An Optimal Stopping Problem with Two Decision Makers

Abstract

We investigate in this paper an optimal stopping problem where two decision makers are involved in the selection of a single offer. Suppose that n offers are examined one at a time by both decision makers. At each stage, a decision must be taken: accept the current offer and stop the selection process, or discard it and examine the next offer. We assume that no recall of previously examined offers is allowed. A conflict arises when one decision maker decides to accept a currently inspected offer and the second decides to discard it. In such conflicting situations, a decision should be taken by defining a stopping rule for the group. We propose to stop the process if either decision maker accepts an offer. We develop the dynamic programming approach for this problem and state the optimal strategy for a fixed utility. Then, we propose an experimental investigation of the problem.

Keywords:

• Dynamic programming
• Game theory
• Group decisions
• Optimal stopping

Subject Classifications:

• 62L15
• 91A05

ACKNOWLEDGMENTS

We thank the Associate Editor for many helpful comments.

Notes

Recommended by N. Mukhopadhyay