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Multiparameter mechanism design and sequential posted pricing
 CoRR
"... We study the classic mathematical economics problem of Bayesian optimal mechanism design where a principal aims to optimize expected revenue when allocating resources to selfinterested agents with preferences drawn from a known distribution. In single parameter settings (i.e., where each agent’s pr ..."
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Cited by 65 (6 self)
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We study the classic mathematical economics problem of Bayesian optimal mechanism design where a principal aims to optimize expected revenue when allocating resources to selfinterested agents with preferences drawn from a known distribution. In single parameter settings (i.e., where each agent’s preference is given by a single private value for being served and zero for not being served) this problem is solved [20]. Unfortunately, these single parameter optimal mechanisms are impractical and rarely employed [1], and furthermore the underlying economic theory fails to generalize to the important, relevant, and unsolved multidimensional setting (i.e., where each agent’s preference is given by multiple values for each of the multiple services available) [25]. In contrast to the theory of optimal mechanisms we develop a theory of sequential posted price mechanisms, where agents in sequence are offered takeitorleaveit prices. We prove that these
Bayesian combinatorial auctions: Expanding single buyer mechanisms to many buyers
 In FOCS. 512–521
"... • Bronze Medal, 13th International Olympiad in Informatics, Tampere, Finland, ..."
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Cited by 37 (2 self)
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• Bronze Medal, 13th International Olympiad in Informatics, Tampere, Finland,
BudgetConstrained Auctions with Heterogeneous Items
, 2012
"... We present the first approximation algorithms for designing revenueoptimal incentivecompatible mechanisms in the following setting: There are multiple (heterogeneous) items, and bidders have arbitrary demand and budget constraints (and additive valuations). Furthermore, the type of a bidder (which ..."
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Cited by 25 (3 self)
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We present the first approximation algorithms for designing revenueoptimal incentivecompatible mechanisms in the following setting: There are multiple (heterogeneous) items, and bidders have arbitrary demand and budget constraints (and additive valuations). Furthermore, the type of a bidder (which specifies her valuations for each item) is private knowledge, and the types of different bidders are drawn from publicly known mutually independent distributions. Our mechanisms are surprisingly simple. First, we assume that the type of each bidder is drawn from a discrete distribution with polynomially bounded support size. This restriction on the typedistribution, however, allows the random variables corresponding to a bidder’s valuations for different items to be arbitrarily correlated. In this model, we describe a sequential allpay mechanism that is truthful in expectation and Bayesian incentive compatible. The outcome of our allpay
Sequential posted pricing and multiparameter mechanism design
 Proc. of 42 nd ACM STOC
"... We consider the classical mathematical economics problem of Bayesian optimal mechanism design where a principal aims to optimize a given objective when allocating resources to selfinterested agents. In singleparameter settings (where each agent preference is given by a private value for being allo ..."
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Cited by 23 (6 self)
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We consider the classical mathematical economics problem of Bayesian optimal mechanism design where a principal aims to optimize a given objective when allocating resources to selfinterested agents. In singleparameter settings (where each agent preference is given by a private value for being allocated the resource and zero for not being allocated) this problem is solved [19]. While this economic solution is tractable whenever the noneconomic optimization problem is tractable, it is complicated enough that it is rarely employed. Moreover, the techniques do not seem to generalize to multiparameter settings. Our first result is that for general product distributions on agent preferences and resource allocation problems that satisfy matroid properties (e.g., multiunit auctions, matchings, spanning trees), sequential posted price mechanisms, where agents are approached inturn and offered a precomputed takeitorleaveit offer, are at most a 4approximation to the optimal singleround mechanism. Furthermore, a suitable sequence of prices can be effectively computed by sampling the agents ’ distributional preferences. Notably, the analysis of this sequential posted price mechanism can be extended to give approximation mechanisms for the unsolved multiparameter setting. In stark contrast to the singleparameter setting, in multiparameter settings there is no general description or tractable implementation of optimal mechanisms. For decades, this unanswered issue has been widely considered one of the most important in the economic theory on mechanism design. We focus on
SupplyLimiting Mechanisms
"... Most results in revenuemaximizing 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 nontrivial revenue. Getting the price right can be hard work, especially when the seller has little or no a priori ..."
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Cited by 20 (5 self)
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Most results in revenuemaximizing 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 nontrivial revenue. Getting the price right can be hard work, especially when the seller has little or no a priori information about bidders’ valuations. A simple alternative approach is to “let the market do the work”, and have prices emerge from competition for scarce goods. The simplestimaginable 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 welfaremaximizing VCG mechanism subject to this limit. We prove that such “supplylimiting mechanisms ” achieve nearoptimal expected revenue in a range of single and multiparameter Bayesian settings. Indeed, despite their simplicity, we prove that they essentially match the stateoftheart in priorindependent mechanism design.
Mechanism Design via Correlation Gap
, 2010
"... For revenue and welfare maximization in singledimensional Bayesian settings, Chawla et al. (STOC10) recently showed that sequential postedprice mechanisms (SPMs), though simple in form, can perform surprisingly well compared to the optimal mechanisms. In this paper, we give a theoretical explanatio ..."
