Sequential Auctions with Partially Substitutable Goods

In this paper, we examine a setting in which a number of partially substitutable goods is sold in sequential single unit auctions. Each bidder needs to buy exactly one of these goods. In previous work, this setting has been simplified by assuming that bidders do not know their valuations for all items a priori, but rather are informed of their true valuation for each item right before the corresponding auction takes place. In our analysis we don’t make this assumption. This complicates significantly the computation of the equilibrium strategies. We examine this setting both for first and second-price auction variants, initially when the closing prices are not announced, for which case we prove that sequential first and second-price auctions are revenue equivalent, and then when the prices are announced; in the latter case, because of the asymmetry in the announced prices between the two auction variants, revenue equivalence does not hold. We finish the paper, by giving some initial results about the case when free disposal is allowed, and therefore a bidder can purchase more than one item.