Mechanism Design for the truthful elicitation of costly probabilistic estimates in Distributed Information Systems

This paper reports on the design of a novel two-stage mechanism, based on strictly proper scoring rules, that allows a centre to acquire a costly forecast of a future event (such as a meteorological phenomenon) or a probabilistic estimate of a specific parameter (such as the quality of an expected service), with a specified minimum precision, from one or more agents. In the first stage, the centre elicits the agents' true costs and identifies the agent that can provide an estimate of the specified precision at the lowest cost. Then, in the second stage, the centre uses an appropriately scaled strictly proper scoring rule to incentivise this agent to generate the estimate with the required precision, and to truthfully report it. In particular, this is the first mechanism that can be applied to settings in which the centre has no knowledge about the actual costs involved in the generation an agents' estimates and also has no external means of evaluating the quality and accuracy of the estimates it receives. En route to this mechanism, we first consider a setting in which any single agent can provide an estimate of the required precision, and the centre can evaluate this estimate by comparing it with the outcome which is observed at a later stage. This mechanism is then extended, so that it can be applied in a setting where the agents' different capabilities are reflected in the maximum precision of the estimates that they can provide, potentially requiring the centre to select multiple agents and combine their individual results in order to obtain an estimate of the required precision. For all three mechanisms (the original and the two extensions), we prove their economic properties (i.e. incentive compatibility and individual rationality) and then perform a number of numerical simulations. For the single agent mechanism we compare the quadratic, spherical and logarithmic scoring rules with a parametric family of scoring rules. We show that although the logarithmic scoring rule minimises both the mean and variance ...