Mechanisms for information elicitation

We study the computational aspects of information elicitation mechanisms in which a principal attempts to elicit the private information of other agents using a carefully selected payment scheme based on proper scoring rules. Scoring rules, like many other mechanisms set in a probabilistic environment, assume that all participating agents share some common belief about the underlying probability of events. In real-life situations however, the underlying distributions are not known precisely, and small differences in beliefs of agents about these distributions may alter their behavior under the prescribed mechanism. We examine two related models for the problem. The first model assumes that agents have a similar notion of the probabilities of events, and we show that this approach leads to efficient design algorithms that produce mechanisms which are robust to small changes in the beliefs of agents. In the second model we provide the designer with a more precise and discrete set of alternative beliefs that the seller of information may hold. We show that construction of an optimal mechanism in that case is a computationally hard problem, which is even hard to approximate up to any constant. For this model, we provide two very different exponential-time algorithms for the design problem that have different asymptotic running times. Each algorithm has a different set of cases for which it is most suitable. Finally, we examine elicitation mechanisms that elicit the confidence rating of the seller regarding its information.