You won't bid against yourself in one auction. Amazon will only enter the one keyword they think has the best chance of winning into a given auction. That does mean that generally they pick the one with the highest bid, so while you don't compete against yourself in the auction, you compete against yourself to get into the auction.
Amazon bid auctions are second price auctions, meaning that the winner of the auction pays the price of the second place bidder if their ad gets clicked.