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Internet ad auctions have evolved from a few lines of text to richerinformational layouts that include images, sitelinks, videos, etc. Ads in thesenew formats occupy varying amounts of space, and an advertiser can providemultiple formats, only one of which can be shown. The seller is now faced witha multi-parameter mechanism design problem. Computing an efficient allocationis computationally intractable, and therefore the standardVickrey-Clarke-Groves (VCG) auction, while truthful and welfare-optimal, isimpractical.  In this paper, we tackle a fundamental problem in the design of modern adauctions. We adopt a ``Myersonian'' approach and study allocation rules thatare monotone both in the bid and set of rich ads. We show that such rules canbe paired with a payment function to give a truthful auction. Our maintechnical challenge is designing a monotone rule that yields a goodapproximation to the optimal welfare. Monotonicity doesn't hold for standardalgorithms, e.g. the incremental bang-per-buck order, that give goodapproximations to ``knapsack-like'' problems such as ours. In fact, we showthat no deterministic monotone rule can approximate the optimal welfare withina factor better than $2$ (while there is a non-monotone FPTAS). Our main resultis a new, simple, greedy and monotone allocation rule that guarantees a $3$approximation.  In ad auctions in practice, monotone allocation rules are often paired withthe so-called Generalized Second Price (GSP) payment rule, which charges theminimum threshold price below which the allocation changes. We prove that, eventhough our monotone allocation rule paired with GSP is not truthful, its Priceof Anarchy (PoA) is bounded. Under standard no overbidding assumption, we provea pure PoA bound of $6$ and a Bayes-Nash PoA bound of $\frac{6}{(1 -\frac{1}{e})}$. Finally, we experimentally test our algorithms on real-worlddata.

Simple Mechanisms for Welfare Maximization in Rich Advertising Auctions