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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
. This improves
, 2015
"... We study the problem of scheduling m tasks to n selfish, unrelated machines in order to minimize the makespan, where the execution times are independent random variables, identical across machines. We show that the VCG mechanism, which myopically allocates each task to its best machine, achieves an ..."
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We study the problem of scheduling m tasks to n selfish, unrelated machines in order to minimize the makespan, where the execution times are independent random variables, identical across machines. We show that the VCG mechanism, which myopically allocates each task to its best machine, achieves an approximation ratio of O lnn ln lnn
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.