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Algorithms for Strategic Agents
, 2014
"... In traditional algorithm design, no incentives come into play: the input is given, and your algorithm must produce a correct output. How much harder is it to solve the same problem when the input is not given directly, but instead reported by strategic agents with interests of their own? The unique ..."
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In traditional algorithm design, no incentives come into play: the input is given, and your algorithm must produce a correct output. How much harder is it to solve the same problem when the input is not given directly, but instead reported by strategic agents with interests of their own? The unique challenge stems from the fact that the agents may choose to lie about the input in order to manipulate the behavior of the algorithm for their own interests, and tools from Game Theory are therefore required in order to predict how these agents will behave. We develop a new algorithmic framework with which to study such problems. Specifically, we provide a computationally efficient blackbox reduction from solving any optimization problem on "strategic input, " often called algorithmic mechanism design to solving a perturbed version of that same optimization problem when the input is directly given, traditionally called algorithm design. We further demonstrate the power of our framework by making significant progress on several longstanding open problems. First, we extend Myerson's celebrated characterization of single item auctions [Mye8l] to multiple items, providing also a computationally efficient implementation of optimal auctions. Next, we design a computationally efficient 2approximate mechanism
On the Complexity of Optimal Lottery Pricing and Randomized Mechanisms
"... We study the optimal lottery problem and the optimal mechanism design problem in the setting of a single unitdemand buyer with item values drawn from independent distributions. Optimal solutions to both problems are characterized by a linear program with exponentially many variables. For the menu s ..."
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We study the optimal lottery problem and the optimal mechanism design problem in the setting of a single unitdemand buyer with item values drawn from independent distributions. Optimal solutions to both problems are characterized by a linear program with exponentially many variables. For the menu size complexity of the optimal lottery problem, we present an explicit, simple instance with distributions of support size 2, and show that exponentially many lotteries are required to achieve the optimal revenue. We also show that, when distributions have support size 2 and share the same high value, the simpler scheme of item pricing can achieve the same revenue as the optimal menu of lotteries. The same holds for the case of two items with support size 2 (but not necessarily the same high value). For the computational complexity of the optimal mechanism design problem, we show that unless the polynomialtime hierarchy collapses (more exactly, PNP = P#P), there is no universal efficient randomized algorithm to implement an optimal mechanism even when distributions have support size 3.
Learning Simple Auctions
, 2016
"... Abstract We present a general framework for proving polynomial sample complexity bounds for the problem of learning from samples the best auction in a class of "simple" auctions. Our framework captures the most prominent examples of "simple" auctions, including anonymous and non ..."
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Abstract We present a general framework for proving polynomial sample complexity bounds for the problem of learning from samples the best auction in a class of "simple" auctions. Our framework captures the most prominent examples of "simple" auctions, including anonymous and nonanonymous item and bundle pricings, with either a single or multiple buyers. The first step of the framework is to show that the set of auction allocation rules have a lowdimensional representation. The second step shows that, across the subset of auctions that share the same allocations on a given set of samples, the auction revenue varies in a lowdimensional way. Our results imply that in typical scenarios where it is possible to compute a nearoptimal simple auction with a known prior, it is also possible to compute such an auction with an unknown prior, given a polynomial number of samples.
MultiItem Auctions Defying Intuition?
, 2013
"... The best way to sell n items to a buyer who values each of them independently and uniformly randomly in [c, c+ 1] is to bundle them together, as long as c is large enough. Still, for any c, the grand bundling mechanism is never optimal for large enough n, despite the sharp concentration of the buyer ..."
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The best way to sell n items to a buyer who values each of them independently and uniformly randomly in [c, c+ 1] is to bundle them together, as long as c is large enough. Still, for any c, the grand bundling mechanism is never optimal for large enough n, despite the sharp concentration of the buyer’s total value for the items as n grows. Optimal multiitem mechanisms are rife with unintuitive properties, making multiitem generalizations of Myerson’s celebrated mechanism a daunting task. We survey recent work on the structure and computational complexity of revenueoptimal multiitem mechanisms, providing structural as well as algorithmic generalizations of Myerson’s result to multiitem settings.