Goals of Research Area I

We sketch below the main types of research problems that we shall study in the future. For most of them, some initial results are already available.

Robustness and mechanisms without transfers.

Mechanism design problems with quasilinear utility but without transfer payments are only partially understood because they are not amenable to the classical optimization tools pioneered by Myerson. In particular, not every monotone allocation function is part of an incentive compatible mechanism (a phenomenon also occurring in design problems with transfers, but multidimensional signals). We shall focus on multi-agent mechanism design problems with both private and interdependent values. The goal is to characterise incentive compatible mechanisms, and to establish the optimality of simple voting mechanisms within the class of Bayes-Nash incentive compatible mechanisms. In addition, we shall experimentally examine institutional features that are used to create incentives, but that do not necessarily rely on monetary payments, e.g. measures that confer different status levels to employees with different performances. The experimental lab here in Bonn offers ideal conditions for this endeavour. An important role in the recent mechanism design literature is played by the relations between robust equilibrium concepts such as dominant strategy or ex-post implementation and between the weaker notion of Bayes-Nash incentive compatibility. Quite surprisingly, several theoretical results that were obtained within the mathematical framework of computed tomography were shown to be relevant for the elucidation of these relations for the private values case with monetary transfers. We shall attempt to extend these applications to mechanism without transfers. Robustness considerations play also a major role for the provision of public goods, and for the creation of proper governance mechanisms for the regulation of financial institutions. These themes constitute focal points for the research within MPIRCG.

Ex-ante strategic decisions and efficiency.

In various economic environments, strategic agents make decisions (e.g. savings, investments, information acquisition) that later affect their trading opportunities. An important question is the design of contracts that govern the ex-post trading stage but that lead to the right (i.e., efficient) ex-ante decisions. A classical environment where this issue arises is two-sided matching with ex-ante investments. Our focus shall be on generalizations of the Cole-Mailath-Postlewaite analysis to the case where the agents’ attributes are multidimensional, and where agents on both sides of the market are privately informed about their attributes. The optimal match is then a solution to a transportation problem (a topic of interest in Research Area G), and there is an interesting formal analogy between the cyclical monotonicity of optimal transport maps and the cyclical monotonicity of incentive compatible allocations. A similar perspective appears in one-sided auctions where we shall study the seller’s incentives to generate information that affects the valuations of potential buyers, or to spend resources (such as advertising) in order to attract more buyers. An important insight is that, by creating correlations among buyers’ values, the seller will be able to extract more surplus. Related questions will be studied in the context of delegated portfolio management and other legal scenarios appearing in contract law where the focus is on the unobservability of the investments and on the combination of remedial legal actions. Finally, the main theme of allocational efficiency will be supplemented by studies of computational efficiency or approximate efficiency in game theoretic problems. This line will be pursued in collaboration with researchers who also (participate in Research Area L).

Stochastic and dynamic games. The analysis of stochastic, dynamic games requires sophisticated tools, e.g. solutions to systems of (stochastic) differential equations. Thus, methods from continuous-time finance (that are studied in Research Area H) can play an important role in the analysis of such games. We wish to note here that a full TP dedicated to ‘Stochastic Dynamics in Economics and Finance’ is planned for 2013. A main topic within our research area is continuous-time contests and dynamic generalizations of the all-pay auction. Roughly speaking, in such games players decide when to stop a privately observed stochastic process while only the player who stops his process at the highest value wins a prize. In cooperation with researchers from computer science, Röglin shall introduce dynamics to congestion games that have, so far, been mostly studied as static interactions. Another focus shall be on several open problems in the theory of bandit games with strategic experimentation, among them the structure of the best/worst symmetric and possibly non-Markovian equilibria, and the construction of Markov equilibria for general correlations among the bandits controlled by the various players. These questions require a blend of game theory and optimal control. A related blend appears in the area of dynamic pricing under conditions of dynamic stochastic demand. While most of the existing operations research literature is restricted to a monopolistic  framework, we shall investigate oligopolistic pricing schemes. Dynamics play also a major role in the study of evolutionary processes. Here, our particular interest lies in various genetic or cultural transmission mechanisms. This is also the subject of ongoing large-scale surveys and experiments conducted by Falk and various co-authors. More generally, the researchers in this area will profit from the extensive infrastructure and close cooperation offered by the Bonn  Econ Lab, whose director is Falk.