SODA '05 Proceedings of the sixteenth annual ACM-SIAM symposium on Discrete algorithms
On profit-maximizing envy-free pricing
SODA '05 Proceedings of the sixteenth annual ACM-SIAM symposium on Discrete algorithms
Algorithmic pricing via virtual valuations
Proceedings of the 8th ACM conference on Electronic commerce
Buying cheap is expensive: hardness of non-parametric multi-product pricing
SODA '07 Proceedings of the eighteenth annual ACM-SIAM symposium on Discrete algorithms
Item pricing for revenue maximization
Proceedings of the 9th ACM conference on Electronic commerce
Optimal envy-free pricing with metric substitutability
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
Dynamic pricing for impatient bidders
ACM Transactions on Algorithms (TALG)
Dynamic and Non-uniform Pricing Strategies for Revenue Maximization
FOCS '09 Proceedings of the 2009 50th Annual IEEE Symposium on Foundations of Computer Science
A quasi-PTAS for profit-maximizing pricing on line graphs
ESA'07 Proceedings of the 15th annual European conference on Algorithms
Envy-free pricing in multi-item markets
ICALP'10 Proceedings of the 37th international colloquium conference on Automata, languages and programming: Part II
Theoretical Computer Science
Envy-free pricing with general supply constraints
WINE'10 Proceedings of the 6th international conference on Internet and network economics
Competitive algorithms for online pricing
COCOON'11 Proceedings of the 17th annual international conference on Computing and combinatorics
Welfare and Profit Maximization with Production Costs
FOCS '11 Proceedings of the 2011 IEEE 52nd Annual Symposium on Foundations of Computer Science
How to sell a graph: guidelines for graph retailers
WG'06 Proceedings of the 32nd international conference on Graph-Theoretic Concepts in Computer Science
Dynamic pricing with limited supply
Proceedings of the 13th ACM Conference on Electronic Commerce
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Given a seller with $$k$$ types of items, $$m$$ of each, a sequence of users $$\{u_1, u_2,\ldots \}$$ arrive one by one. Each user is single-minded, i.e., each user is interested only in a particular bundle of items. The seller must set the price and assign some amount of bundles to each user upon his/her arrival. Bundles can be sold fractionally. Each $$u_i$$ has his/her value function $$v_i(\cdot )$$ such that $$v_i(x)$$ is the highest unit price $$u_i$$ is willing to pay for $$x$$ bundles. The objective is to maximize the revenue of the seller by setting the price and amount of bundles for each user. In this paper, we first show that a lower bound of the competitive ratio for this problem is $$\Omega (\log h+\log k)$$, where $$h$$ is the highest unit price to be paid among all users. We then give a deterministic online algorithm, Pricing, whose competitive ratio is $$O(\sqrt{k}\cdot \log h\log k)$$. When $$k=1$$ the lower and upper bounds asymptotically match the optimal result $$O(\log h)$$.