Recent years have witnessed the rapid development of online auctions. Currently, some online auctions, such as eBay, introduce a proxy bidding policy, under which bidders submit their maximum bids and delegate to a proxy agent to automatically outbid other competitors for the top bidder, whereas other online auctions do not. This paper compares these two widely used auction mechanisms (proxy setting and non-proxy setting) and characterizes the equilibrium bidding behavior and the seller's expected revenue. We find the proxy auction outperforms the non-proxy auction in terms of the seller's expected revenue. This dominance result is not prone to the specific bid announcement policy, the bidder's knowledge regarding the number of bidders, the impact of traffic congestion along the bidding process, the number of items sold through the auction, and the existence of a reserve price.

We further find that the proxy setting usually fails to sustain the truthful bidding as a dominant strategy equilibrium even if no minimum bid increments are adopted, and the possibility of a low-valuation-bidder dilemma where the low-valuation bidders could be better off if all bidders collude to bid at the last minute. We also discuss the dramatically different equilibrium bidding behaviors under the two auction mechanisms.