Computationally efficient and revenue optimized auctioneer's strategy for expanding auctions

An expanding auction---a special type of an ascending-price open-cry auction---allows the auctioneer to dynamically add (identical) items to the single item offered initially. Expanding auctions are becoming an increasingly popular business-to-consumer auction mechanism. The auctioneer's revenue from an expanding auction depends, in large part, on its schedule for increasing the number of units offered. As we show, the naïve strategies commonly used for increasing the number of items offered in contemporary e-commerce implementations of expanding auctions are sub-optimal. In this study we provide a strategy that, given some assumptions about buyers' behaviors, maximizes the expected revenues of the auctioneer in an expanding auction. We model the auction process as a state graph in which nodes are auction states and edges are transitions. With this model, finding the optimal strategy is equivalent to solving a search problem on the state graph. We prove that the search problem to be solved, although seemingly exponentially complex, is actually linearly bounded. Based on this result, we introduce an informed decision strategy that optimizes the auctioneer's revenue.