Game theorists and market designers focus on the impact of the rules of the game on the behavior of the participants. Participants in internet markets can be human bidders bidding in person or artificial agents used by human bidders. Thus, the performance of market rules depends on what behavior the rules elicit from human and artificial agents. At the same time, the performance of software agents, and the decisions of bidders whether to use them, depends on how they interact with humans and other software agents in the market. Thus, market design and artificial agent design are closely related.
In this article, we report on an ongoing study of internet auctions. We focus here on how a small difference in the rules used in auctions run by eBay and Amazon, both of which supply bidders with simple software agents, elicit different behavior from bidders and different use of software agents. We briefly consider how these issues look from the perspectives of the buyers, the sellers, the market makers (the auction houses), and the third-party suppliers of software agents. (The results and data discussed here are taken from Ariely, Ockenfels, and Roth 2002; Ockenfels and Roth 2001; Roth and Ockenfels 2002).
One of the big attractions of internet auctions is that buyers do not all have to gather at the same place to participate, so that sellers can use internet auctions to sell even relatively low-value items to a potentially wide audience. However, the size of the market would be limited if all potential bidders had to be online at the same time, and for this reason, most auctions are conducted over a period of days, often a week. To make it simple for bidders to participate in a week-long auction, without having to be constantly vigilant, or to be online at the close of the auction, most internet auction houses make available a simple kind of software bidding agent; eBay calls it proxy bidding.
eBay asks the bidders to submit maximum bids (called proxy bids) and explains that "eBay will bid incrementally on your behalf up to your maximum bid, which is kept secret from other eBay users." That is, once a bidder submits his/her maximum bid, his/her resulting bid registers as the minimum increment above the previous high bid. As subsequent proxy bids by other bidders come in, the bid of the bidder in question automatically rises by the minimum increment until the second-highest submitted proxy bid is exceeded (or until his/her own maximum is exceeded by some other bidder). At the end of the auction, the bidder who submitted the highest proxy bid wins the object being auctioned and pays a price that is a small increment above the second-highest maximum (proxy) bid. (1)
To understand the bidding behavior that the proxy bidding system elicits, it will help to first consider how different the auction would be if instead of informing all bidders about the bid history at each point of time during the auction, the auction were a second-price sealed-bid auction (in which nobody is informed about the proxy bids of other bidders until the auction is over). Then, the proxy bidding agent provided by eBay would make incremental or multiple bidding unnecessary. Suppose, for example, that your maximum willingness to pay for an antique coin auctioned on eBay were $100. Then, bidding your maximum willingness to pay in a second-price sealed-bid auction is your dominant strategy; that is, you can never do better than by bidding $100. The reason is that your proxy bid does not affect the price of the coin in case you win the auction (recall that the price is determined by the second-highest proxy bid). Your proxy bid only determines whether you win the auction. If you submit your maximum willingness to pay, you will win the auction if and only if your maximum is higher than the price; so, there is no reason to over- or understate your willingness to pay. eBay explains the economics of second-price auctions to their bidders along these lines and extends the conclusion to its own auctions, in which bids are processed as they come in: "eBay always recommends bidding the absolute maximum that one is willing to pay for an item early in the auction. …