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, whereas 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.