Obtaining costly unverifiable valuations from a single agent

We consider the problem of a principal who needs to elicit the true worth of an object she owns from an agent who has a unique ability to compute this information. The correctness of the information cannot be verified by the principal, so it is important to incentivize the agent to report truthfully. Previous works coped with this un-verifiability by employing two or more information agents and awarding them according to the correlation between their reports. In this paper we show that even with only one information agent truthful information can be elicited, as long as the object is valuable for the agent too. In particular the paper introduces a mechanism that, under mild realistic assumptions, is proved to elicit the information truthfully, even when computing the information is costly for the agent. Moreover, using this mechanism, the principal obtains the truthful information incurring an arbitrarily small expense beyond whatever unavoidable costs the setting dictates. Full version is available at https://arxiv.org/abs/1804.08314.