Incentives in Online Auctions via Linear Programming

Online auctions in which items are sold in an online fashion with little knowledge about future bids are common in the internet environment. We study here a problem in which an auctioneer would like to sell a single item, say a car. A bidder may make a bid for the item at any time but expects an immediate irrevocable decision. The goal of the auctioneer is to maximize her revenue in this uncertain environment. Under some reasonable assumptions, it has been observed that the online auction problem has strong connections to the classical secretary problem in which an employer would like to choose the best candidate among

n

competing candidates [HKP04]. However, a direct application of the algorithms for the secretary problem to online auctions leads to undesirable consequences since these algorithms do not give a fair chance to every candidate and candidates arriving early in the process have an incentive to delay their arrival.

In this work we study the issue of incentives in the online auction problem where bidders are allowed to change their arrival time if it benefits them. We derive incentive compatible mechanisms where the best strategy for each bidder is to first truthfully arrive at their assigned time and then truthfully reveal their valuation. Using the linear programming technique introduced in Buchbinder et al [BJS10], we first develop new mechanisms for a variant of the secretary problem. We then show that the new mechanisms for the secretary problem can be used as a building block for a family of incentive compatible mechanisms for the online auction problem which perform well under different performance criteria. In particular, we design a mechanism for the online auction problem which is incentive compatible and is 3/16 ≈ 0.187-competitive for revenue, and a (different) mechanism that is

$\frac{1}{2\sqrt{e}} \approx 0.303$

-competitive for efficiency.