3 research outputs found
Asymptotically Optimal Welfare of Posted Pricing for Multiple Items with MHR Distributions
We consider the problem of posting prices for unit-demand buyers if all
buyers have identically distributed valuations drawn from a distribution with
monotone hazard rate. We show that even with multiple items asymptotically
optimal welfare can be guaranteed.
Our main results apply to the case that either a buyer's value for different
items are independent or that they are perfectly correlated. We give mechanisms
using dynamic prices that obtain a -fraction of the optimal social welfare in expectation. Furthermore,
we devise mechanisms that only use static item prices and are -competitive compared to the
optimal social welfare. As we show, both guarantees are asymptotically optimal,
even for a single item and exponential distributions.Comment: To appear at the 29th Annual European Symposium on Algorithms (ESA
2021
Tight Revenue Gaps among Multi-Unit Mechanisms
This paper considers Bayesian revenue maximization in the -unit setting,
where a monopolist seller has copies of an indivisible item and faces
unit-demand buyers (whose value distributions can be non-identical). Four basic
mechanisms among others have been widely employed in practice and widely
studied in the literature: {\sf Myerson Auction}, {\sf Sequential
Posted-Pricing}, {\sf -th Price Auction with Anonymous Reserve}, and
{\sf 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, {\sf Myerson Auction} and {\sf Sequential Posted-Pricing}, and
(ii)~the anonymous mechanism group, {\sf Anonymous Reserve} and {\sf Anonymous
Pricing}. Within one group, the involved two mechanisms have an asymptotically
tight revenue gap of . In contrast, any two
mechanisms from the different groups have an asymptotically tight revenue gap
of