Computationally feasible VCG mechanisms
Proceedings of the 2nd ACM conference on Electronic commerce
Optimal approximation for the submodular welfare problem in the value oracle model
STOC '08 Proceedings of the fortieth annual ACM symposium on Theory of computing
Posted prices vs. negotiations: an asymptotic analysis
Proceedings of the 9th ACM conference on Electronic commerce
Simple versus optimal mechanisms
Proceedings of the 10th ACM conference on Electronic commerce
Proceedings of the 10th ACM conference on Electronic commerce
Revenue maximization with a single sample
Proceedings of the 11th ACM conference on Electronic commerce
Robust mechanisms for risk-averse sellers
Proceedings of the 11th ACM conference on Electronic commerce
Correlation robust stochastic optimization
SODA '10 Proceedings of the twenty-first annual ACM-SIAM symposium on Discrete Algorithms
Approximation schemes for sequential posted pricing in multi-unit auctions
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
Submodular function maximization via the multilinear relaxation and contention resolution schemes
Proceedings of the forty-third annual ACM symposium on Theory of computing
Dynamic pricing with limited supply
Proceedings of the 13th ACM Conference on Electronic Commerce
Asymptotically optimal algorithm for stochastic adwords
Proceedings of the 13th ACM Conference on Electronic Commerce
Mechanism design for a risk averse seller
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
Prior-independent mechanisms for scheduling
Proceedings of the forty-fifth annual ACM symposium on Theory of computing
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For revenue and welfare maximization in single-dimensional Bayesian settings, Chawla et al. (STOC10) recently showed that sequential posted-price mechanisms (SPMs), though simple in form, can perform surprisingly well compared to the optimal mechanisms. In this paper, we give a theoretical explanation of this fact, based on a connection to the notion of correlation gap. Loosely speaking, for auction environments with matroid constraints, we can relate the performance of a mechanism to the expectation of a monotone submodular function over a random set. This random set corresponds to the winner set for the optimal mechanism, which is highly correlated, and corresponds to certain demand set for SPMs, which is independent. The notion of correlation gap of Agrawal et al. (SODA10) quantifies how much we "lose" in the expectation of the function by ignoring correlation in the random set, and hence bounds our loss in using certain SPM instead of the optimal mechanism. Furthermore, the correlation gap of a monotone and submodular function is known to be small, and it follows that certain SPM can approximate the optimal mechanism by a good constant factor. Exploiting this connection, we give tight analysis of a greedy-based SPM of Chawla et al. for several environments. In particular, we show that it gives an e/(e − 1)-approximation for matroid environments, gives asymptotically a 1/(1--1/√2πk)-approximation for the important sub-case of k-unit auctions, and gives a (p + 1)-approximation for environments with p-independent set system constraints.