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Item Pricing for Revenue Maximization
"... We consider the problem of pricing n items to maximize revenue when faced with a series of unknown buyers with complex preferences, and show that a simple pricing scheme achieves surprisingly strong guarantees. We show that in the unlimited supply setting, a random single price achieves expected rev ..."
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We consider the problem of pricing n items to maximize revenue when faced with a series of unknown buyers with complex preferences, and show that a simple pricing scheme achieves surprisingly strong guarantees. We show that in the unlimited supply setting, a random single price achieves expected revenue within a logarithmic factor of the total social welfare for customers with general valuation functions, which may not even necessarily be monotone. This generalizes work of Guruswami et. al [18], who show a logarithmic factor for only the special cases of singleminded and unitdemand customers. In the limited supply setting, we show that for subadditive valuations, a random single price achieves revenue within a factor of 2 O( √ log n log log n) of the total social welfare, i.e., the optimal revenue the seller could hope to extract even if the seller could price each bundle differently for every buyer. This is the best approximation known for any item pricing scheme for subadditive (or even submodular) valuations, even using multiple prices. We complement this result with a lower bound showing a sequence of subadditive (in fact, XOS) buyers for which any single price has approximation ratio 2 Ω(log1/4 n), thus showing that single price schemes cannot achieve a polylogarithmic ratio. This lower bound demonstrates a clear distinction between revenue maximization and social welfare maximization in this setting, for which [12, 10] show that a fixed price achieves a logarithmic approximation in the case of XOS [12], and more generally subadditive [10], customers.
Price of Anarchy for Greedy Auctions
"... We study mechanisms for utilitarian combinatorial allocation problems, where agents are not assumed to be singleminded. This class of problems includes combinatorial auctions, multiunit auctions, unsplittable flow problems, and others. We focus on the problem of designing mechanisms that approximat ..."
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Cited by 21 (8 self)
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We study mechanisms for utilitarian combinatorial allocation problems, where agents are not assumed to be singleminded. This class of problems includes combinatorial auctions, multiunit auctions, unsplittable flow problems, and others. We focus on the problem of designing mechanisms that approximately optimize social welfare at every BayesNash equilibrium (BNE), which is the standard notion of equilibrium in settings of incomplete information. For a broad class of greedy approximation algorithms, we give a general blackbox reduction to deterministic mechanisms with almost no loss to the approximation ratio at any BNE. We also consider the special case of Nash equilibria in fullinformation games, where we obtain tightened results. This solution concept is closely related to the wellstudied price of anarchy. Furthermore, for a rich subclass of allocation problems, pure Nash equilibria are guaranteed to exist for our mechanisms. For many problems, the approximation factors we obtain at equilibrium improve upon the best known results for deterministic truthful mechanisms. In particular, we exhibit a simple deterministic mechanism for general combinatorial auctions that obtains an O ( √ m) approximation at every BNE. 1
BlackBox Randomized Reductions in Algorithmic Mechanism Design
"... Abstract—We give the first blackbox reduction from arbitrary approximation algorithms to truthful approximation mechanisms for a nontrivial class of multiparameter problems. Specifically, we prove that every packing problem that admits an FPTAS also admits a truthfulinexpectation randomized mech ..."
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Abstract—We give the first blackbox reduction from arbitrary approximation algorithms to truthful approximation mechanisms for a nontrivial class of multiparameter problems. Specifically, we prove that every packing problem that admits an FPTAS also admits a truthfulinexpectation randomized mechanism that is an FPTAS. Our reduction makes novel use of smoothed analysis, by employing small perturbations as a tool in algorithmic mechanism design. We develop a “duality” between linear perturbations of the objective function of an optimization problem and of its feasible set, and use the “primal ” and “dual ” viewpoints to prove the running time bound and the truthfulness guarantee, respectively, for our mechanism.
Auctions with online supply
 In Fifth Workshop on Ad Auctions
, 2009
"... We study the problem of selling identical goods to n unitdemand bidders in a setting in which the total supply of goods is unknown to the mechanism. Items arrive dynamically, and the seller must make the allocation and payment decisions online with the goal of maximizing social welfare. We consider ..."
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Cited by 9 (3 self)
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We study the problem of selling identical goods to n unitdemand bidders in a setting in which the total supply of goods is unknown to the mechanism. Items arrive dynamically, and the seller must make the allocation and payment decisions online with the goal of maximizing social welfare. We consider two models of unknown supply: the adversarial supply model, in which the mechanism must produce a welfare guarantee for any arbitrary supply, and the stochastic supply model, in which supply is drawn from a distribution known to the mechanism, and the mechanism need only provide a welfare guarantee in expectation. Our main result is a separation between these two models. We show that all truthful mechanisms, even randomized, achieve a diminishing fraction of the optimal social welfare (namely, no better than a Ω(log log n) approximation) in the adversarial setting. In sharp contrast, in the stochastic model, under a standard monotone hazardrate condition, we present a truthful mechanism that achieves a constant approximation. We show that the monotone hazard rate condition is necessary, and also characterize a natural subclass of truthful mechanisms in our setting, the set of onlineenvyfree mechanisms. All of the mechanisms we present fall into this class, and we prove almost optimal lower bounds for such mechanisms. Since auctions with unknown supply are regularly run in many onlineadvertising settings, our main results emphasize the importance of considering distributional information in the design of auctions in such environments. 1
Approximation Schemes for Sequential Posted Pricing in MultiUnit
, 2010
"... We design algorithms for computing approximately revenuemaximizing sequential postedpricing mechanisms (SPM) in Kunit auctions, in a standard Bayesian model. A seller has K copies of an item to sell, and there are n buyers, each interested in only one copy, who have some value for the item. The se ..."
