Robust Mechanisms Under Common Valuation

Du, Songzi

doi:10.3982/ecta14993

Cited by 47 publications

(8 citation statements)

References 30 publications

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“…In the many‐bidder limit, the optimal profit guarantee converges to the ex ante gains from trade. This generalizes a result of Du (2018) to the case where there may not be common knowledge of gains from trade. Moreover, this limit obtains even if the good is always sold, and at the same optimal rate of

O false(1 false/ \sqrt{N} false)

.…”

Section: Introductionsupporting

confidence: 69%

“…In fact, as N goes to infinity, the optimal profit guarantee converges to the expected surplus. This remarkable fact is implied by the earlier result of Du (2018), who constructed a particular sequence of mechanisms and profit guarantees (the diamonds) which converge to the expected value. A fortiori, the optimal profit guarantee must converge as well.…”

Section: Maxmin Auctions In the Many‐bidder Limitmentioning

confidence: 80%

“…The literature to which we contribute has previously shown that it is possible to obtain nontrivial profit guarantees across all information structures and equilibria, even with simple mechanisms like the first‐price auction (Bergemann, Brooks, and Morris (2017)). It has also shown that there are mechanisms whose profit guarantees are unimprovable when the number of bidders is large (Du (2018)). Our marginal contribution is to establish, in a rich class of environments, the precise limit of what can be attained.…”

Section: Discussionmentioning

confidence: 99%

“…The most closely related papers are Du (2018) and Bergemann, Brooks, and Morris (2016). Du (2018) solves our maxmin mechanism design problem in the limit as the number of bidders goes to infinity and the production cost is zero. Specifically, Du constructs a sequence of mechanisms and associated lower bounds on profit that converge to the expected surplus in the many‐bidder limit.…”

Section: Introductionmentioning

confidence: 99%

“…Specifically, Du constructs a sequence of mechanisms and associated lower bounds on profit that converge to the expected surplus in the many‐bidder limit. The mechanisms from Du (2018) do not achieve the optimal profit guarantee when the number of bidders is finite and more than 1 3 . In contrast, Bergemann, Brooks, and Morris (2016) construct what is essentially a strong maxmin solution for the special case of two bidders and two possible values.…”

Section: Introductionmentioning

confidence: 99%

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Optimal Auction Design With Common Values: An Informationally Robust Approach

Brooks

2021

ECTA

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A profit‐maximizing seller has a single unit of a good to sell. The bidders have a pure common value that is drawn from a distribution that is commonly known. The seller does not know the bidders' beliefs about the value and thinks that beliefs are designed adversarially by Nature to minimize profit. We construct a strong maxmin solution to this joint mechanism design and information design problem, consisting of a mechanism, an information structure, and an equilibrium, such that neither the seller nor Nature can move profit in their respective preferred directions, even if the deviator can select the new equilibrium. The mechanism and information structure solve a family of maxmin mechanism design and minmax information design problems, regardless of how an equilibrium is selected. The maxmin mechanism takes the form of a proportional auction: each bidder submits a one‐dimensional bid, the aggregate allocation and aggregate payment depend on the aggregate bid, and individual allocations and payments are proportional to bids. We report a number of additional properties of the maxmin mechanisms, including what happens as the number of bidders grows large and robustness with respect to the prior over the value.

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