I have an Adwords campaign, which consists of 2 ad groups. And there are a few keywords that exist in both ad groups.
My question is, when a user types in those keywords, will this cause self-bidding at the Google Adwords end? Is the adwords program intelligent enough to realize that these keywords are coming from the same campaign and the price of that keyword shouldn't be bidden up?
Adwords will not have your multiple campaigns with similar keywords compete with each other. Bidding based on account, not campaign. When keywords from your different campaigns match:
Refer to adwords support.