Optimal Auctions when a seller is bound to sell to collusive bidders (new version of "using lotteries...")

I consider optimal auctions for a seller who is bound to sell a single item to one of two potential buyers, organized in a `well-coordinated' cartel. I show that, even though the seller cannot deter collusion, he can optimally accommodate it by employing a simple mechanism which imposes an inefficient allocation on the bidders unless they pay a sufficiently high amount to avoid it.