Sellers competing for buyers in online markets: Reserve prices, shill bids, and auction fees

We consider competition between sellers offering similar items in concurrent online auctions through a mediating auction institution, 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., bidding as a buyer in its own auction). This shill bidding is undesirable as it introduces inefficiencies within the market. However, through the use of an evolutionary simulation, we extend the analytical results beyond the two-seller case, and we then show that these inefficiencies can be effectively reduced when the mediating auction institution uses auction fees based on the difference between the auction closing and reserve prices.