Chapter 1: Efficient Design of an Auction with Discrete Bid Levels

This paper studies one of auction design issues: the choice of bid levels. Full efficiency is generally unachievable with a discrete auction. Since there may be more than one bidder who submits the same bid, the auction cannot completely sort bidders by valuation. In effort to maximize efficiency, the social planner tries to choose the partition rule-a rule dictating how type space is partitioned to group bidders who submit the same bid together-to maximize efficiency. With the efficient partition rule, we implement bid levels with sealed-bid and clock auctions. We find that the efficient bid levels in the sealed-bid second-price auction may be non-unique and efficient bid increments in a clock auction with highest-rejected bid may be decreasing. We also show that revealing demand is efficiency-enhancing even in the independent private valuation setting where price discovery is not important.

Chapter 2: Pricing Rule in a Clock Auction

We analyze a discrete clock auction with lowest-accepted bid (LAB) pricing and provisional winners, as adopted by India for its 3G spectrum auction. In a perfect Bayesian equilibrium, the provisional winner shades her bid while provisional losers do not. Such differential shading leads to inefficiency. An auction with highest-rejected bid (HRB) pricing and exit bids is strategically simple, has no bid shading, and is fully efficient. In addition, it has higher revenues than the LAB auction, assuming profit maximizing bidders. The bid shading in the LAB auction exposes a bidder to the possibility of losing the auction at a price below the bidder's value. Thus, a fear of losing at profitable prices may cause bidders in the LAB auction to bid more aggressively than predicted assuming profit-maximizing bidders. We extend the model by adding an anticipated loser's regret to the payoff function. Revenue from the LAB auction yields higher expected revenue than the HRB auction when bidders' fear of losing at profitable prices is sufficiently strong. This would provide one explanation why India, with an expressed objective of revenue maximization, adopted the LAB auction for its upcoming 3G spectrum auction, rather than the seemingly superior HRB auction.

Chapter 3: Discrete Clock Auctions: An Experimental Study

We analyze the implications of different pricing rules in discrete clock auctions. The two most common pricing rules are highest-rejected bid (HRB) and lowest-accepted bid (LAB). Under HRB, the winners pay the lowest price that clears the market; under LAB, the winners pay the highest price that clears the market. Both the HRB and LAB auctions maximize revenues and are fully efficient in our setting. Our experimental results indicate that the LAB auction achieves higher revenues. This also is the case in a version of the clock auction with provisional winners. This revenue result may explain the frequent use of LAB pricing. On the other hand, HRB is successful in eliciting true values of the bidders both theoretically and experimentally.