Competitive auctions and digital goods
SODA '01 Proceedings of the twelfth annual ACM-SIAM symposium on Discrete algorithms
Multi-unit auctions with budget-constrained bidders
Proceedings of the 6th ACM conference on Electronic commerce
On profit-maximizing envy-free pricing
SODA '05 Proceedings of the sixteenth annual ACM-SIAM symposium on Discrete algorithms
Revenue maximization when bidders have budgets
SODA '06 Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm
Algorithmic pricing via virtual valuations
Proceedings of the 8th 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
Multi-unit Auctions with Budget Limits
FOCS '08 Proceedings of the 2008 49th Annual IEEE Symposium on Foundations of Computer Science
Simple versus optimal mechanisms
Proceedings of the 10th ACM conference on Electronic commerce
Maximizing revenue in sequential auctions
WINE'07 Proceedings of the 3rd international conference on Internet and network economics
Multi-parameter mechanism design and sequential posted pricing
Proceedings of the forty-second ACM symposium on Theory of computing
Incentive compatible budget elicitation in multi-unit auctions
SODA '10 Proceedings of the twenty-first annual ACM-SIAM symposium on Discrete Algorithms
Pricing randomized allocations
SODA '10 Proceedings of the twenty-first annual ACM-SIAM symposium on Discrete Algorithms
Bayesian algorithmic mechanism design
Proceedings of the forty-second ACM symposium on Theory of computing
When LP is the cure for your matching woes: improved bounds for stochastic matchings
ESA'10 Proceedings of the 18th annual European conference on Algorithms: Part II
Selective call out and real time bidding
WINE'10 Proceedings of the 6th international conference on Internet and network economics
Approximation schemes for sequential posted pricing in multi-unit auctions
WINE'10 Proceedings of the 6th international conference on Internet and network economics
Single valued combinatorial auctions with budgets
Proceedings of the 12th ACM conference on Electronic commerce
Bayesian mechanism design for budget-constrained agents
Proceedings of the 12th ACM conference on Electronic commerce
On optimal single-item auctions
Proceedings of the forty-third annual ACM symposium on Theory of computing
Optimal auctions with correlated bidders are easy
Proceedings of the forty-third annual ACM symposium on Theory of computing
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
On the approximability of budget feasible mechanisms
Proceedings of the twenty-second annual ACM-SIAM symposium on Discrete Algorithms
Bayesian incentive compatibility via fractional assignments
Proceedings of the twenty-second annual ACM-SIAM symposium on Discrete Algorithms
Optimizing budget allocation among channels and influencers
Proceedings of the 21st international conference on World Wide Web
Prior-independent multi-parameter mechanism design
WINE'11 Proceedings of the 7th international conference on Internet and Network Economics
Budget feasible mechanism design: from prior-free to bayesian
STOC '12 Proceedings of the forty-fourth annual ACM symposium on Theory of computing
An algorithmic characterization of multi-dimensional mechanisms
STOC '12 Proceedings of the forty-fourth annual ACM symposium on Theory of computing
Bayesian optimal auctions via multi- to single-agent reduction
Proceedings of the 13th ACM Conference on Electronic Commerce
Mechanisms and allocations with positive network externalities
Proceedings of the 13th ACM Conference on Electronic Commerce
Symmetries and optimal multi-dimensional mechanism design
Proceedings of the 13th ACM Conference on Electronic Commerce
WINE'12 Proceedings of the 8th international conference on Internet and Network Economics
A stochastic probing problem with applications
IPCO'13 Proceedings of the 16th international conference on Integer Programming and Combinatorial Optimization
Optimal auctions via the multiplicative weight method
Proceedings of the fourteenth ACM conference on Electronic commerce
Mechanism design via optimal transport
Proceedings of the fourteenth ACM conference on Electronic commerce
Auctions with unique equilibria
Proceedings of the fourteenth ACM conference on Electronic commerce
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In this paper, we present the first approximation algorithms for the problem of designing revenue optimal Bayesian incentive compatible auctions when there are multiple (heterogeneous) items and when bidders have arbitrary demand and budget constraints (and additive valuations). Our mechanisms are surprisingly simple: We show that a sequential all-pay mechanism is a 4 approximation to the revenue of the optimal ex-interim truthful mechanism with a discrete type space for each bidder, where her valuations for different items can be correlated. We also show that a sequential posted price mechanism is a O(1) approximation to the revenue of the optimal ex-post truthful mechanism when the type space of each bidder is a product distribution that satisfies the standard hazard rate condition. We further show a logarithmic approximation when the hazard rate condition is removed, and complete the picture by showing that achieving a sub-logarithmic approximation, even for regular distributions and one bidder, requires pricing bundles of items. Our results are based on formulating novel LP relaxations for these problems, and developing generic rounding schemes from first principles.