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19
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 40 (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 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.,
Budget feasible mechanism design: from priorfree to bayesian
 In STOC
, 2012
"... Budget feasible mechanism design studies procurement combinatorial auctions in which the sellers have private costs to produce items, and the buyer (auctioneer) aims to maximize a social valuation function on subsets of items, under the budget constraint on the total payment. One of the most importa ..."
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Cited by 7 (1 self)
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Budget feasible mechanism design studies procurement combinatorial auctions in which the sellers have private costs to produce items, and the buyer (auctioneer) aims to maximize a social valuation function on subsets of items, under the budget constraint on the total payment. One of the most important questions in the field is “which valuation domains admit truthful budget feasible mechanisms with ‘small ’ approximations (compared to the social optimum)?” Singer [35] showed that additive and submodular functions have a constant approximation mechanism. Recently, Dobzinski, Papadimitriou, and Singer [20] gave an O(log 2 n) approximation mechanism for subadditive functions; further, they remarked that: “A fundamental question is whether, regardless of computational constraints, a constantfactor budget feasible mechanism exists for subadditive functions.” In this paper, we address this question from two viewpoints: priorfree worst case analysis and Bayesian analysis, which are two standard approaches from computer science and economics, respectively. • For the priorfree framework, we use a linear program (LP) that describes the fractional cover of the valuation function; the LP is also connected to the concept of approximate core in cooperative game theory. We provide a mechanism for subadditive functions whose approximation is O(I), via the worst case integrality gap I of this LP. This implies an O(log n)approximation for subadditive valuations, O(1)approximation for XOS valuations, as well as for valuations having a constant
NearOptimal MultiUnit Auctions with Ordered Bidders
, 2013
"... We construct priorfree auctions with constantfactor approximation guarantees with ordered bidders, in both unlimited and limited supply settings. We compare the expected revenue of our auctions on a bid vector to the monotone price benchmark, the maximum revenue that can be obtained from a bid vec ..."
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Cited by 2 (1 self)
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We construct priorfree auctions with constantfactor approximation guarantees with ordered bidders, in both unlimited and limited supply settings. We compare the expected revenue of our auctions on a bid vector to the monotone price benchmark, the maximum revenue that can be obtained from a bid vector using supplyrespecting prices that are nonincreasing in the bidder ordering and bounded above by the secondhighest bid. As a consequence, our auctions are simultaneously nearoptimal in a wide range of Bayesian multiunit environments.
A lower bound on seller revenue in single buyer monopoly auctions. Arxiv preprint arXiv:1204.5551
, 2012
"... We consider a monopoly seller who optimally auctions a single object to a single potential buyer, with a known distribution of valuations. We show that a tight lower bound on the seller’s expected revenue is 1/e times the geometric expectation of the buyer’s valuation, and that this bound is uniquel ..."
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We consider a monopoly seller who optimally auctions a single object to a single potential buyer, with a known distribution of valuations. We show that a tight lower bound on the seller’s expected revenue is 1/e times the geometric expectation of the buyer’s valuation, and that this bound is uniquely achieved for the equal revenue distribution. We show also that when the valuation’s expectation and geometric expectation are close, then the seller’s expected revenue is close to the expected valuation. 1
Optimal Platform Design
"... An auction house cannot generally provide the optimal auction technology to every client. Instead it provides one or several auction technologies, and clients select the most appropriate one. For example, eBay provides ascending auctions and “buyitnow ” pricing. For each client the offered technol ..."
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An auction house cannot generally provide the optimal auction technology to every client. Instead it provides one or several auction technologies, and clients select the most appropriate one. For example, eBay provides ascending auctions and “buyitnow ” pricing. For each client the offered technology may not be optimal, but it would be too costly for clients to create their own. We call these mechanisms, which emphasize generality rather than optimality, platform mechanisms. A platform mechanism will be adopted by a client if its performance exceeds that of the client’s outside option, e.g., hiring (at a cost) a consultant to design the optimal mechanism. We ask two related questions. First, for what costs of the outside option will the platform be universally adopted? Second, what is the structure of good platform mechanisms? We answer these questions using a novel priorfree analysis framework in which we seek mechanisms that are approximately optimal for every prior.