In practice, common knowledge is hard to obtain. In certain situations it is not neccessary if things happen simultaneously. The
coordination does not have to be perfect. Let us take a look at the Byzantine Generals problem again. It might be sufficient when
the generals attack a certain amount of time ε after each other: we wat the events to hold at most ε time units apart.
The knowledge that is attained in this way, is an approximation of true common knowledge, which is called shared knowledge or
ε-common knowledge.
Let us go back to the Alice and Bob example. When ε=0, then they both achieve common knowledge of the sent message directly
after it is sent. In this way, they both immediately know the contents of the message and the fact that the message has been sent.
As we have seen, if ε becomes larger, then Alice does not know that Bob received her message immediately after she has sent it.
She does know that Bob will receive the message within ε time units from the moment the message has been sent. No matter to
how many agents she sent the message, she knows that within ε time units, everyone knows that the situation holds.
We call the way of coordinating this way ε-coordination. This way of coordination is often attainable in practice, even in systems
where the sending time of the messages is uncertain. In lots of systems, where the ε is sufficiently small, ε-coordination
works practically as good as perfect coordination.
The interactive movie below shows the way ε-coordination works. A message is being sent, and it arrives within a certain time
frame ε. Everybody knows that everybody receives the message within that time frame, so as soon the time window has passed,
shared knowledge, or ε-common knowledge is attained by all relevant agents.