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- W4300920900 abstract "Since the 1990s spectrum auctions have been implemented world-wide. This has provided for a practical examination of an assortment of auction mechanisms and, amongst these, two simultaneous ascending price auctions have proved to be extremely successful. These are the simultaneous multiround ascending auction (SMRA) and the combinatorial clock auction (CCA). It has long been known that, for certain classes of valuation functions, the SMRA provides good theoretical guarantees on social welfare. However, no such guarantees were known for the CCA. In this paper, we show that CCA does provide strong guarantees on social welfare provided the price increment and stopping rule are well-chosen. This is very surprising in that the choice of price increment has been used primarily to adjust auction duration and the stopping rule has attracted little attention. The main result is a polylogarithmic approximation guarantee for social welfare when the maximum number of items demanded $mathcal{C}$ by a bidder is fixed. Specifically, we show that either the revenue of the CCA is at least an $OmegaBig(frac{1}{mathcal{C}^{2}log nlog^2m}Big)$-fraction of the optimal welfare or the welfare of the CCA is at least an $OmegaBig(frac{1}{log n}Big)$-fraction of the optimal welfare, where $n$ is the number of bidders and $m$ is the number of items. As a corollary, the welfare ratio -- the worst case ratio between the social welfare of the optimum allocation and the social welfare of the CCA allocation -- is at most $O(mathcal{C}^2 cdot log n cdot log^2 m)$. We emphasize that this latter result requires no assumption on bidders valuation functions. Finally, we prove that such a dependence on $mathcal{C}$ is necessary. In particular, we show that the welfare ratio of the CCA is at least $Omega Big(mathcal{C} cdot frac{log m}{log log m}Big)$." @default.
- W4300920900 created "2022-10-04" @default.
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- W4300920900 date "2016-01-10" @default.
- W4300920900 modified "2023-10-16" @default.
- W4300920900 title "On the Economic Efficiency of the Combinatorial Clock Auction" @default.
- W4300920900 hasPublicationYear "2016" @default.
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