We explore the optimal selection problem where two decision makers are involved in the evaluation of the arriving offers. We develop three stopping rules to avoid conflictual situations where a decision makers agrees with a current offer and the other wishes to discard it. The three stopping rules are then implemented in C language and runned on a series of problems with various sizes. The experimental results show that the selection rules generate different behaviours of the decision makers. Finally, we compare our problem with the optimal selection problem including a single decision maker and show the loss of utility generated by the introduction of an additional decision maker.