Pricing Problems with Buyer Preselection

We investigate the problem of preselecting a subset buyers (also called agents) participating in market so as to optimize performance stable outcomes. consider four scenarios arising from combination two stability notions, namely envy-freeness and agent envy-freeness, with state-of-the-art objective functions social welfare seller’s revenue. When insisting on we prove that cannot be approximated within n 1−ε (with being number buyers) for any ε > 0, under both functions; also provide approximation algorithms an ratio tight up subpolynomial multiplicative factors The negative result, particular, holds even markets single-minded buyers. maximizing revenue is NP-hard single buyer, thus closing previous open question. Under functions, instead, design polynomial time algorithm transforming outcome involving into whole without worsening its performance. This result creates interesting middle-ground situation where, if one hand buyer preselection improve envy-free outcomes, other it can used tool simplifying combinatorial structure buyers’ valuation given market. Finally, restricted case multi-unit markets, where all items are same type assigned price. For these show may outcomes considered scenarios, corresponding algorithms.