Eliciting Multidimensional Private Information

This project is about the role of information in economic interactions. In many situations, in which two or more parties try to reach an agreement, like regarding a trade, there are not only differences between the interests of those involved, but also between their information. For example a seller and a buyer have opposite goals for determining the price. But how strongly these are pronounced, i.e., how much a buyer is maximally willing to pay or which further opportunities for a sale the seller expects, depends on the own information as well as that of the respective opponent. The seller usually knows the objective qualities of the trade good better, but does not know exactly which of these the buyer particularly appreciates or rather not. Both sides then have an interest to obtain information from the other, but they do not freely reveal theirs for strategic reasons. This observation applies also in many other situations, for instance when a joint project is to be realized and the question arises how much each member of the group contributes or what the realization should be in detail. The exchange of information is thus an essential part of every agreement. The meaning of unequally distributed information for the possibilities to reach agreements is well known within Microeconomics. When such situations are represented by mathematical models, it is possible to make clear predictions based on logical reasoning as to how far differing information can influence the result of a negotiation process. However, there are considerable differences between such models and hence the assumptions that are postulated. Some results are very abstract and widely valid, whereas others are quite special and only applicable under particular circumstances. The approach in this project aims at an intermediate level, to better understand the background of the often contrary results and to obtain new insights that are more systematic and have a more general applicability. For this goal, certain structural assumptions will be made regarding the interests of the involved parties and their information. These will be sufficiently general, however, to cover significantly more than specific examples. Correspondingly, new methods will be developed and applied for the analysis of these models. The central aspect for the investigation will be the complexity of the relevant information, in particular if it is multi- or one-dimensional. Sometimes it can be measured on a single scale, like a willingness to pay or an important performance figure. Many times, however, several factors are relevant and the scientific insights for this case are still quite scattered. This project is going to contribute to a more systematic and complete view.

If someone has private information, the question arises to what extent it can be used strategically. For example, salespeople consider how they present their products in order to persuade customers to make certain purchasing decisions; for this purpose, certain properties may be particularly emphasized and others only vaguely named or concealed. Also experts who are engaged for providing advice often have their own interest in the decision of their clients and can try to influence them by only indirectly reporting their specialist knowledge. Such strategic communication has been studied in the economic literature under various assumptions from a theoretical point of view, leading to some important fundamental insights. For example, the answer to the question of how much benefit can be drawn from the information monopoly depends heavily on the extent to which the information conveyed can be verified. In many interactions, however, communication is informal; then it is particularly difficult for the information holder to be credible and the possibility of exerting influence is very limited in the case of differing interests. In our project, we have taken up surprising, more recent results that show that private information can particularly also be used profitably when the information owner's interests in the other party's decision are fully known and independent of the actual information. This is the case, for example, when only achieving a sale counts and not whether the product meets the customer's needs. At least part of the information can still be conveyed credibly by blurring it. We examined how critical the central assumption for this result is. More generally, we asked ourselves how robust the equilibria of formal models of strategic communication are with respect to small deviations from certain preferences of the actors. For this, we first developed a suitable formal concept of robustness, which finally made it possible to achieve differentiated, meaningful results. For reasons of complexity, we initially concentrated on models in which the relevant information is only which of two possible scenarios applies; whether, for example, a certain condition is met or not. Within this framework, we were then able to achieve a full characterization of the robust equilibria. Building on this, we have been able to show, as a particularly concise result, that the equilibrium that is best for the information holder is always robust, while many other equilibria critically depend on special preferences. Through these robustness considerations, we come to a more concise statement as to what the outcomes of the theoretical models are.