Unraveling of value-rankings in auctions with resale

Consider a single-unit auction with resale and two risk neutral bidders. The ranking of the valuations is known to both the bidders-that is, the bidders know the identity of the highest and lowest valuation bidders. We show that, when the value-rankings are revealed, the classic result of "bid symmetrization" does not hold. Surprisingly, the bidder with the lowest valuation produces a stronger bid distribution than the bidder with the highest valuation. We also show that the revelation of value-rankings in auctions with resale asymmetrizes the bidding strategies. Finally, for a special family of probability distributions, we show that the first-price auction is revenue superior to the second-price auction.