On revenue maximization with sharp multi-unit demands

Ning Chen (), Xiaotie Deng (), Paul W. Goldberg () and Jinshan Zhang ()
Additional contact information
Ning Chen: Nanyang Technological University
Xiaotie Deng: Shanghai Jiao Tong University
Paul W. Goldberg: University of Oxford
Jinshan Zhang: University of Liverpool

Journal of Combinatorial Optimization, 2016, vol. 31, issue 3, No 16, 1174-1205

Abstract: Abstract We consider markets consisting of a set of indivisible items, and buyers that have sharp multi-unit demand. This means that each buyer $$i$$ i wants a specific number $$d_i$$ d i of items; a bundle of size less than $$d_i$$ d i has no value. 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 $$i$$ i has a valuation $$v_iq_j$$ v i q j for item $$j$$ j , where $$v_i$$ v i and $$q_j$$ q j are positive quantities associated with buyer $$i$$ i and item $$j$$ 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.

Keywords: Position auction; Revenue maximization; Envy-free; Competitive equilibrium; Sharp demand (search for similar items in EconPapers)
Date: 2016
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Citations: View citations in EconPapers (1)

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DOI: 10.1007/s10878-014-9817-y

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