On Profit-Maximizing Pricing for the Highway and Tollbooth Problems
SAGT '09 Proceedings of the 2nd International Symposium on Algorithmic Game Theory
On Stackelberg Pricing with Computationally Bounded Consumers
WINE '09 Proceedings of the 5th International Workshop on Internet and Network Economics
Budget constrained auctions with heterogeneous items
Proceedings of the forty-second ACM symposium on Theory of computing
Envy-free makespan approximation: extended abstract
Proceedings of the 11th ACM conference on Electronic commerce
Pricing randomized allocations
SODA '10 Proceedings of the twenty-first annual ACM-SIAM symposium on Discrete Algorithms
Envy-free pricing in multi-item markets
ICALP'10 Proceedings of the 37th international colloquium conference on Automata, languages and programming: Part II
Improved hardness of approximation for stackelberg shortest-path pricing
WINE'10 Proceedings of the 6th international conference on Internet and network economics
Envy-free pricing with general supply constraints
WINE'10 Proceedings of the 6th international conference on Internet and network economics
The power of uncertainty: bundle-pricing for unit-demand customers
WAOA'10 Proceedings of the 8th international conference on Approximation and online algorithms
On optimal multidimensional mechanism design
ACM SIGecom Exchanges
Multi-parameter mechanism design under budget and matroid constraints
ESA'11 Proceedings of the 19th European conference on Algorithms
Optimal Envy-Free Pricing with Metric Substitutability
SIAM Journal on Computing
A global characterization of envy-free truthful scheduling of two tasks
WINE'11 Proceedings of the 7th international conference on Internet and Network Economics
Envy-Free Makespan Approximation
SIAM Journal on Computing
On envy-free pareto efficient pricing
FAW-AAIM'12 Proceedings of the 6th international Frontiers in Algorithmics, and Proceedings of the 8th international conference on Algorithmic Aspects in Information and Management
Online pricing for multi-type of items
FAW-AAIM'12 Proceedings of the 6th international Frontiers in Algorithmics, and Proceedings of the 8th international conference on Algorithmic Aspects in Information and Management
A QPTAS for ε-envy-free profit-maximizing pricing on line graphs
ICALP'12 Proceedings of the 39th international colloquium conference on Automata, Languages, and Programming - Volume Part II
WINE'12 Proceedings of the 8th international conference on Internet and Network Economics
Envy-free pricing in multi-item markets
ACM Transactions on Algorithms (TALG)
Online pricing for bundles of multiple items
Journal of Global Optimization
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We consider the unit-demand min-buying pricing problem, in which we want to compute revenue maximizing prices for a set of products $\mathcal{P}$ assuming that each consumer from a set of consumer samples $\mathcal{C}$ will purchase her cheapest affordable product once prices are fixed. We focus on the special uniform-budget case, in which every consumer has only a single non-zero budget for some set of products. This constitutes a special case also of the unit-demand envy-free pricing problem.We show that, assuming specific hardness of the balanced bipartite independent set problem in constant degree graphs or hardness of refuting random 3CNF formulas, the unit-demand min-buying pricing problem with uniform budgets cannot be approximated in polynomial time within $\mathcal{O}(\log ^{\varepsilon} |\mathcal{C}|)$ for some 驴 0. This is the first result giving evidence that unit-demand envy-free pricing, as well, might be hard to approximate essentially better than within the known logarithmic ratio.We then introduce a slightly more general problem definition in which consumers are given as an explicit probability distribution and show that in this case the envy-free pricing problem can be shown to be inapproximable within $\mathcal{O}(|\mathcal{P}|^{\varepsilon})$ assuming NP $\nsubseteq \bigcap _{\delta 0}$ BPTIME($2^{\mathcal{O}(n^{\delta})}$). Finally, we briefly argue that all the results apply to the important setting of pricing with single-minded consumers as well.