Optimal allocation of MRI scan capacity among competitive hospital departments

We consider an MRI scanning facility run by a Radiology department. Several hospital departments compete for capacity and have private information regarding their demand for scans. The fairness of the capacity allocation by the Radiology department depends on the quality of the information provided by the hospital departments. We employ a generic Bayesian game approach that stimulates the disclosure of true demand (truth-telling), so that capacity can be allocated fairly. We derive conditions under which truth-telling is a Bayesian Nash equilibrium. The usefulness of the approach is illustrated with a numerical example.