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• W2949941323 abstract "We consider markets consisting of a set of indivisible items, and buyers that have {em sharp} multi-unit demand. This means that each buyer $i$ wants a specific number $d_i$ of items; a bundle of size less than $d_i$ has no value, while a bundle of size greater than $d_i$ is worth no more than the most valued $d_i$ items (valuations being additive). We consider the objective of setting prices and allocations in order to maximize the total revenue of the market maker. The pricing problem with sharp multi-unit demand buyers has a number of properties that the unit-demand model does not possess, and is an important question in algorithmic pricing. We consider the problem of computing a revenue maximizing solution for two solution concepts: competitive equilibrium and envy-free pricing. For unrestricted valuations, these problems are NP-complete; we focus on a realistic special case of correlated values where each buyer $i$ has a valuation $v_iqual_j$ for item $j$, where $v_i$ and $qual_j$ are positive quantities associated with buyer $i$ and item $j$ respectively. We present a polynomial time algorithm to solve the revenue-maximizing competitive equilibrium problem. For envy-free pricing, if the demand of each buyer is bounded by a constant, a revenue maximizing solution can be found efficiently; the general demand case is shown to be NP-hard." @default.
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• W2949941323 date "2012-09-30" @default.
• W2949941323 modified "2023-10-13" @default.
• W2949941323 title "On Revenue Maximization with Sharp Multi-Unit Demands" @default.
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• W2949941323 doi "https://doi.org/10.48550/arxiv.1210.0203" @default.
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