| What is the coordinated attack problem? What is its significance?

A classical example of the importance of common knowledge is the
coordinated attack problem. Two generals on two hills separated by a
valley containing an enemy army have made no a priori plan of
attack. If they attack simultaneously, they will defeat the enemy, but
if one attacks alone, his army will be defeated. Their only form of
communication is via a messenger running between the two
hills. However, this messenger can get lost or captured along the
way. Consequently, there is always some uncertainty as to whether or
not a message has gotten through. The result is that the generals will
never attack.

This problem demonstrates that as long as there may be uncertainty about
message delivery time in a system, common knowledge is unattainable, so
coordination is not possible, since common knowledge is a prerequisite for
agreement. However, it is sometimes the case that a weaker form of common
knowledge, such as e-common knowledge (given a sentence p, after e time
everybody will know p, after e time everybody will know that after e time
everybody will know p, etc.), can be obtained, and sometimes the
correspondingly weaker form of coordination is sufficient for the domain.
Also, many times the possibility of attaining common knowledge depends on
the granularity of the model of time; i.e., the more fine-grained the
model, the harder it is to attain common knowledge. 

More generally, the analysis of this problem and subsequent results
demonstrated the power of the knowledge-based approach for understanding
and providing insight into distributed protocols.