Essays on Multidimensional Information

Abstract

This thesis consists of three independent contributions in the area of microeconomic theory. All three contributions share the feature of agents holding multidimensional private information which motivates the title of the thesis.<br /> Part 1, entitled “Consistency and Communication in Committees”, is based on a working paper under the same title which is joint work with Inga Deimen and Mark T. Le Quement, both from the University of Bonn. In this paper, we generalize the classical binary Condorcet jury model by introducing a richer state and signal space, thereby generating a concern for consistency in the evaluation of aggregate information. Information is of multidimensional nature here as it does not only provide information about the defendant being guilty or innocent but also indicates a particular modality of guilt or innocence. As coherent evidence for a particular variant of either guilt or innocence is more meaningful than if that information were dispersed, the consistency of signals constitutes a second informative dimension besides the mere number of signals indicating guilt or innocence when deciding whether to acquit or convict the defendant. We use this approach to analyze truthtelling incentives in pre-vote communication in heterogeneous committees and find that full pooling of information followed by sincere voting is compatible with a positive probability of ex post conflict in the committee. This is in stark contrast to the benchmark finding for the binary signal model in Coughlan (2000). We furthermore characterize implementability conditions for a wide class of decision rules including the rule that maximizes committee welfare.<br /> Parts 2 and 3 analyze more classical instances of multidimensional information such as different production costs or different valuations for different goods which give rise to multidimensional screening problems. Both parts have in common that they provide explicit characterizations of the optimal mechanisms, a feature that is often not achievable in the multidimensional screening literature.<br /> Under the title “A Baseline Model of Multidimensional Screening”, part 2 generalizes upon a model of multidimensional screening from Armstrong and Rochet (1999) by allowing for interaction between the dimensions through the utility function. Identifying sets of binding incentive constraints with properties of the allocation I provide a full classification of the potential solutions to this model. While a large variety of solutions can be generated within the modeling approach, I show that a substantial combination of interaction and asymmetry between dimensions is necessary to distort allocations away from classical properties such as “no distortion at the top” and “no upward binding incentive constraints”. Some fundamental properties of the optimal allocation are shown to carry over from the first best allocation to the case of private information. Part 2 is framed as an analysis of multiproduct monopoly regulation. Its focus, however, is not so much on a particular application but on the general properties of the underlying model which applies to various contexts.<br /> Part 3 is entitled “Pricing a Package of Services - When (not) to Bundle” and is based on a joint paper under the same title with Dezsö Szalay from the University of Bonn and CEPR. In this paper, we study a tractable two-dimensional model of price discrimination. Consumers combine a rigid with a more flexible choice, such as choosing the location of a house and its quality or size. We show that the optimal pricing scheme involves no bundling, that is, additively separable prices if consumer types are affiliated. Conversely, if consumer types are negatively affiliated over some portion of types then some bundling occurs.