Agreement is determined by comparing simultaneous recorded offers at a cutoff moment. [definitional]
Next, what do we mean by "agreement"? For simplicity, suppose that each player keeps (or may keep) his current "official" offer recorded in some manner that will be visible to the referee when the bell rings. Perhaps he keeps it written on a blackboard that the other player can see; perhaps he keeps it in a sealed envelope that is surrendered to the referee when the bell rings; perhaps he keeps it punched into a private keyboard that records his current offer in the referee's room. When the bell rings, the blackboard is photographed, the envelope surrendered, or the keyboard locked, so that the referee needs only to inspect the two "current" offers as they exist at midnight to see whether they are compatible or not.
Thomas C. Schelling, The Strategy of Conflict, loc. 616