Sharing the cost of muliticast transmissions (preliminary version)
STOC '00 Proceedings of the thirty-second annual ACM symposium on Theory of computing
Truth revelation in approximately efficient combinatorial auctions
Proceedings of the 1st ACM conference on Electronic commerce
Competitive auctions and digital goods
SODA '01 Proceedings of the twelfth annual ACM-SIAM symposium on Discrete algorithms
On approximating optimal auctions
Proceedings of the 3rd ACM conference on Electronic Commerce
A combinatorial strongly polynomial algorithm for minimizing submodular functions
Journal of the ACM (JACM)
Competitive generalized auctions
STOC '02 Proceedings of the thiry-fourth annual ACM symposium on Theory of computing
An approximate truthful mechanism for combinatorial auctions with single parameter agents
SODA '03 Proceedings of the fourteenth annual ACM-SIAM symposium on Discrete algorithms
SODA '03 Proceedings of the fourteenth annual ACM-SIAM symposium on Discrete algorithms
Profit-maximizing multicast pricing by approximating fixed points [Extended Abstract]
Proceedings of the 4th ACM conference on Electronic commerce
Truthful Mechanisms for One-Parameter Agents
FOCS '01 Proceedings of the 42nd IEEE symposium on Foundations of Computer Science
Bayesian algorithmic mechanism design
Proceedings of the forty-second ACM symposium on Theory of computing
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One of the most fundamental problems in mechanism design is that of designing the auction that gives the optimal profit to the auctioneer. For the case that the probability distributions on the valuations of the bidders are known and independent, Myerson [15] reduces the problem to that of maximizing the common welfare by considering the virtual valuations in place of the bidders' actual valuations. The Myerson auction maximizes the seller's profit over the class of all mechanisms that are truthful and individually rational for all the bidders; however, the mechanism does not satisfy ex post individual rationality for the seller. In other words, there are examples in which for certain sets of bidder valuations, the mechanism incurs a loss. We consider the problem of merging the worst case no-deficit (or ex post seller individual rationality) condition with this average case Bayesian expected profit maximization problem. When restricting our attention to ex post incentive compatible mechanisms for this problem, we find that the Myerson mechanism is the optimal no-deficit mechanism for supermodular costs, that Myerson merged with a simple thresholding mechanism is optimal for all-or-nothing costs, and that neither mechanism is optimal for general submodular costs. Addressing the computational side of the problem, we note that for supermodular costs the Myerson mechanism is NP-hard to compute. Furthermore, we show that for all-or-nothing costs the optimal thresholding mechanism is NP-hard to compute. Finally, we consider relaxing the ex post incentive compatibility constraint and show that there is a Bayesian incentive compatible mechanism that achieves the same expected profit as Myerson, but never incurs a loss.