What should be done when two people wish to apply the Sunnah of the Prophet, may Allah bless him and grant him peace, regarding not withdrawing one's hand first, and both refuse to initiate the withdrawal of their hand?

The Prophet, peace and blessings be upon him, would not withdraw his hand from the hand of one he was shaking until the other person withdrew his hand first. This was a teaching for his Ummah (nation) on how to honor and show respect to a companion. It is recommended for the handshake to continue until the conversation and questioning have concluded, and it is disliked to withdraw the hand quickly. Scholars have agreed that this is among the Sunnahs of shaking hands, and whoever anticipates that his companion will withdraw his hand, it is recommended for him to hold on. However, if he anticipates that his companion will hold on, then the one who initiated the handshake is the one who should initiate the withdrawal. This Sunnah should be free from pretentiousness and hardship. Scholars have clarified that the one holding on should hold on until the other person withdraws his hand, unless there is shyness or harm in delaying.