###Will the DoJ object to this auction because it violates anti-trust regulations?

We think this is extremely unlikely, but strongly recommend applicants to seek their own legal advice. A good starting point for asking your legal counsel about the topic is pointing them to [this article by a lawyer with 20 years experience as an antitrust attorney][1]. Some more practical thoughts on the topic can be found in [this blog post][2], and [this one][3]. 

[3]: http://rightofthedot.com/2013/04/does-the-use-of-private-auctions-to-resolve-new-gtld-contention-sets-automatically-violate-federal-antitrust-laws/

[2]: http://domainnamewire.com/2013/03/19/doj-private-auctions/

[1]: http://www.circleid.com/posts/20130406_much_ado_about_nothing

Of the applicants we spoke to on the topic, those who have sought independent legal advice are generally much less worried than ones who have not; for this and other reasons, we strongly recommend applicants to seek counsel on the matter and make their own judgment.  

Another data point that some applicants may consider noteworthy is that the neutral party that drafted the contracts and will be instructing the escrow agent is well-known law firm [Morrison & Foerster LLP][4].

[4]: http://www.mofo.com/James-Tanenbaum/