{"id":324941,"date":"2016-11-20T20:20:59","date_gmt":"2016-11-21T04:20:59","guid":{"rendered":"https:\/\/www.microsoft.com\/en-us\/research\/?post_type=msr-research-item&#038;p=324941"},"modified":"2018-10-16T20:21:47","modified_gmt":"2018-10-17T03:21:47","slug":"constant-competitive-prior-free-auction-ordered-bidders","status":"publish","type":"msr-research-item","link":"https:\/\/www.microsoft.com\/en-us\/research\/publication\/constant-competitive-prior-free-auction-ordered-bidders\/","title":{"rendered":"Constant-Competitive Prior-Free Auction with Ordered Bidders"},"content":{"rendered":"<p>A central problem in Microeconomics is to design auctions with good revenue properties. In this setting, the bidders&#8217; valuations for the items are private knowledge, but they are drawn from publicly known prior distributions. The goal is to find a truthful auction (no bidder can gain in utility by misreporting her valuation) that maximizes the expected revenue.<br \/>\nNaturally, the optimal-auction is sensitive to the prior distributions. An intriguing question is to design a truthful auction that is oblivious to these priors, and yet manages to get a constant factor of the optimal revenue. Such auctions are called prior-free.<br \/>\nGoldberg et al. presented a constant-approximate prior-free auction when there are identical copies of an item available in unlimited supply, bidders are unit-demand, and their valuations are drawn from i.i.d. distributions. The recent work of Leonardi et al. [STOC 2012] generalized this problem to non i.i.d. bidders, assuming that the auctioneer knows the ordering of their reserve prices. Leonardi et al. proposed a prior-free auction that achieves a<span id=\"MathJax-Element-1-Frame\" class=\"MathJax\" tabindex=\"0\"><span id=\"MathJax-Span-1\" class=\"math\"><span id=\"MathJax-Span-2\" class=\"mrow\"><span id=\"MathJax-Span-3\" class=\"mi\">O<\/span><span id=\"MathJax-Span-4\" class=\"mo\">(<\/span><span id=\"MathJax-Span-5\" class=\"msubsup\"><span id=\"MathJax-Span-6\" class=\"mi\">log<\/span><span id=\"MathJax-Span-7\" class=\"mo\">\u2217<\/span><\/span><span id=\"MathJax-Span-8\" class=\"mo\"><\/span><span id=\"MathJax-Span-9\" class=\"mi\">n<\/span><span id=\"MathJax-Span-10\" class=\"mo\">)<\/span><\/span><\/span><\/span> approximation. We improve upon this result, by giving the first prior-free auction with constant approximation guarantee<\/p>\n","protected":false},"excerpt":{"rendered":"<p>A central problem in Microeconomics is to design auctions with good revenue properties. In this setting, the bidders&#8217; valuations for the items are private knowledge, but they are drawn from publicly known prior distributions. The goal is to find a truthful auction (no bidder can gain in utility by misreporting her valuation) that maximizes the 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