Journal of the ACM (JACM)
On the complexity of price equilibria
Journal of Computer and System Sciences - STOC 2002
On profit-maximizing envy-free pricing
SODA '05 Proceedings of the sixteenth annual ACM-SIAM symposium on Discrete algorithms
Combination can be hard: approximability of the unique coverage problem
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
A Nonparametric Approach to Multiproduct Pricing
Operations Research
Algorithmic pricing via virtual valuations
Proceedings of the 8th ACM conference on Electronic commerce
SODA '07 Proceedings of the eighteenth annual ACM-SIAM symposium on Discrete algorithms
Buying cheap is expensive: hardness of non-parametric multi-product pricing
SODA '07 Proceedings of the eighteenth annual ACM-SIAM symposium on Discrete algorithms
On Stackelberg Pricing with Computationally Bounded Consumers
WINE '09 Proceedings of the 5th International Workshop on Internet and Network Economics
Envy, Multi Envy, and Revenue Maximization
WINE '09 Proceedings of the 5th International Workshop on Internet and Network Economics
Envy-Free Allocations for Budgeted Bidders
WINE '09 Proceedings of the 5th International Workshop on Internet and Network Economics
Envy-free makespan approximation: extended abstract
Proceedings of the 11th ACM conference on Electronic commerce
Envy-free pricing in multi-item markets
ICALP'10 Proceedings of the 37th international colloquium conference on Automata, languages and programming: Part II
Envy-free pricing with general supply constraints
WINE'10 Proceedings of the 6th international conference on Internet and network economics
Market equilibrium with transaction costs
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
Competitive algorithms for online pricing
COCOON'11 Proceedings of the 17th annual international conference on Computing and combinatorics
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
Buying Cheap Is Expensive: Approximability of Combinatorial Pricing Problems
SIAM Journal on Computing
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
Online pricing for bundles of multiple items
Journal of Global Optimization
Hi-index | 0.00 |
We study the envy-free pricing problem faced by a profit maximizing seller when there is metric substitutability among the items --- consumer i's value for item j is vi -- ci,j, and the substitution costs, {ci,j}, form a metric. Our model is motivated from the observation that sellers often sell the same product at different prices in different locations, and rational consumers optimize the tradeoff between prices and substitution costs. While the general envy-free pricing problem is hard to approximate, the addition of metric substitutability constraints allows us to solve the problem exactly in polynomial time by reducing it to an instance of weighted independent set on a perfect graph. When the substitution costs do not form a metric, even in cases when a (1+ε)--approximate triangle inequality holds, the problem becomes NP-hard. Our results show that triangle inequality is the exact sharp threshold for the problem of going from "tractable" to "hard". We then turn our attention to the multi-unit demand case, where consumers request multiple copies of the item. This problem has an interesting paradoxical non-monotonicity: The optimal revenue the seller can extract can actually decrease when consumers' demands increase. We show that in this case the revenue maximization problem becomes APX-hard and give an O(log D) approximation algorithm, where D is the ratio of the largest to smallest demand. We extend these techniques to the more general case of arbitrary non-decreasing value functions, and give an O(log3 D) approximation algorithm.