Asymptotically Optimal Welfare of Posted Pricing for Multiple Items with MHR Distributions

07/01/2021

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by   Alexander Braun, et al.

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We consider the problem of posting prices for unit-demand buyers if all n 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 1 - Θ( 1/log n)-fraction of the optimal social welfare in expectation. Furthermore, we devise mechanisms that only use static item prices and are 1 - Θ( logloglog n/log n)-competitive compared to the optimal social welfare. As we show, both guarantees are asymptotically optimal, even for a single item and exponential distributions.