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
Algorithmic Game Theory
Bayesian algorithmic mechanism design
Proceedings of the forty-second ACM symposium on Theory of computing
Multi-parameter mechanism design and sequential posted pricing
Proceedings of the forty-second ACM symposium on Theory of computing
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
Pricing randomized allocations
SODA '10 Proceedings of the twenty-first annual ACM-SIAM symposium on Discrete Algorithms
Optimal auctions with correlated bidders are easy
Proceedings of the forty-third annual ACM symposium on Theory of computing
Bayesian Combinatorial Auctions: Expanding Single Buyer Mechanisms to Many Buyers
FOCS '11 Proceedings of the 2011 IEEE 52nd Annual Symposium on Foundations of Computer Science
Extreme-Value Theorems for Optimal Multidimensional Pricing
FOCS '11 Proceedings of the 2011 IEEE 52nd Annual Symposium on Foundations of Computer Science
Bayesian incentive compatibility via matchings
Proceedings of the twenty-second annual ACM-SIAM symposium on Discrete Algorithms
An algorithmic characterization of multi-dimensional mechanisms
STOC '12 Proceedings of the forty-fourth annual ACM symposium on Theory of computing
WINE'12 Proceedings of the 8th international conference on Internet and Network Economics
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
Protecting moving targets with multiple mobile resources
Journal of Artificial Intelligence Research
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We efficiently solve the optimal multi-dimensional mechanism design problem for independent additive bidders with arbitrary demands when either the number of bidders is held constant or the number of items is held constant. In the first setting, we need that each bidder's values for the items are sampled from a possibly correlated, item-symmetric distribution, allowing different distributions for each bidder. In the second setting, we allow the values of each bidder for the items to be arbitrarily correlated, but assume that the distribution of bidder types is bidder-symmetric. These symmetric distributions include i.i.d. distributions, as well as many natural correlated distributions. E.g., an item-symmetric distribution can be obtained by taking an arbitrary distribution, and "forgetting" the names of items; this could arise when different members of a bidder population have various sorts of correlations among the items, but the items are "the same" with respect to a random bidder from the population. For all ∈0, we obtain a computationally efficient additive ∈-approximation, when the value distributions are bounded, or a multiplicative (1-∈)-approximation when the value distributions are unbounded, but satisfy the Monotone Hazard Rate condition, covering a widely studied class of distributions in Economics. Our running time is polynomial in max{#items,#bidders}, and not the size of the support of the joint distribution of all bidders' values for all items, which is typically exponential in both the number of items and the number of bidders. Our mechanisms are randomized, explicitly price bundles, and in some cases can also accommodate budget constraints. Our results are enabled by several new tools and structural properties of Bayesian mechanisms, which we expect to find applications beyond the settings we consider here; indeed, there has already been follow-up research [Cai et al. 2012; Cai and Huang 2012] making use of our tools in both symmetric and non-symmetric settings. In particular, we provide a symmetrization technique that turns any truthful mechanism into one that has the same revenue and respects all symmetries in the underlying value distributions. We also prove that item-symmetric mechanisms satisfy a natural strong-monotonicity property which, unlike cyclic-monotonicity, can be harnessed algorithmically. Finally, we provide a technique that turns any given ∈-BIC mechansism (i.e. one where incentive constraints are violated by ∈) into a truly-BIC mechanism at the cost of O(√∈) revenue.