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Tight Revenue Gaps among MultiUnit Mechanisms
This paper considers Bayesian revenue maximization in the kunit setting, where a monopolist seller has k copies of an indivisible item and faces n unitdemand buyers (whose value distributions can be nonidentical). Four basic mechanisms among others have been widely employed in practice and widely studied in the literature: Myerson Auction, Sequential PostedPricing, (k + 1)th Price Auction with Anonymous Reserve, and Anonymous Pricing. Regarding a pair of mechanisms, we investigate the largest possible ratio between the two revenues (a.k.a. the revenue gap), over all possible value distributions of the buyers. Divide these four mechanisms into two groups: (i) the discriminating mechanism group, Myerson Auction and Sequential PostedPricing, and (ii) the anonymous mechanism group, Anonymous Reserve and Anonymous Pricing. Within one group, the involved two mechanisms have an asymptotically tight revenue gap of 1 + Θ(1 / √(k)). In contrast, any two mechanisms from the different groups have an asymptotically tight revenue gap of Θ(log k).
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