A dynamic approach for the two-decision maker selection problem with group interviewing options

The present paper proposes a generalization of the Optimal Stopping Problem where two decision makers are involved in the interviewing of groups of offers. In the studied variant, the DMs are required to select jointly a single offer from an n-sized sequence, dispatched in g groups. At each time step, a new group is received and a varying number of options are inspected. Since the objective is to select the best offer of the whole sequence, the DMs have an interest in declining the less interesting offers by abandoning the current group and continuing to the next, and selecting the offer they expect to be the best and stopping the selection process. A dynamic programming solution approach based on conflict management rules is proposed to select a compromise offer. We test our approach on several data sets and for different DMs' utilities, and we finally show the relevance of our approach via convenient performance measures.