare it with previous constructions in a unified framework. Empirically, we find that that all countries gain a priori voting power in the Council as a result of Brexit. We rely on data from the Chapel Hill Expert survey to compute a posteriori power and find that it is more unequally distributed than a priori power. Specifically, a posteriori power is almost exclusively held by relatively few rather populous states (yet not the United Kingdom). As regards Brexit, France appears as the main benefactor in terms of gaining a posteriori power; Poland loses substantive power in several areas but remains one of the most powerful EU member states.

We present clean experimental evidence that a methodological confound was introduced by Andreoni and Miller (2002) that leads to diametrically opposed conclusions regarding comparisons of preferences between categories of fellow human beings distinguished by gender or age. Our study is a warning not to run the Andreoni-Miller tests of the consistency of altruistic preferences on the basis of their ‘interactive’ experimental protocol, and in particular not to perform preference estimations with the purpose of said comparisons. It is more interpretable and controllable to run the traditional, standard dictator game.

Experimental implementations of dictator games are found to differ in terms of their underlying strategic incentives. We explore this discovery in two separate directions. Theoretically, assuming identical other-regarding preferences, we show that the two most widely used protocols can generate strongly contrasting rational-choice predictions, from which different interpretations of dictator giving arise. Experimentally, a tailor-made experiment reveals significant differences between the two protocols but rejects full rationality as a satisfactory explanatory theory. Our findings indicate that several previously drawn conclusions regarding other-regarding preferences among humans distinguished by social class, gender, generation, nationality, etc. may be more ambiguous than hitherto believed.

The European Commission has proposed a refugee distribution key, which yields respective quotas for European Union/European Free Trade Association member states. It is based on four quantities: GDP, population, asylum applications per capita in the past, and unemployment rates. I show that the given distribution key has properties which contradict the European Commission's intentions. Exemplarily, states with low (high) unemployment may experience a lower (higher) quota when unemployment is taken into account compared to when it is not. These deviations are single-digit percentages. As a remedy, I propose an alternative distribution key, which avoids the undesired properties. It is modeled in the spirit of the European Commission's proposal and is based on the same four quantities. Deviations between the two distribution keys are up to two-digit percentages.

We propose a new family of mechanisms, whereby players may give more or less directly to one another. A cornerstone case is the regular linear public goods mechanism (LPGM), where all contribute into a single common group account, the total amount of which is then distributed equally among players. We show that with sufficiently (yet not necessarily fully) pro-social preferences, the social optimum can be reached in Nash equilibrium in all social dilemma situations described by our mechanisms (including the LPGM). In addition, for a given heterogeneity of pro-social preferences, we help to identify which specific mechanisms perform best in terms of incentivizing giving. Our results are therefore relevant from two vantage points. One, they provide proper rational choice benchmarks based on Nash equilibrium under the assumption of other-regarding preferences. Two, they provide arguments in favor of re-structuring many collective action problems currently implemented as LPGMs when it is feasible to gain some information concerning who has concern for whom.

We propose a simple new a posteriori power index and apply it to the Council of the European Union as a case in point.Our index is developed within a framework that allows for a systematization and generalization of several existing a posteriori voting power indices as well as a transparent and intuitive connection with standard a priori power indices. Critically, our analysis reveals various conceptual difficulties of existing approaches to which our own index can be seen as a minimal remedy.Empirical results are based on data from the Chapel Hill Expert survey and indicate that a posteriori power in the Council is more unequally distributed than a priori power. More precisely, it is almost exclusively held by relatively few rather populous states, predominantly by France, Germany and Poland. The United Kingdom, by contrast, is usually found to be significantly less powerful. As regards Brexit, France appears as the main benefactor in terms of gaining a posteriori power; Poland loses substantive power in several areas but remains one of the most powerful EU member states.

We prove an adiabatic theorem for the non-autonomous Gross-Pitaevskii equation in the case of a weak trap. More precisely, we assume that the external potential decays suitably at infinity and admits exactly one bound state.

We analyze the problem of dividing a fixed amount of a single commodity between two players on the basis of the Nash bargaining solution (NBS). For one-shot negotiations, a cornerstone result of Roth (Axiomatic models of bargaining. Springer, Berlin, 1979 ) establishes that the more risk averse player will obtain less than half the total amount. In the present paper, we assume that the bargaining procedure occurs over several rounds. In each round, an increasing share of the total amount is negotiated over in accordance with the NBS, the disagreement point being determined by the outcome of the previous round. In line with Roth’s result, the final amount received by the more risk averse player is still bounded by half the total amount. As a new feature, however, this player does not lose from bargaining for more rounds if his opponent exhibits non-increasing absolute risk aversion. What is more, both players’ risk profiles become essentially irrelevant if successive bargaining takes place over sufficiently small commodity increments. Each player then gets approximately half of the commodity.

