Competing sellers in online markets: reserve prices, shill bidding, and auction fees

In this paper, we consider competition between sellers offering similar items in concurrent online auctions, where each seller must set its individual auction parameters (such as the reserve price) in such a way as to attract buyers. We show that in the case of two sellers with asymmetric production costs, there exists a pure Nash equilibrium in which both sellers set reserve prices above their production costs. In addition, we show that, rather than setting a reserve price, a seller can further improve its utility by shill bidding (i.e., pretending to be a buyer in order to bid in its own auction). But, through the use of an evolutionary simulation, we show that this shill bidding introduces inefficiences within the market. However, we then go on to show that these inefficiences can be reduced when the mediating auction institution uses appropriate auction fees that deter sellers from submitting shill bids. Specifically, we compare two types of auction fees and show that, in this respect, those based on the difference between the closing price and the reserve price are more effective than the commonly used fees that are based on closing price alone.