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22
Simple versus Optimal Mechanisms
"... The monopolist’s theory of optimal singleitem auctions for agents with independent private values can be summarized by two statements. The first is from Myerson [8]: the optimal auction is Vickrey with a reserve price. The second is from Bulow and Klemperer [1]: it is better to recruit one more bid ..."
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Cited by 79 (26 self)
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The monopolist’s theory of optimal singleitem auctions for agents with independent private values can be summarized by two statements. The first is from Myerson [8]: the optimal auction is Vickrey with a reserve price. The second is from Bulow and Klemperer [1]: it is better to recruit one more bidder and run the Vickrey auction than to run the optimal auction. These results hold for singleitem auctions under the assumption that the agents ’ valuations are independently and identically drawn from a distribution that satisfies a natural (and prevalent) regularity condition. These fundamental guarantees for the Vickrey auction fail to hold in general singleparameter agent mechanism design problems. We give precise (and weak) conditions under which approximate analogs of these two results hold, thereby demonstrating that simple mechanisms remain almost optimal in quite general singleparameter agent settings.
Revenue maximization with a single sample
 IN: PROCEEDINGS OF 12TH ACM CONFERENCE ON ELECTRONIC COMMERCE (2010
"... We design and analyze approximately revenuemaximizing auctions in general singleparameter settings. Bidders have publicly observable attributes, and we assume that the valuations of indistinguishable bidders are independent draws from a common distribution. Crucially, we assume all valuation dis ..."
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Cited by 28 (6 self)
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We design and analyze approximately revenuemaximizing auctions in general singleparameter settings. Bidders have publicly observable attributes, and we assume that the valuations of indistinguishable bidders are independent draws from a common distribution. Crucially, we assume all valuation distributions are a priori unknown to the seller. Despite this handicap, we show how to obtain approximately optimal expected revenue — nearly as large as what could be obtained if the distributions were known in advance — under quite general conditions. Our most general result concerns arbitrary downwardclosed singleparameter environments and valuation distributions that satisfy a standard hazard rate condition. We also assume that no bidder has a unique attribute value, which is obviously necessary with unknown and attributedependent valuation distributions. Here, we give an auction that, for every such environment and unknown valuation distributions, has expected revenue at least a constant fraction of the expected optimal welfare (and hence revenue). A key idea in our auction is to associate each bidder with another that has the same attribute, with the second bidder’s valuation acting as a random reserve price for the first. Conceptually, our analysis shows that even a single sample from a distribution — the second bidder’s valuation — is sufficient information to obtain nearoptimal expected revenue, even in quite general settings.
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 22 (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 21 (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 13 (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
Robust Mechanisms for RiskAverse Sellers
"... The existing literature on optimal auctions focuses on optimizing the expected revenue of the seller, and is appropriate for riskneutral sellers. In this paper, we identify good mechanisms for riskaverse sellers. As is standard in the economics literature, we model the riskaversion of a seller by ..."
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Cited by 10 (1 self)
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The existing literature on optimal auctions focuses on optimizing the expected revenue of the seller, and is appropriate for riskneutral sellers. In this paper, we identify good mechanisms for riskaverse sellers. As is standard in the economics literature, we model the riskaversion of a seller by endowing the seller with a monotone, concave utility function. We then seek robust mechanisms that are approximately optimal for all sellers, no matter what their levels of riskaversion are. We have two main results for multiunit auctions with unitdemand bidders whose valuations are drawn i.i.d. from a regular distribution. First, we identify a postedprice mechanism called the Hedge mechanism, which gives a universal constant factor approximation; we also show for the unlimited supply case that this mechanism is in a sense the best possible. Second, we show that the VCG mechanism gives a universal constant factor approximation when the number of bidders is even a small multiple of the number of items. Along the way we point out that Myerson’s characterization [11] fails to extend to utilitymaximization for riskaverse sellers, and establish interesting properties of regular distributions and monotone hazard rate distributions.
The Simple Economics of Approximately Optimal Auctions Arvix
, 2012
"... The intuition that profit is optimized by maximizing marginal revenue is a guiding principle in microeconomics. In the classical auction theory for agents with quasilinearutility and singledimensional preferences, Bulow and Roberts (1989) show that the optimal auction of Myerson (1981) is in fact o ..."
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Cited by 8 (3 self)
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The intuition that profit is optimized by maximizing marginal revenue is a guiding principle in microeconomics. In the classical auction theory for agents with quasilinearutility and singledimensional preferences, Bulow and Roberts (1989) show that the optimal auction of Myerson (1981) is in fact optimizing marginal revenue. In particular Myerson’s virtual values are exactly the derivative of an appropriate revenue curve. Thispaperconsidersmechanismdesigninenvironmentswheretheagentshavemultidimensional and nonlinear preferences. Understanding good auctions for these environments is considered to be the main challenge in Bayesian optimal mechanism design. In these environments maximizing marginal revenue may not be optimal, and furthermore, there is sometimes no direct way to implementing the marginal revenue maximization mechanism. Our contributions are three fold: we characterize the settings for which marginal revenue maximization is optimal, we give simple procedures for implementing marginal revenue maximization in general, and we show that marginal revenue maximization is approximately optimal. Our approximation factor smoothly degrades in a term that quantifies how far the environment is from an ideal one (i.e.,
Envy, Truth, and Profit
"... We consider profit maximizing (incentive compatible) mechanism design in general environments that include, e.g., position auctions (for selling advertisements on Internet search engines) and singleminded combinatorial auctions. We analyze optimal envyfree pricings in these settings, and give econ ..."
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Cited by 4 (2 self)
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We consider profit maximizing (incentive compatible) mechanism design in general environments that include, e.g., position auctions (for selling advertisements on Internet search engines) and singleminded combinatorial auctions. We analyze optimal envyfree pricings in these settings, and give economic justification for using the optimal revenue of envyfree pricings as a benchmark for priorfree mechanism design and analysis. Moreover, we show that envyfree pricing has a simple nice structure and a strong connection to incentive compatible mechanism design, and we exploit this connection to design priorfree mechanisms with strong approximation guarantees.