Algebro-Geometric Aspects of the Classical Yang-Baxter Equation

In this thesis we consider algebro-geometric aspects of the Classical Yang-Baxter Equation and the Generalised Classical Yang-Baxter Equation. In chapter one we present a method to construct solutions of the Generalised Classical Yang-Baxter Equation starting with certain sheaves of Lie algebras on algebraic curves. Furthermore we discuss a criterion to check unitarity of such solutions. In chapter two we consider the special class of solutions coming from sheaves of traceless endomorphisms of simple vector bundles on the nodal cubic curve. These solutions are quasi-trigonometric and we describe how they fit into the classification scheme of such solutions. Moreover, we describe a concrete formula for these solutions. In the third and final chapter we show that any unitary, rational solution of the Classical Yang-Baxter Equation can be obtained via the method of chapter one applied to a sheaf of Lie algebras on the cuspidal cubic curve.

Economics of Ethical and Prosocial Behavior: Experiments on Social Responsibility, Ignorance, and Cheating

In this thesis I experimentally investigate prosocial and ethical behavior in economic interactions. The thesis consists of three experimental research papers that have a broad range of research questions on social responsibility, ignorance and cheating. With these experiments I aim to better understand when and why people behave ethically and/or prosocially and which consequences it has on their own and other players’ payoffs, and on overall efficiency. The results from the three experimental studies suggest that (i) donations to charity by employees are rewarded in an experimental setting, and the effect is driven by reciprocal concerns; (ii) there is a significant fraction of people who decide not to know about negative consequences of own actions, and the sorting of social agents of a low type into ignorance drives self-interested behavior of ignorant agents; and (iii) if the possibility of being exposed as a liar is small, the tendency to lie increases with incentives, indicating that some people have positive and finite costs of lying. Furthermore, when the participants lie, they lie to the full extent, which suggests that the intrinsic cost of lying is fixed.