Is there any competition between daily deal sites?

A deal's a deal, the people who buy groupons don't have a "groupon" budget where they have only x dollars to spend on discounted services a day. They are looking for deals that works for them, and are all impulse buyers.

Groupon, Google Offers, various clones are not so much competing with each other, the buyers will buy whatever deal(s) they like the most. If groupon is offering a deal on Indian food, and google offers is offering a deal on foot massages, and the buyer loves Indian food and foot massages he will buy both.

As long as these sites can keep offering compelling deals, they all will thrive as people love bargain hunting.