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Revenue Maximizing Envy-Free Pricing in Matching Markets with Budgets

16 February 2017 at 12:01 PM - 1:00 PM

Room 207, Campus on Viale Romania, 32

Speaker: Riccardo Colini-Baldeschi, LUISS

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 Ω(min{n,m}1/2−ε) for any ε > 0, unless P = NP. 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.