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Cited by 5 (3 self)
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We design algorithms for computing approximately revenuemaximizing sequential postedpricing mechanisms (SPM) in Kunit auctions, in a standard Bayesian model. A seller has K copies of an item to sell, and there are n buyers, each interested in only one copy, who have some value for the item. The seller must post a price for each buyer, the buyers arrive in a sequence enforced by the seller, and a buyer buys the item if its value exceeds the price posted to it. The seller does not know the values of the buyers, but have Bayesian information about them. An SPM specifies the ordering of buyers and the posted prices, and may be adaptive or nonadaptive in its behavior. The goal is to design SPM in polynomial time to maximize expected revenue. We compare against the expected revenue of optimal SPM, and provide a polynomial time approximation scheme (PTAS) for both nonadaptive and adaptive SPMs. This is achieved by two algorithms: an efficient algorithm that gives a (1 − 1 √)approximation (and hence a PTAS for sufficiently 2πK large K), and another that is a PTAS for constant K. The first algorithm yields a nonadaptive SPM that yields its approximation guarantees against an optimal adaptive SPM – this implies that the adaptivity gap in SPMs vanishes as K becomes larger. 1
Beyond equilibria: Mechanisms for repeated combinatorial auctions
, 2009
"... We study the design of mechanisms in combinatorial auction domains. We focus on settings where the auction is repeated, motivated by auctions for licenses or advertising space. We consider models of agent behaviour in which they either apply common learning techniques to minimize the regret of thei ..."
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We study the design of mechanisms in combinatorial auction domains. We focus on settings where the auction is repeated, motivated by auctions for licenses or advertising space. We consider models of agent behaviour in which they either apply common learning techniques to minimize the regret of their bidding strategies, or apply shortsighted bestresponse strategies. We ask: when can a blackbox approximation algorithm for the base auction problem be converted into a mechanism that approximately preserves the original algorithm’s approximation factor on average over many iterations? We present a general reduction for a broad class of algorithms when agents minimize external regret. We also present a mechanism for the combinatorial auction problem that attains an O (√m) approximation on average when agents apply bestresponse dynamics.
Truthful Spectrum Auctions With Approximate SocialWelfare
"... In cellular networks, a recent trend is to make spectrum access dynamic in the spatial and temporal dimensions, for the sake of efficient utilization of spectrum. In such a model, the spectrum is divided into channels and periodically allocated to competing base stations using an auctionbased mark ..."
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Cited by 4 (0 self)
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In cellular networks, a recent trend is to make spectrum access dynamic in the spatial and temporal dimensions, for the sake of efficient utilization of spectrum. In such a model, the spectrum is divided into channels and periodically allocated to competing base stations using an auctionbased market mechanism. An efficient auction mechanism is essential to the success of such a dynamic spectrum access model. Two of the key objectives of an efficient auction mechanism are, viz., “truthfulness ” (which encourages bidders to truthfully declare their true valuations), and maximizing “socialwelfare ” (i.e., the total valuation, so that the spectrum is allocated to the bidders who value it the most). Prior works on design of spectrum auction mechanism have only addressed one of the above objectives, and in limited contexts. In this article, we design a spectrum auction mechanism that is truthful and yields an allocation that has a socialwelfare of within a constantfactor of the optimal. We consider general (pairwise and physical) interference and bidding models. To the best of our knowledge, ours is the first work to design a spectrum auction mechanism satisfying both the above mentioned objectives. We demonstrate the performance of our designed technique through simulations over random and real cellular networks.
Utilitarian Mechanism Design for MultiObjective Optimization
"... In a classic optimization problem the complete input data is known to the algorithm. This assumption may not be true anymore in optimization problems motivated by the Internet where part of the input data is private knowledge of independent selfish agents. The goal of algorithmic mechanism design is ..."
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In a classic optimization problem the complete input data is known to the algorithm. This assumption may not be true anymore in optimization problems motivated by the Internet where part of the input data is private knowledge of independent selfish agents. The goal of algorithmic mechanism design is to provide (in polynomial time) a solution to the optimization problem and a set of incentives for the agents such that disclosing the input data is a dominant strategy for the agents. In case of NPhard problems, the solution computed should also be a good approximation of the optimum. In this paper we focus on mechanism design for multiobjective optimization problems, where we are given the main objective function, and a set of secondary objectives which are modeled via budget constraints. Multiobjective optimization is a natural setting for mechanism design as many economical choices ask for a compromise between different, partially conflicting, goals. Our main contribution is showing that two of the main tools for the design of approximation algorithms for multiobjective optimization problems, namely approximate Pareto curves and Lagrangian relaxation, can lead to truthful approximation schemes. By exploiting the method of approximate Pareto curves, we devise truthful FPTASs for multiobjective optimization problems whose exact version admits a pseudopolynomialtime algorithm, as for instance the multibudgeted versions of minimum spanning tree,
Bargaining and Pricing in Networked Economic Systems
, 2011
"... Economic systems can often be modeled as games involving several agents or players who act according to their own individual interests. Our goal is to understand how various features of an economic system affect its outcomes, and what may be the best strategy for an individual agent. In this work, w ..."
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Economic systems can often be modeled as games involving several agents or players who act according to their own individual interests. Our goal is to understand how various features of an economic system affect its outcomes, and what may be the best strategy for an individual agent. In this work, we model an economic system as a combination of many bilateral economic opportunities, such as that between a buyer and a seller. The transactions are complicated by the existence of many economic opportunities, and the influence they have on each other. For example, there may be several prospective sellers and buyers for the same item, with possibly differing costs and values. Such a system may be modeled by a network, where the nodes represent players and the edges represent opportunities. We study the effect of network structure on the outcome of bargaining among players, through theoretical