Two-stage Game Theoretic Model for the Allocation of Physician Appointments in an Outpatient Clinic

The paper proposes a method for doctor scheduling, which incorporates two game-theoretic models with consideration of morning, afternoon, and evening shifts. First, each of the twelve non-cooperative games models the weekly interactions between a group of outpatients and a physician, the Nash equilibrium is then applied to calculate a workload value (WV) for each physician. Second, the Shapley-Shubik power index is calculated for each physician in a cooperative game based on the workload values of all physicians. Outpatient appointments scheduled for the next week are determined by the doctor's expected marginal contribution. The experiment results demonstrate that the administrator can apply this model to determine the allocation of appointment availability for three shifts per day by assessing the appointment workload value for each physician.