An approximate truthful mechanism for combinatorial auctions with single parameter agents
SODA '03 Proceedings of the fourteenth 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
Probability and Computing: Randomized Algorithms and Probabilistic Analysis
Probability and Computing: Randomized Algorithms and Probabilistic Analysis
Truthful randomized mechanisms for combinatorial auctions
Proceedings of the thirty-eighth annual ACM symposium on Theory of computing
Algorithmic pricing via virtual valuations
Proceedings of the 8th ACM conference on Electronic commerce
Mechanism design, machine learning, and pricing problems
ACM SIGecom Exchanges
Uniform Budgets and the Envy-Free Pricing Problem
ICALP '08 Proceedings of the 35th international colloquium on Automata, Languages and Programming, Part I
Truthful Approximation Schemes for Single-Parameter Agents
FOCS '08 Proceedings of the 2008 49th Annual IEEE Symposium on Foundations of Computer Science
Budget constrained auctions with heterogeneous items
Proceedings of the forty-second ACM symposium on Theory of computing
The power of randomness in bayesian optimal mechanism design
Proceedings of the 11th ACM conference on Electronic commerce
The power of uncertainty: bundle-pricing for unit-demand customers
WAOA'10 Proceedings of the 8th international conference on Approximation and online algorithms
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
Bayesian optimal auctions via multi- to single-agent reduction
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
Using lotteries to approximate the optimal revenue
Proceedings of the 2013 international conference on Autonomous agents and multi-agent systems
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Randomized mechanisms, which map a set of bids to a probability distribution over outcomes rather than a single outcome, are an important but ill-understood area of computational mechanism design. We investigate the role of randomized outcomes (henceforth, "lotteries") in the context of a fundamental and archetypical multi-parameter mechanism design problem: selling heterogeneous items to unit-demand bidders. To what extent can a seller improve her revenue by pricing lotteries rather than items, and does this modification of the problem affect its computational tractability? Our results show that the answers to these questions hinge on whether consumers can purchase only one lottery (the buy-one model) or purchase any set of lotteries and receive an independent sample from each (the buy-many model). In the buy-one model, there is a polynomial-time algorithm to compute the revenue-maximizing envy-free prices (thus overcoming the inapproximability of the corresponding item pricing problem) and the revenue of the optimal lottery system can exceed the revenue of the optimal item pricing by an unbounded factor as long as the number of item types is at least 4. In the buy-many model with n item types, the profit achieved by lottery pricing can exceed item pricing by a factor of Θ(log n) but not more, and optimal lottery pricing cannot be approximated within a factor of O(nε) for some ε 0, unless NP ⊆ ∩δ0 BPTIME(2O(nδ)). Our lower bounds rely on a mixture of geometric and algebraic techniques, whereas the upper bounds use a novel rounding scheme to transform a mechanism with randomized outcomes into one with deterministic outcomes while losing only a bounded amount of revenue.