Exposure problem in multi-unit auctions

Abstract

We characterize the optimal bidding strategies of local and global bidders for two heterogeneous licenses in a multi-unit simultaneous ascending auction (SAA) like the one used in the 2008 Canadian Advanced Wireless Spectrum license auction. The global bidder wants to win both licenses to enjoy synergies; therefore, she bids more than her stand-alone valuation of a license. This exposes her to the risk of losing money even when she wins all licenses. We determine the optimal bidding strategies in the presence of an exposure problem. By using simulation methods, first, we show that the probability of ine cient allocations in the simultaneous ascending auction can be up to 9 per cent. Second, we show that the global bidder can end up with a loss with 6 per cent probability depending on the distribution. We also investigate the relation between ine cient allocation and the revenue of SAA and VCG auctions.JEL Codes: D44, D82

Bid credits in simultaneous ascending auctions

“…To minimize the effect of heterogeneity across licenses arising from population size, I normalize all bids by the population in the calibration so that values are in per capita terms. In a more flexible two-license model, Meng and Gunay (2017) allow for heterogeneity in how bidders value licenses. A limitation of using that model, however, is that it requires a shared ranking of licenses, in the sense that all bidders prefer one license over the other.…”

“…I extend their analysis by including bid credits and calibrating it to observed outcomes from the FCC. Meng and Gunay (2017) also develop an equilibrium model of bidding in a similar environment with two licenses, but they allow for heterogeneity in bidder license values. Although such heterogeneity is likely to occur in my setting, I use the more general model as a basis for my study and transform the data in the empirical analysis so that licenses in the calibrated model are roughly similar.…”

Strategy and design of multi‐unit auction in grouped asymmetric setting

“…The equilibrium analysis of the auction model is still the theoretical basis of most auction research. In terms of equilibrium solution, many scholars have made a series of attempts under different assumptions, such as two-bidder (Dobzinski & Nisan, 2015), three-bidder (Perry & Reny, 2005), two-item (Alvarez & Maz on, 2012;Meng & Gunay, 2017), multi-unit (Viehmann et al, 2021), discrete bid (Kastl, 2012;Markakis & Telelis, 2015), multi-attribute (Chetan et al, 2018;Ran et al, 2018) and different auction types (Xu et al, 2021). Most of these studies follow the framework of Wilson (1979), which regards the bidder strategy as a bid on the symmetric surplus supply curve and derives the optimal bidding curve through Euler equation.…”

Experiments on the Different Numbers of Bidders in Sequential Auctions

“…Assuming one global bidder is accepted in the literature since the strategies when there are multi global bidders cannot be defined analytically in the literature. See[MG17] for more on this.…”