Distributionally Robust Pricing in Auctions

Uncertainty in Mechanism Design

“…A number of recent papers give important results along both of these lines for particular problems and under natural restrictions on beliefs. Examples include Schlag (2008, 2011) and Carrasco et al (2018), on the problem of a monopoly seller facing a single buyer, and Neeman (2003), Koçyigit et al (2020), andSuzdaltsev (2020), on the problem of a seller facing multiple bidders for a single indivisible item. Many open questions along similar lines remain and would be important directions for future work.…”

“…A number of papers consider distributionally robust versions of standard problems, in which the designer does not know all relevant distributions but might have some partial information, such as that distributions belong to a set with certain properties, bounds on the supports, or restrictions on means or other moments. Much of this work studies optimal mechanisms under worst case maxmin revenue guarantees or other revenue or welfare goals, including Auster (2018), Bergemann and Schlag (2008), Bergemann and Schlag (2011), Carrasco, Luz, Kos, Messner, Monteiro and Moreira (2018), Fu, Haghpanah, Hartline and Kleinberg (2017, Koçyigit, Iyengar, Kuhn and Wiesemann (2020), Neeman (2003), andSuzdaltsev (2020). Similarly, Ollár andPenta (2017, 2019) study full and partial implementation under moment conditions on the set of possible distributions.…”

An Optimal Distributionally Robust Auction

“…This paper contributes to the growing literature on robust mechanism design. The closest contributions to ours are Carrasco et al (2018a), Koçyigit et al (2017), Neeman (2003) and Suzdaltsev (2020). Carrasco et al (2018a) study the problem of selling the good to a single agent by seller who maximizes worst-case expected revenue while knowing the first N moments of distribution.…”

Robust Reserve Pricing in Auctions Under Mean Constraints

“…There is much work that addresses robust design in auctions, such as Bergemann et al (2016), Bergemann et al (2019), Brooks and Du (2019), and Du (2018). 2 The papers closest to ours are: He and Li (2019), Suzdaltsev (2018), Kocyigit et al (2019), and Carrasco et al (2018). He and Li (2019) consider a similar second-price auction setting in which a seller is uncertain over the joint distribution of valuations but knows the full marginal distributions.…”

“…Kocyigit et al (2019) study the Stackelberg version of our robust second price auction problem, in which nature has a second-mover advantage and fully knows the reserve price before choosing the worst-case distribution (subject to the same symmetric mean and range constraints). 3 Suzdaltsev (2018) considers the Stackelberg version of the second price auction problem under mean and variance constraints, and under the additional restriction that the distributions must be independently and identically distributed.…”