Online Auction and List Price Revenue Management

Abstract

We analyze a revenue management problem in which a seller facing a Poisson arriving stream of customers operates an online multiunit auction. Customers have an alternative list price channel where to get the product from. We consider two variants of this problem: In the first one, the list price is an external channel run by another firm. In the second variant, the seller manages simultaneously both the auction and the list price channels.Each consumer, trying to maximize his own surplus, must decide either to buy at the posted price and get the item at no risk, or to join the auction and wait until its end, where the winners are revealed and the auction price is disclosed.Our approach consists of two parts. First, we study structural properties of the problem, and show that the equilibrium strategy for both versions of this game is of the threshold type, meaning that a consumer will join the auction only if his arrival time is above a function of his own valuation. This consumer's strategy can be computed using an iterative algorithm in a function space, provably convergent under some conditions. Unfortunately, this procedure is computationally intensive.To overcome this, we formulate an asymptotic version of the problem, in which the demand rate and the initial number of units grow proportionally large. We get a simple closed form for the equilibrium strategy in this regime, which is then used as an approximated solution for the original problem. Numerical computations show that this heuristic is very accurate. The asymptotic solution culminates then in simple and precise recipes for how bidders should behave, and how the seller should structure the auction, and price the product in the dual channel case.

Strategic Customer Behavior, Commitment, and Supply Chain Performance

“…MS-0001-1922.65 7 display formats (display all vs. display one) on the seller's expected profits. There are also papers that consider strategic consumers in dynamic auction settings (see, e.g., Caldentey andVulcano, 2004, andGallien andGupta, 2005). All the above papers only study the interaction between strategic consumers and a single seller, while our paper also considers the vertical relationship between manufacturers and retailers.…”

Towards Optimal Capacity Segmentation with Hybrid Cloud Pricing

“…We note that there exist some works in the literature of economics that discuss a similar resource allocation problem in the retail market, where two pricing channels are used to sell products, the auction market and the regular pay-as-you-go pricing [15], [16]. However, neither the model nor the analysis applies to the cloud environment.…”

Temporary and Permanent Buyout Prices in Online Auctions

“…Finally a paper very closely related to ours is Caldentey and Vulcano [11]. As in our paper, they assume a dynamic market environment where bidders with independent private valuations arrive as a Poisson process.…”

“…In their model, as in ours, the equilibrium participation strategy of the bidders is a threshold strategy. There are important differences between their work and ours, however,: The model in [11] assumes that when bidders arrive at a multi-unit auction they are informed only about the initial number of units and not the number of units remaining. In a single-unit auction, this would correspond to bidders not knowing whether the item listed is available or not.…”