A dynamic axiomatic approach to first-price auctions

The first-price auction is popular in practice for its simplicity and transparency. Moreover, its potential virtues grow in complex settings where incentive compatible auctions may generate little or no revenue. Unfortunately, the first-price auction is poorly understood in theory because equilibrium is not a priori a credible predictor of bidder behavior.

We take a dynamic approach to studying first-price auctions: rather than basing performance guarantees solely on static equilibria, we study the repeated setting and show that robust performance guarantees may be derived from simple axioms of bidder behavior. For example, as long as a loser raises her bid quickly, a standard first-price auction will generate at least as much revenue as a second-price auction.

We generalize this dynamic technique to complex pay-your-bid auction settings: as long as losers do not wait too long to raise bids, a first-price auction will reach an envy-free state that implies a strong lower-bound on revenue; as long as winners occasionally experiment by lowering their bids, the outcome will near the boundary of this envy-free set so bidders do not overpay; and when players with the largest payoffs are the least patient, bids converge to the egalitarian equilibrium. Significantly, bidders need only know whether they are winning or losing in order to implement such behavior.

Along the way, we find that the auctioneer's choice of bidding language is critical when generalizing beyond the single-item setting, and we propose a specific construction called the utility-target auction that performs well. The utility-target auction includes a bidder's final utility as an additional parameter, identifying the single dimension along which she wishes to compete. This auction is closely related to profit-target bidding in first-price and ascending proxy package auctions and gives strong revenue guarantees for a variety of complex auction environments. Of particular interest, the guaranteed existence of a pure-strategy equilibrium in the utility-target auction shows how Overture might have eliminated the cyclic behavior in their generalized first-price sponsored search auction if bidders could have placed more sophisticated bids.