Inbal Talgam-Cohen

Supply-limiting mechanisms

Most results in revenue-maximizing auction design hinge on getting the price right --- offering goods to bidders at a price low enough to encourage a sale, but high enough to garner non-trivial revenue. Getting the price right can be hard work, especially when the seller has little or no a priori information about bidders valuations.n A simple alternative approach is to let the market do the work, and have prices emerge from competition for scarce goods. The simplest-imaginable implementation of this idea is the following: first, if necessary, impose an artificial limit on the number of goods that can be sold; second, run the welfare-maximizing VCG mechanism subject to this limit.n We prove that such supply-limiting mechanisms achieve near-optimal expected revenue in a range of single- and multi-parameter Bayesian settings. Indeed, despite their simplicity, we prove that they essentially match the state-of-the-art in prior-independent mechanism design.

Vertex sparsifiers: new results from old techniques

Given a capacitated graph G = (V, E) and a set of terminals K ⊆ V, how should we produce a graph H only on the terminals K so that every (multicommodity) flow between the terminals in G could be supported in H with low congestion, and vice versa? (Such a graph H is called a flow-sparsifier for G.) What if we want H to be a simple graph? What if we allow H to be a convex combination of simple graphs? n nImproving on results of Moitra [FOCS 2009] and Leighton and Moitra [STOC 2010], we give efficient algorithms for constructing: (a) a flow-sparsifier H that maintains congestion up to a factor ofO(log k/log log k) where k = |K|. (b) a convex combination of trees over the terminals K that maintains congestion up to a factor of O(log k). (c) for a planar graph G, a convex combination of planar graphs that maintains congestion up to a constant factor. This requires us to give a new algorithm for the 0-extension problem, the first one in which the preimages of each terminal are connected in G. Moreover, this result extends to minor-closed families of graphs. n nOur bounds immediately imply improved approximation guarantees for several terminal-based cut and ordering problems.

Optimal and near-optimal mechanism design with interdependent values

We study optimal and approximately-optimal mechanism design questions in the interdependent values model, which generalizes the standard setting of independent and private values. We focus our attention on ex post incentive compatible and individually rational mechanisms, and develop an analog of Myersons optimal auction theory that applies to many interdependent settings of interest. We demonstrate two applications for specific interdependent settings: First, a parallel result to the well-known optimality of the second-price auction with reserve for i.i.d.~bidders, where the English auction replaces the second-price one. Second, we identify good prior-independent auctions --- auctions with near-optimal expected revenue across a wide range of priors --- for certain interdependent value settings.

Ad auctions with data

The holy grail of online advertising is to target users with ads matched to their needs with such precision that the users respond to the ads, thereby increasing both advertisers and users value. The current approach to this challenge utilizes information about the users: their gender, their location, the websites they have visited before, and so on. Incorporating this data in ad auctions poses an economic challenge: can this be done in a way that the auctioneers revenue does not decrease at least on average? This is the problem we study in this paper. Our main result is that in Myersons optimal mechanism, for a general model of data in auctions, additional data leads to additional expected revenue. In the context of ad auctions we show that for the simple and common mechanisms, namely second price auction with reserve prices, there are instances in which additional data decreases the expected revenue, but this decrease is by at most a small constant factor under a standard regularity assumption.

A direct reduction from k-player to 2-player approximate nash equilibrium

We present a direct reduction from k-player games to 2- player games that preserves approximate Nash equilibrium. Previously, the computational equivalence of computing approximate Nash equilibrium in k-player and 2-player games was established via an indirect reduction. This included a sequence of works defining the complexity class PPAD, identifying complete problems for this class, showing that computing approximate Nash equilibrium for k-player games is in PPAD, and reducing a PPAD-complete problem to computing approximate Nash equilibrium for 2-player games. Our direct reduction makes no use of the concept of PPAD, eliminating some of the difficulties involved in following the known indirect reduction.

A Simple and Approximately Optimal Mechanism for a Buyer with Complements: Abstract

We consider a revenue-maximizing seller with m heterogeneous items and a single buyer whose valuation v for the items may exhibit both substitutes (i.e., for some S, T, v(S ∪ T) < v(S) + v(T)) and complements (i.e., for some S, T, v(S ∪ T) > v(S) + v(T)). We show that the mechanism first proposed by Babaioff et al. [2014] -- the better of selling the items separately and bundling them together -- guarantees a Θ(d) fraction of the optimal revenue, where

The Competition Complexity of Auctions: A Bulow-Klemperer Result for Multi-Dimensional Bidders

d

Modularity and greed in double auctions

is a measure on the degree of complementarity. Note that this is the first approximately optimal mechanism for a buyer whose valuation exhibits any kind of complementarity. It extends the work of Rubinstein and Weinberg [2015], which proved that the same simple mechanisms achieve a constant factor approximation when buyer valuations are subadditive, the most general class of complement-free valuations. Our proof is enabled by the recent duality framework developed in Cai et al. [2016], which we use to obtain a bound on the optimal revenue in this setting. Our main technical contributions are specialized to handle the intricacies of settings with complements, and include an algorithm for partitioning edges in a hypergraph. Even nailing down the right model and notion of degree of complementarity to obtain meaningful results is of interest, as the natural extensions of previous definitions provably fail.

When Are Welfare Guarantees Robust

A seminal result of Bulow and Klemperer [1989] demonstrates the power of competition for extracting revenue: when selling a single item to n bidders whose values are drawn i.i.d. from a regular distribution, the simple welfare-maximizing VCG mechanism (in this case, a second price-auction) with one additional bidder extracts at least as much revenue in expectation as the optimal mechanism. The beauty of this theorem stems from the fact that VCG is a prior-independent mechanism, where the seller possesses no information about the distribution, and yet, by recruiting one additional bidder it performs better than any prior-dependent mechanism tailored exactly to the distribution at hand (without the additional bidder). In this work, we establish the first full Bulow-Klemperer results in multi-dimensional environments, proving that by recruiting additional bidders, the revenue of the VCG mechanism surpasses that of the optimal (possibly randomized, Bayesian incentive compatible) mechanism. For a given environment with i.i.d. bidders, we term the number of additional bidders needed to achieve this guarantee the environments competition complexity. Using the recent duality-based framework of Cai et al. [2016] for reasoning about optimal revenue, we show that the competition complexity of n bidders with additive valuations over m independent, regular items is at most n+2m-2 and at least log(m). We extend our results to bidders with additive valuations subject to downward-closed constraints, showing that these significantly more general valuations increase the competition complexity by at most an additive m-1 factor. We further improve this bound for the special case of matroid constraints, and provide additional extensions as well.

Welfare and Revenue Guarantees for Competitive Bundling Equilibrium

Abstract Designing double auctions is a complex problem, especially when there are restrictions on the sets of buyers and sellers that may trade with one another. The goal of this paper is to develop a modular approach to the design of double auctions, by relating it to the exhaustively-studied problem of designing one-sided mechanisms with a single seller (or, alternatively, a single buyer). We consider several desirable properties of a double auction: feasibility, dominant-strategy incentive compatibility, the still stronger incentive constraints offered by a deferred-acceptance implementation, exact and approximate welfare maximization, and budget balance. For each of these properties, we identify sufficient conditions on two one-sided algorithms—one for ranking the buyers, one for ranking the sellers—and on a method for their composition into trading pairs, which guarantee the desired property of the double auction. Our framework also offers new insights into classic double auction designs, such as the VCG and McAfee auctions with unit-demand buyers and unit-supply sellers.