An inverse or negative auction

In this Technical Report we describe a type of auction mechanism where the auctioneer A wants to auction an item among a certain number of bidders of a set B that submit bids in the auction with the aim of not getting that item.
Owing to this feature we call this mechanism an inverse or negative auction.
The main motivation of this mechanism is that both the bidders and the auctioneer give a negative value to the auctioned item (and so they see it as a bad rather than a good).
The mechanism is presented in its basic simple version and with some possible extensions that account for the payment of a fee for not attending the auction, the interactions among the bidders and the presence of other supporting actors.