Will same keywords located in different ad groups under a single campaign bid with each other?

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:

• The win goes to the exact match with the search query
• The win goes to the most restrictive match type
• Closest geographic targeting
• Highest ad rank

Refer to adwords support.