Why didn't Draper fire Peter?

Question

In season 1, Peter Campbell tries to blackmail Draper into giving him the job of head of accounts by using his secret past against him. Draper refuses to budge, and Peter's plan backfires when their boss Cooper doesn't seem to care about Draper's past. When Peter leaves, Cooper gives Draper his blessing to fire Peter (in contrast with him protecting Peter the last time Draper wanted to fire Peter). Yet Draper doesn't. I've never understood his reasoning for it. Why didn't Draper fire this person who is so openly antagonistic to him?

Note: I've only seen season 1 and part of 2 so far.

Answer 1

Pete makes good on the threat of exposing Don's true identity to Bert Cooper but Bert says Who cares?, neutralizing the threat. This is presumably because Don is such an effective idea man that Bert doesn't care what Don's name really is. In addition, Bert gives Don the option of keeping him or firing him—whichever he thinks best. As a WW I soldier, he knows that decision gives Don his best advantage. But Bert later uses this knowledge to pressure Don into signing a contract Don is not inclined to.

On one hand, Don can fire and replace him, but Don would be starting off effectively fresh with someone new and not know the balance of skills and ambition. On the other hand, Don has the advantage over Pete and Pete has played his most effective strategy and lost. As a result, they both then know that Don is the alpha male—Pete won't cross Don again.