Prior-Independent Optimal Auctions

Abstract

Auctions are widely used in practice. Although auctions are also extensively studied in the literature, most of the developments rely on the significant common prior assumption. We study the design of optimal prior-independent selling mechanisms: buyers do not have any information about their competitors, and the seller does not know the distribution of values but only knows a general class to which it belongs. Anchored on the canonical model of buyers with independent and identically distributed values, we analyze a competitive ratio objective in which the seller attempts to optimize the worst-case fraction of revenues garnered compared with those of an oracle with knowledge of the distribution. We characterize properties of optimal mechanisms and in turn establish fundamental impossibility results through upper bounds on the maximin ratio. By also deriving lower bounds on the maximin ratio, we are able to crisply characterize the optimal performance for a spectrum of families of distributions. In particular, our results imply that a second price auction is an optimal mechanism when the seller only knows that the distribution of buyers has a monotone nondecreasing hazard rate, and it guarantees at least 71.53% of oracle revenues against any distribution within this class. Furthermore, a second price auction is near optimal when the class of admissible distributions is that of those with nondecreasing virtual value function (a.k.a. regular). Under this class, it guarantees a fraction of 50% of oracle revenues, and no mechanism can guarantee more than 55.6%. This paper was accepted by Kalyan Talluri, revenue management and market analytics.

The emergence of guiding cases in China

“…Dhangwatnotai et al (2010) show that in a single-item two-agent setting when the values are drawn independently and identically from regular distributions, the second-price auction is a 2-approximation in terms of the prior-independent ratio. For this setting, Fu et al (2015) showed that the ratio of 2 is not tight, while Allouah and Besbes (2020) showed that the ratio must lie in the range [1.80, 1.95]. Hartline et al (2020) resolved this question by showing a ratio of 1.91, while also proving that it is tight.…”

Concept and scope of technical measures to trade

“…Prior-Independent Mechanism Design & Implementation Theory Robust forecast aggregation shares the same spirit as the prior-independent mechanism design (Dhangwatnotai et al, 2010;Devanur et al, 2011;Chawla et al, 2013;Fu et al, 2015;Allouah and Besbes, 2020;Hartline et al, 2020). The problem is formulated as a min-max game between the designer, who designs the aggregator/mechanism, and nature, who picks the prior distribution from a class.…”

Regret Minimization and Separation in Multi-Bidder, Multi-Item Auctions

“…We hope that the insights distilled in this paper will pave the way towards more general separation results with a broader range of applications. This paper also relates to the literature on approximately optimal mechanism design, see, e.g., Dhangwatnotai et al (2015), Hart and Nisan (2017), Allouah and Besbes (2020) and the references therein. Under this modeling paradigm, the seller aims to identify a mechanism for which some objective function (e.g., the expected revenue) is guaranteed to be close to a full information benchmark value (e.g., the maximum expected revenue achievable) under every probability distribution consistent with the assumptions made.…”