Abstract
We study envy-free pricing mechanisms in matching markets with m items and n budget constrained buyers. Each buyer is interested in a subset of the items on sale, and she appraises at some single-value every item in her preference-set. Moreover, each buyer has a budget that constraints the maximum affordable payment, while she aims to obtain as many items as possible of her preference-set. Our goal is to compute an envy-free pricing allocation that maximizes the revenue. This pricing problem is hard to approximate better than \(\varOmega (\mathrm{min} \{n,m\}^{1/2-\epsilon })\) for any \(\epsilon >0\), unless \(P=NP\) [7]. The goal of this paper is to circumvent the hardness result by restricting ourselves to specific settings of valuations and budgets. Two particularly significant scenarios are: each buyer has a budget that is greater than her single-value valuation, and each buyer has a budget that is lower than her single-value valuation. Surprisingly, in both scenarios we are able to achieve a 1/4-approximation to the optimal envy-free revenue.
This work is partly supported by the EU FET project MULTIPLEX no. 317532 and the Google Focused Award on “Algorithms for Large-scale Data Analysis”.
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Notes
- 1.
A bundle pricing scheme is able to extract more revenue than an item pricing scheme. Thus, competing against the optimal bundle-price envy-free revenue is the hardest task in this context. See Sect. 1.1.
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Colini-Baldeschi, R., Leonardi, S., Zhang, Q. (2016). Revenue Maximizing Envy-Free Pricing in Matching Markets with Budgets. In: Cai, Y., Vetta, A. (eds) Web and Internet Economics. WINE 2016. Lecture Notes in Computer Science(), vol 10123. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-54110-4_15
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