We prove an adiabatic theorem for the non-autonomous Gross-Pitaevskii equation in the case of a weak trap. More precisely, we assume that the external potential decays suitably at infinity and admits exactly one bound state.

We give results on the absence of singular continuous spectrum of the one-particle Hamiltonian underlying the electronic black box model.

We investigate the low energy excitation spectrum of a Bose gas with weak, long range repulsive interactions. In particular, we prove that the Bogoliubov spectrum of elementary excitations with linear dispersion relation for small momentum becomes exact in the mean-field limit.

We develop an adiabatic theory for generators of contracting evolution on Banach spaces. This provides a uniform framework for a host of adiabatic theorems ranging from unitary quantum evolutions through quantum evolutions of open systems generated by Lindbladians all the way to classically driven stochastic systems. In all these cases the adiabatic evolution approximates, to lowest order, the natural notion of parallel transport in the manifold of instantaneous stationary states. The dynamics in the manifold of instantaneous stationary states and transversal to it have distinct characteristics: The former is irreversible and the latter is transient in a sense that we explain. Both the gapped and gapless cases are considered. Some applications are discussed.

We consider a family of time-dependent dephasing Lindblad generators which model the monitoring of the instantaneous Hamiltonian of a system by a Markovian bath. In this family the time dependence of the dephasing operators is (essentially) governed by the instantaneous Hamiltonian. The evolution in the adiabatic limit admits a geometric interpretation and can be solved by quadrature. As an application we derive an analog of the Landau-Zener tunneling formula for this family.

We show that, provided dephasing is taken into account, there is a unique timetable which maximizes the fidelity with a target state in adiabatic evolutions. The optimum has constant tunneling rate along the path. Application to quantum search algorithms recovers the Grover result for appropriate scaling of the dephasing with the size of the database. Moreover, the Grover bound imposes constraints on the dephasing rates of systems coupled to a universal Markovian bath.

This thesis is concerned with the examination of systems whose external parameters change slowly in time. The slowness assumption allows for the so called adiabatic approximation in many situations and is a useful means to study a variety of physical question. Both aspects are addressed here: On the one hand we present adiabatic theorems for linear as well as nonlinear evolution equations. On the other hand several applications are being discussed with main focus on quantum mechanical systems. In a first – purely mathematical – part, we adopt a relatively abstract framework, namely that of time-dependent generators of contraction semigroups on a Banach space. If such generators satisfy a certain spectral gap condition there exists a perturbation expansion in the parameter measuring the slowness. The structure of the expansion has a geometric meaning entailing a distinction between terms which are local and terms which are non-local in time. If the gap condition is abandoned an adiabatic theorem can still be proved, though without information on the rate of convergence in the limit of infinite slowness. We will see that the appreciation of the geometric structure allows for fairly simple proofs in both cases. Our theorems are likewise applicable to closed and open quantum systems described by a family of Hamiltonians or Lindbladians, respectively. A short introduction to the latter is the subject of the second part of this thesis. In view of our physical examples a particular emphasis is placed on the special class of dephasing Lindbladians. They model decoherence without dissipation: for them, a structural theorem is presented. A third part then treats the combination of adiabatic and quantum theory resulting in a considerable range of applications: The coefficients in the above mentioned perturbation expansion have a different physical interpretation in closed as opposed to open quantum systems. After highlighting this fact in some generality we turn to more specific settings: An analogue of the Landau-Zener formula for transitions near an avoided crossings of eigenvalues is derived in the dephasing case. Furthermore, an optimization problem in adiabatic quantum computing is investigated in absence and in presence of dephasing. As a result, constraints on the physically allowed dephasing parameters are revealed in the case of Grover’s search algorithm. Subsequently, we turn to slowly driven stochastic systems in order to illustrate the applicability of adiabatic perturbation expansions outside of quantum mechanics. The chapter is rounded off by a discussion of the adiabatic theorem in closed and open quantum systems without the condition of a spectral gap. All these results are finally complemented in a forth part by an example of a nonlinear adiabatic theorem. More precisely, we study the time-dependent Gross-Pitaevskii equation which describes the dynamics of a weakly interacting Bose-Einstein condensate which is trapped by a slowly in time varying potential with exactly one eigenstate. The fact that the propagator of the linearized equation is not a contraction complicates the control of error terms considerably and asks for additional techniques in comparison to the linear case. That said however, the more concrete setting – that of a partial differential equation and a function space – allows for further structure and in particular we have dispersive estimates for the linear Schrödinger equation at hand. In connection with a bootstrap argument they enable us to prove the desired result.