According to ApplicantAuction.com the first private auction for new gTLD strings are underway.
Although other than .Club which publicly announced it would be participating in the auction which started today, there hasn’t been any public announcement on how many other auctions are going on or what the string are.
Both Donuts and Demand Media, Inc. (DMD) announced it was entering the private auction for a number of new gTLD strings they applied for but there has not been confirmation by other parties that have competing applications.
According to ApplicantAuction.com the third round is now underway and closes in minutes with an unlimited number of subsequent rounds until a winner is determined.
Also under ApplicantAuction, each of the strings in the auction are being auctioned off at the same time
According to the ICANN applicant guidebook, if the parties to a competing application cannot resolve their differences the new gTLD string will go to an ICANN auction which will be held at a yet to be determined time.