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38
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 29 (4 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
Budget constrained auctions with heterogeneous items
 In Proceedings 42nd ACM Symposium on Theory of Computing
, 2010
"... In this paper, we present the first approximation algorithms for the celebrated problem of designing revenue optimal Bayesian incentive compatible auctions when there are multiple (heterogeneous) items and when bidders can have arbitrary demand and budget constraints. Our mechanisms are surprisingly ..."
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Cited by 17 (2 self)
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In this paper, we present the first approximation algorithms for the celebrated problem of designing revenue optimal Bayesian incentive compatible auctions when there are multiple (heterogeneous) items and when bidders can have arbitrary demand and budget constraints. Our mechanisms are surprisingly simple: We show that a sequential allpay mechanism is a 4 approximation to the revenue of the optimal exinterim truthful mechanism with discrete correlated type space for each bidder. We also show that a sequential posted price mechanism is a O(1) approximation to the revenue of the optimal expost truthful mechanism when the type space of each bidder is a product distribution that satisfies the standard hazard rate condition. We further show a logarithmic approximation when the hazard rate condition is removed, and complete the picture by showing that achieving a sublogarithmic approximation, even for regular distributions and one bidder, requires pricing bundles of items. Our results are based on formulating novel LP relaxations for these problems, and developing generic rounding schemes from first principles. We believe this approach will be useful in other Bayesian mechanism design contexts.
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 16 (4 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
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 15 (2 self)
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• Bronze Medal, 13th International Olympiad in Informatics, Tampere, Finland,
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 8 (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
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 5 (0 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.
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 4 (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 3 (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.
PriorFree Auctions with Ordered Bidders
"... Priorfree auctions are robust auctions that assume no distribution over bidders ’ valuations and provide worstcase (inputbyinput) approximation guarantees. In contrast to previous work on this topic, we pursue good priorfree auctions with nonidentical bidders. Priorfree auctions can approxima ..."
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Cited by 3 (1 self)
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Priorfree auctions are robust auctions that assume no distribution over bidders ’ valuations and provide worstcase (inputbyinput) approximation guarantees. In contrast to previous work on this topic, we pursue good priorfree auctions with nonidentical bidders. Priorfree auctions can approximate meaningful benchmarks for nonidentical bidders only when “sufficient qualitative information ” about the bidder asymmetry is publicly known. We consider digital goods auctions where there is a total ordering of the bidders that is known to the seller, where earlier bidders are in some sense thought to have higher valuations. We use the framework of Hartline and Roughgarden (STOC ’08) to define an appropriate revenue benchmark: the maximum revenue that can be obtained from a bid vector using prices that are nonincreasing in the bidder ordering and bounded above by the secondhighest bid. This monotoneprice benchmark is always as large as the wellknown fixedprice benchmark F (2) , so designing priorfree auctions with good approximation guarantees is only harder. By design, an auction that approximates the monotoneprice benchmark satisfies a very strong guarantee: it is, in particular, simultaneously nearoptimal for essentially every Bayesian environment in which bidders ’ valuation distributions have nonincreasing monopoly prices, or in which the distribution of each bidder stochastically dominates that of the next. Of course, even if there is no distribution over bidders ’ valuations, such an auction still provides a quantifiable inputbyinput performance guarantee. In this paper, we design a simple priorfree auction for digital goods with ordered bidders, the Random Price Restriction (RPR) auction. We prove that its expected revenue on every bid profile b is Ω(M (2) (b) / log ∗ n), where M (2) denotes the monotoneprice benchmark and log ∗ n denotes