Yaron Singer

Budget Feasible Mechanisms

We study a novel class of mechanism design problems in which the outcomes are constrained by the payments. This basic class of mechanism design problems captures many common economic situations, and yet it has not been studied, to our knowledge, in the past. We focus on the case of procurement auctions in which sellers have private costs, and the auctioneer aims to maximize a utility function on subsets of items, under the constraint that the sum of the payments provided by the mechanism does not exceed a given budget. Standard mechanism design ideas such as the VCG mechanism and its variants are not applicable here. We show that, for general functions, the budget constraint can render mechanisms arbitrarily bad in terms of the utility of the buyer. However, our main result shows that for the important class of sub modular functions, a bounded approximation ratio is achievable. Better approximation results are obtained for subclasses of the sub modular functions. We explore the space of budget feasible mechanisms in other domains and give a characterization under more restricted conditions.

On the Hardness of Being Truthful

The central problem in computational mechanism design is the tension between incentive compatibility and computational efficiency. We establish the first significant approximability gap between algorithms that are both truthful and computationally-efficient, and algorithms that only achieve one of these two desiderata. This is shown in the context of a novel mechanism design problem which we call the combinatorial public project problem (cppp). cpppis an abstraction of many common mechanism design situations, ranging from elections of kibbutz committees to network design.Our result is actually made up of two complementary results -- one in the communication-complexity model and one in the computational-complexity model. Both these hardness results heavily rely on a combinatorial characterization of truthful algorithms for our problem. Our computational-complexity result is one of the first impossibility results connecting mechanism design to complexity theory; its novel proof technique involves an application of the Sauer-Shelah Lemma and may be of wider applicability, both within and without mechanism design.

Learning on a budget: posted price mechanisms for online procurement

We study online procurement markets where agents arrive in a sequential order and a mechanism must make an irrevocable decision whether or not to procure the service as the agent arrives. Our mechanisms are subject to a budget constraint and are designed for stochastic settings in which the bidders are either identically distributed or, more generally, permuted in random order. Thus, the problems we study contribute to the literature on budget-feasible mechanisms as well as the literature on secretary problems and online learning in auctions. Our main positive results are as follows. We present a constant-competitive posted price mechanism when agents are identically distributed and the buyer has a symmetric submodular utility function. For nonsymmetric submodular utilities, under the random ordering assumption we give a posted price mechanism that is O(log n)-competitive and a truthful mechanism that is O(1)-competitive but uses bidding rather than posted pricing.

Adaptive Seeding in Social Networks

The algorithmic challenge of maximizing information diffusion through word-of-mouth processes in social networks has been heavily studied in the past decade. While there has been immense progress and an impressive arsenal of techniques has been developed, the algorithmic frameworks make idealized assumptions regarding access to the network that can often result in poor performance of state-of-the-art techniques. In this paper we introduce a new framework which we call Adaptive Seeding. The framework is a two-stage stochastic optimization model designed to leverage the potential that typically lies in neighboring nodes of arbitrary samples of social networks. Our main result is an algorithm which provides a constant factor approximation to the optimal adaptive policy for any influence function in the Triggering model.

Computation and incentives in combinatorial public projects

The Combinatorial Public Projects Problem (CPPP) is an abstraction of resource allocation problems in which agents have preferences over alternatives, and an outcome that is to be collectively shared by the agents is chosen so as to maximize the social welfare. We explore CPPP from both computational perspective and a mechanism design perspective. We examine CPPP in the hierarchy of complement free (subadditive) valuation classes and present positive and negative results for both unrestricted and truthful algorithms.

Mechanisms for complement-free procurement

We study procurement auctions when the buyer has complement-free (subadditive) objectives in the budget feasibility model (Singer 2010). For general subadditive functions we give a randomized universally truthful mechanism which is an O(log2 n) approximation, and an O(log3 n) deterministic truthful approximation mechanism; both mechanisms are in the demand oracle model. For cut functions, an interesting case of nonincreasing objectives, we give both randomized and deterministic truthful and budget feasible approximation mechanisms that achieve a constant approximation factor.

Influence at Scale: Distributed Computation of Complex Contagion in Networks

We consider the task of evaluating the spread of influence in large networks in the well-studied independent cascade model. We describe a novel sampling approach that can be used to design scalable algorithms with provable performance guarantees. These algorithms can be implemented in distributed computation frameworks such as MapReduce. We complement these results with a lower bound on the query complexity of influence estimation in this model. We validate the performance of these algorithms through experiments that demonstrate the efficacy of our methods and related heuristics.

Scalable Methods for Adaptively Seeding a Social Network

In recent years, social networking platforms have developed into extraordinary channels for spreading and consuming information. Along with the rise of such infrastructure, there is continuous progress on techniques for spreading information effectively through influential users. In many applications, one is restricted to select influencers from a set of users who engaged with the topic being promoted, and due to the structure of social networks, these users often rank low in terms of their influence potential. An alternative approach one can consider is an adaptive method which selects users in a manner which targets their influential neighbors. The advantage of such an approach is that it leverages the friendship paradox in social networks: while users are often not influential, they often know someone who is. Despite the various complexities in such optimization problems, we show that scalable adaptive seeding is achievable. In particular, we develop algorithms for linear influence models with provable approximation guarantees that can be gracefully parallelized. To show the effectiveness of our methods we collected data from various verticals social network users follow. For each vertical, we collected data on the users who responded to a certain post as well as their neighbors, and applied our methods on this data. Our experiments show that adaptive seeding is scalable, and importantly, that it obtains dramatic improvements over standard approaches of information dissemination.

Inapproximability of Combinatorial Public Projects

We study the Combinatorial Public Project Problem ( CPPP ) in which n agents are assigned a subset of m resources of size k so as to maximize the social welfare. Combinatorial public projects are an abstraction of many resource-assignment problems (Internet-related network design, elections, etc.). It is known that if all agents have submodular valuations then a constant approximation is achievable in polynomial time. However, submodularity is a strong assumption that does not always hold in practice. We show that (unlike similar problems such as combinatorial auctions) even slight relaxations of the submodularity assumption result in non-constant lower bounds for approximation.

Efficiency-revenue trade-offs in auctions

When agents with independent priors bid for a single item, Myersons optimal auction maximizes expected revenue, whereas Vickreys second-price auction optimizes social welfare. We address the natural question of trade-offs between the two criteria, that is, auctions that optimize, say, revenue under the constraint that the welfare is above a given level. If one allows for randomized mechanisms, it is easy to see that there are polynomial-time mechanisms that achieve any point in the trade-off (the Pareto curve) between revenue and welfare. We investigate whether one can achieve the same guarantees using deterministic mechanisms. We provide a negative answer to this question by showing that this is a (weakly) NP-hard problem. On the positive side, we provide polynomial-time deterministic mechanisms that approximate with arbitrary precision any point of the trade-off between these two fundamental objectives for the case of two bidders, even when the valuations are correlated arbitrarily. The major problem left open by our work is whether there is such an algorithm for three or more bidders with independent valuation distributions.