English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

Multi-item revenue-optimal mechanisms are known to be extremely complex,often offering buyers randomized lotteries of goods. In the standard buy-onemodel, it is known that optimal mechanisms can yield revenue infinitely higherthan that of any "simple" mechanism -- the ones with size polynomial in thenumber of items -- even with just two items and a single buyer (Briest et al.2015, Hart and Nisan 2017).  We introduce a new parameterized class of mechanisms, buy-$k$ mechanisms,which smoothly interpolate between the classical buy-one mechanisms and therecently studied buy-many mechanisms (Chawla et al. 2019, Chawla et al. 2020,Chawla et al. 2022). Buy-$k$ mechanisms allow the buyer to buy up to $k$ manymenu options. We show that restricting the seller to the class of buy-$n$incentive-compatible mechanisms suffices to overcome the bizarre, infiniterevenue properties of the buy-one model. Our main result is that the revenuegap with respect to bundling, an extremely simple mechanism, is bounded by$O(n^2)$ for any arbitrarily correlated distribution $\mathcal{D}$ over $n$items for the case of an additive buyer. Our techniques also allow us to provesimilar upper bounds for arbitrary monotone valuations, albeit with anexponential factor in the approximation.  On the negative side, we show that allowing the buyer to purchase a smallnumber of menu options does not suffice to guarantee sub-exponentialapproximations, even when we weaken the benchmark to the optimal buy-$k$deterministic mechanism. If an additive buyer is only allowed to buy $k =\Theta(n^{1/2-\varepsilon})$ many menu options, the gap between therevenue-optimal deterministic buy-$k$ mechanism and bundling may be exponentialin $n$. In particular, this implies that no "simple" mechanism can obtain asub-exponential approximation in this regime.

Fine-Grained Buy-Many Mechanisms Are Not Much Better Than Bundling