Welfare and Rationality Guarantees for the Simultaneous Multiple-Round Ascending Auction
Abstract
The simultaneous multiple-round auction (SMRA) and the combinatorial clock auction (CCA) are the two primary mechanisms used to sell bandwidth. Recently, it was shown that the CCA provides good welfare guarantees for general classes of valuation functions [7]. This motivates the question of whether similar welfare guarantees hold for the SMRA in the case of general valuation functions.
We show the answer is no. But we prove that good welfare guarantees still arise if the degree of complementarities in the bidder valuations are bounded. In particular, if bidder valuations functions are \(\alpha \)-near-submodular then, under truthful bidding, the SMRA has a welfare ratio (the worst case ratio between the social welfare of the optimal allocation and the auction allocation) of at most \((1+\alpha )\). However, for \(\alpha >1\), this is a bicriteria guarantee, to obtain good welfare under truthful bidding requires relaxing individual rationality. We prove this bicriteria guarantee is asymptotically (almost) tight.
Finally, we examine what strategies are required to ensure individual rationality in the SMRA with general valuation functions. First, we provide a weak characterization, namely secure bidding, for individual rationality. We then show that if the bidders use a profit-maximizing secure bidding strategy the welfare ratio is at most \(1+\alpha \). Consequently, by bidding securely, it is possible to obtain the same welfare guarantees as truthful bidding without the loss of individual rationality.
Keywords
Ascending auctions SMRA Welfare guarantee Individual rationality Near-submodularReferences
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