In a distributed system is it possible for both parties to simultaneously agree a message exchange was made?
I think it is the "two general" problem.

The "two general" problem is informally stated as follows [1]:


  The commanding general of the first division wishes to coordinate a simultaneous attack. The generals can communicate only by means of messengers. Normally, it takes a messenger one hour to get from one encampment to the other. However, it is possible that he will get lost in the dark or, worse yet, be captured by the enemy. 


What is the difference between this and your "message-exchanging" problem?



[1] Reasoning about Knowledge. By Ronald Fagin, Joseph Y. Halpern, Yoram Moses and Moshe Vardi.