On Simple Mechanisms for Dependent Items

by   Yang Cai, et al.

We study the problem of selling n heterogeneous items to a single buyer, whose values for different items are dependent. Under arbitrary dependence, Hart and Nisan show that no simple mechanism can achieve a non-negligible fraction of the optimal revenue even with only two items. We consider the setting where the buyer's type is drawn from a correlated distribution that can be captured by a Markov Random Field, one of the most prominent frameworks for modeling high-dimensional distributions with structure. If the buyer's valuation is additive or unit-demand, we extend the result to all MRFs and show that max(SRev,BRev) can achieve an Ω(1/e^O(Δ))-fraction of the optimal revenue, where Δ is a parameter of the MRF that is determined by how much the value of an item can be influenced by the values of the other items. We further show that the exponential dependence on Δ is unavoidable for our approach and a polynomial dependence on Δ is unavoidable for any approach. When the buyer has a XOS valuation, we show that max(Srev,Brev) achieves at least an Ω(1/e^O(Δ)+1/√(nγ))-fraction of the optimal revenue, where γ is the spectral gap of the Glauber dynamics of the MRF. Note that in the special case of independently distributed items, Δ=0 and 1/nγ≤ 1, and our results recover the known constant factor approximations for a XOS buyer. We further extend our parametric approximation to several other well-studied dependency measures such as the Dobrushin coefficient and the inverse temperature. Our results are based on the Duality-Framework by Cai et al. and a new concentration inequality for XOS functions over dependent random variables.



page 1

page 2

page 3

page 4


Smoothed Analysis of Multi-Item Auctions with Correlated Values

Consider a seller with m heterogeneous items for sale to a single additi...

A Simple Mechanism for a Budget-Constrained Buyer

We study a classic Bayesian mechanism design setting of monopoly problem...

99% Revenue via Enhanced Competition

A sequence of recent studies show that even in the simple setting of a s...

Prophet Inequalities with Linear Correlations and Augmentations

In a classical online decision problem, a decision-maker who is trying t...

Optimal (and Benchmark-Optimal) Competition Complexity for Additive Buyers over Independent Items

The Competition Complexity of an auction setting refers to the number of...

Optimal Deterministic Mechanisms for an Additive Buyer

We study revenue maximization by deterministic mechanisms for the simple...

On Infinite Separations Between Simple and Optimal Mechanisms

We consider a revenue-maximizing seller with k heterogeneous items for s...
This week in AI

Get the week's most popular data science and artificial intelligence research sent straight to your inbox every Saturday.