Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
On profit-maximizing envy-free pricing
SODA '05 Proceedings of the sixteenth annual ACM-SIAM symposium on Discrete algorithms
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SODA '06 Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm
Single-minded unlimited supply pricing on sparse instances
SODA '06 Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm
Approximation algorithms and online mechanisms for item pricing
EC '06 Proceedings of the 7th ACM conference on Electronic commerce
Item pricing for revenue maximization
Proceedings of the 9th ACM conference on Electronic commerce
Uniform Budgets and the Envy-Free Pricing Problem
ICALP '08 Proceedings of the 35th international colloquium on Automata, Languages and Programming, Part I
FOCS '08 Proceedings of the 2008 49th Annual IEEE Symposium on Foundations of Computer Science
On Profit-Maximizing Pricing for the Highway and Tollbooth Problems
SAGT '09 Proceedings of the 2nd International Symposium on Algorithmic Game Theory
Envy, Multi Envy, and Revenue Maximization
WINE '09 Proceedings of the 5th International Workshop on Internet and Network Economics
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ESA'07 Proceedings of the 15th annual European conference on Algorithms
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WAOA'10 Proceedings of the 8th international conference on Approximation and online algorithms
Optimal Envy-Free Pricing with Metric Substitutability
SIAM Journal on Computing
Near-optimal pricing in near-linear time
WADS'05 Proceedings of the 9th international conference on Algorithms and Data Structures
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In this article, we study revenue maximizing envy-free pricing in multi-item markets: There are m indivisible items with unit supply each and n potential buyers where each buyer is interested in acquiring one item. The goal is to determine allocations (a matching between buyers and items) and prices of all items to maximize total revenue given that all buyers are envy-free. We give a polynomial time algorithm to compute a revenue maximizing envy-free pricing when every buyer evaluates at most two items at a positive valuation, by reducing it to an instance of weighted independent set in a perfect graph and applying the Strong Perfect Graph Theorem. We complement our result by showing that the problem becomes NP-hard if some buyers are interested in at least three items.