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Cited by 14 (0 self)
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For revenue and welfare maximization in singledimensional Bayesian settings, Chawla et al. (STOC10) recently showed that sequential postedprice mechanisms (SPMs), though simple in form, can perform surprisingly well compared to the optimal mechanisms. In this paper, we give a theoretical explanation of this fact, based on a connection to the notion of correlation gap. Loosely speaking, for auction environments with matroid constraints, we can relate the performance of a mechanism to the expectation of a monotone submodular function over a random set. This random set corresponds to the winner set for the optimal mechanism, which is highly correlated, and corresponds to certain demand set for SPMs, which is independent. The notion of correlation gap of Agrawal et al. (SODA10) quantifies how much we “lose ” in the expectation of the function by ignoring correlation in the random set, and hence bounds our loss in using certain SPM instead of the optimal mechanism. Furthermore, the correlation gap of a monotone and submodular function is known to be small, and it follows that certain SPM can approximate the optimal mechanism by a good constant factor. Exploiting this connection, we give tight analysis of a greedybased SPM of Chawla et al. for several environments. In particular, we show that it gives an e/(e − 1)approximation for matroid environments, gives asymptotically a 1/(1 − 1 / √ 2πk)approximation for the important subcase of kunit auctions, and gives a (p + 1)approximation for environments with pindependent set system constraints. 1
Priorindependent multiparameter mechanism design
 In Workshop on Internet and Network Economics (WINE
, 2011
"... Abstract. In a unitdemand multiunit multiitem auction, an auctioneer is selling a collection of different items to a set of agents each interested in buying at most unit. Each agent has a different private value for each of the items. We consider the problem of designing a truthful auction that m ..."
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Cited by 11 (5 self)
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Abstract. In a unitdemand multiunit multiitem auction, an auctioneer is selling a collection of different items to a set of agents each interested in buying at most unit. Each agent has a different private value for each of the items. We consider the problem of designing a truthful auction that maximizes the auctioneer’s profit in this setting. Previously, there has been progress on this problem in the setting in which each value is drawn from a known prior distribution. Specifically, it has been shown how to design auctions tailored to these priors that achieve a constant factor approximation ratio [2, 5]. In this paper, we present a priorindependent auction for this setting. This auction is guaranteed to achieve a constant fraction of the optimal expected profit for a large class of, so called, “regular ” distributions, without specific knowledge of the distributions. 1
Buyitnow or Takeachance: A Simple Sequential Screening Mechanism
"... We present a simple auction mechanism which extends the secondprice auction with reserve and is truthful in expectation. This mechanism is particularly effective in private value environments where the distribution of valuations are irregular. Bidders can “buyitnow”, or alternatively “takeachanc ..."
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Cited by 8 (0 self)
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We present a simple auction mechanism which extends the secondprice auction with reserve and is truthful in expectation. This mechanism is particularly effective in private value environments where the distribution of valuations are irregular. Bidders can “buyitnow”, or alternatively “takeachance”where the top d bidders are equally likely to win. The randomized takeachance allocation incentivizes high valuation bidders to buyitnow. We show that for a large class of valuations, this mechanism achieves similar allocations and revenues as Myerson’s optimal mechanism, and outperforms the secondprice auction with reserve. In addition, we present an evaluation of bid data from Microsoft’s AdECN platform. We find the valuations are irregular, and counterfactual experiments suggest our BINTAC mechanism would improve revenue by 11 % relative to an optimal secondprice mechanism with reserve.
Optimal and Efficient Parametric Auctions
 In submission
"... Consider a seller who seeks to provide service to a collection of interested parties, subject to feasibility constraints on which parties may be simultaneously served. Assuming that a distribution is known on the value of each party for service—arguably a strong assumption— Myerson’s seminal work pr ..."
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Cited by 8 (1 self)
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Consider a seller who seeks to provide service to a collection of interested parties, subject to feasibility constraints on which parties may be simultaneously served. Assuming that a distribution is known on the value of each party for service—arguably a strong assumption— Myerson’s seminal work provides revenue optimizing auctions [12]. We show instead that, for very general feasibility constraints, only knowledge of the median of each party’s value distribution, or any other quantile of these distributions, or approximations thereof, suffice for designing simple auctions that simultaneously approximate both the optimal revenue and the optimal welfare. Our results apply to all downwardclosed feasibility constraints under the assumption that the underlying, unknown value distributions are monotone hazard rate, and to all matroid feasibility constraints under the weaker assumption of regularity of the underlying distributions. Our results jointly generalize the singleitem results obtained by Azar and Micali [2] on parametric auctions, and Daskalakis and Pierrakos [6] for simultaneously approximately optimal and efficient auctions.
Priorindependent Auctions for Riskaverse Agents
, 2013
"... We study simple and approximately optimal auctions for agents with a particular form of riskaverse preferences. We show that, for symmetric agents, the optimal revenue (given a prior distribution over the agent preferences) can be approximated by the firstprice auction (which is prior independent) ..."
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Cited by 8 (3 self)
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We study simple and approximately optimal auctions for agents with a particular form of riskaverse preferences. We show that, for symmetric agents, the optimal revenue (given a prior distribution over the agent preferences) can be approximated by the firstprice auction (which is prior independent), and, for asymmetric agents, the optimal revenue can be approximated by an auction with simple form. These results are based on two technical methods. The first is for upperbounding the revenue from a riskaverse agent. The second gives a payment identity for We study optimal and approximately optimal auctions for agents with riskaverse preferences. The economics literature on this subject is largely focused on either comparative statics, i.e., is the firstprice or secondprice auction better when agents are risk averse, or deriving the optimal auction, e.g., using techniques from optimal control, for specific distributions of agent preferences. The