 The most related model of bidding is Jeitschko (1999), who finds that relatively to exogenous and
certain future supply, exogenous but uncertain future supply leads to a proportional bid increase.In contrast, high-valuation bidders shade more than low valuation bidders here.The most related model of optimal sequential auctioning by Vulcano, van Ryzin,
and Maglaras (2002) (VRM), who study a monopolist selling to unit-demand strategic buyers who each only lives for one period.