Sequential Auctions with Generalized Interdependent Values

A common assumption in the analysis of symmetric auctions is that the bidders' value estimates exhibit positive informational externalities (PIE). This assumption implies upward drifting price sequences at sequential auctions, which is challenged by an empirical regularity, known as the "declining price anomaly," that observed price sequences at real sequential auctions tend to be downward-drifting. This paper extends the existing analysis to a generalized interdependent values environment, in which the bidders' values can exhibit both PIE and NIE (negative informational externalities). The case of NIE can arise naturally when competing bidders are also competitors in the same product market. If a bidder's type is related to his or his firm's ensuing competitive advantage, then an increase of a bidder's type increases his own but may decrease other bidders' expected values. We consider a general sequential auction mechanism that sells m identical objects through K (≤m) consecutive rounds, each round involving possibly a different number of objects for sale and a different payment rule. For risk neutral bidders having unit demand and independent types, we obtain two major results. First, the direct sequentially incentive compatible auction mechanisms, which implement the performance of essentially all standard auctions, are feasible under both PIE and NIE. Second, while the total expected revenue is invariant to sequencing and payment rules, the expected selling prices from different rounds of the auction are not the same. In a PIE environment the expected price sequence tends to be upward drifting, whereas in an NIE environment the expected price sequence is strongly downward drifting: the expected lowest price in round k exceeds the expected highest price in round k+1. The declining price "anomaly" could, therefore, be evidence of bidders' values featuring NIE or post-auction competition.