
FURTHER RESEARCH TOPICS
Based on a discovery we made with Peter Bank in the framework of Hindy–Huang–Kreps preferences, we are able to provide a new approach to the theory of irreversible investment. The new approach allows to identify a socalled base capacity. The base capacity is an index that tells the firm when it should increase capacity, and when it should stay idle. (Finance and Stochastics 2011). In a current research project funded by the German research association DFG, we extend this approach to dynamic oligopoly and public good games under uncertainty.
In an interdisciplinary research project with the linguist Gerhard Jaeger, we studied some fundamental questions in linguistics with the help of game theory. It has long been argued in linguistics that the meaning of a word should correspond to a convex set in some suitable space of sensations. It turns out that such a conjecture can be proved with the help of game theory. In the context of a signaling game, where the speaker (informed agent) obtains a complex signal from an infinite type space and tries to signal his information to a hearer (receiver) with the help of only finitely many words, the type space is partitioned into convex tessels in any strict Nash equilibrium. One can show even that these partitions need to form a centered Voronoi tessellation of the type space. This is a typical instance of the power of mathematical modeling: it allows to clarify a conjecture and to prove even more than was anticipated. Some of the equilibria are less efficient than others, as is the case for natural languages as well. (Games and Economic Behavior 2011)
In joint work with Peter Bank (Technical University Berlin), Frank Riedel studied nontimeadditive intertemporal preferences that were developed by Hindy, Huang, and Kreps. The standard timeadditive approach to intertemporal utility, although mathematically very simple, is actually the wrong approach for several reasons. First of all, real humans do not display timeadditive preferences. My consumption for milk today and in two days is not independent of my consumption of milk tomorrow. But this is what timeadditivity implies. It just makes sense to study nontimeadditive preferences. On the technical side, the preferences introduced by Hindy–Huang–Kreps lead to a number of challenges. In particular, the question whether a competitive equilibrium exists was open for a long time. We solved this issue with Peter Bank (Finance and Stochastics 2001). Furthermore we investigated the structure of the resulting equilibrium prices with Filipe MartinsdaRocha (Université Paris Dauphine, Annals of Finance 2006, Journal of Economic Theory 2010). Our studies of demand behavior for such agents with Peter Bank led to a new approach to singular control problems that is based on a stochastic backward equation instead of optimal control techniques. This technique turned out to be useful in quite a number of other problems as well. (Annals of Applied Probability 2001)
The labour market constitutes a large part of the economic system, in developed countries labour income accounts for about two thirds of the national income, and roughly a half of the working age population in these countries is made up of wageearners. Therefore a sound understanding of the labour market and its dynamics is crucial for the economic policy aiming at increasing the social welfare. Search and matching theory is one of the newest research directions in labour economics. It is a modern economic tool allowing researchers to analyze and predict the aggregate transitions of workers in and out of unemployment as well as and the distribution of wages and inequality in a frictional labour market. Undoubtedly aggregate transitions are driven by the underlying individual decisions of workers. What is the effect of a more intensive labour mobility on the individual decision to stop or prolong the education? What is the impact of this decision on wage dispersion and the equilibrium unemployment? These and other questions are in the focus of the research team at the Center for Mathematical Economics.
Our research interests cover the broad area of Behavioral Economics. We are particularly interested in the following questions: What factors drive economic decisions of individuals? How do cognitive limitations affect decision making process? How can elements of bounded rationality be integrated into the field of mechanism design and how can the frame be manipulated in order to decrease the loss of efficiency due to bounded rationality?