License auctions with exit (and entry) options : alternative remedies for the exposure problem

Inspired by some spectrum auctions, we consider a stylized license auction with incumbents and one entrant. Whereas the entrant values only the bundle of several units (synergy), incumbents are subject to non-increasing demand. The seller proactively encourages entry and restricts incumbent bidders. In this framework, an English clock auction gives rise to an exposure problem that distorts efficiency and impairs revenue. We consider three remedies: a (constrained) Vickrey package auction, an English clock auction with exit option that allows the entrant to annul his bid, and an English clock auction with exit and entry option that lifts the bidding restriction if entry failed.