Allocations and Price Trends in Sequential Auctions under Complete Information with Symmetric Bidders

We analyze sequential second-price auctions under complete information involving two or more bidders with similar decreasing marginal valuations. Krishna (1999) designed a 2-bidder numerical example to show the existence of two symmetric equilibria characterized by an asymmetric allocation and weakly declining prices. We generalize Krishna's insights by showing that symmetric (asymmetric) allocations imply constant (weakly declining) price patterns and we derive the necessary conditions supporting symmetric allocations. The conditions become increasingly restrictive as the number of object increases.