Multi-parameter mechanism design and sequential posted pricing
Proceedings of the forty-second ACM symposium on Theory of computing
Robust mechanisms for risk-averse sellers
Proceedings of the 11th ACM conference on Electronic commerce
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
Mechanism design via correlation gap
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
Bayesian optimal auctions via multi- to single-agent reduction
Proceedings of the 13th ACM Conference on Electronic Commerce
Price of Correlations in Stochastic Optimization
Operations Research
Optimal auctions via the multiplicative weight method
Proceedings of the fourteenth ACM conference on Electronic commerce
Truthfulness and stochastic dominance with monetary transfers
Proceedings of the fourteenth ACM conference on Electronic commerce
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We develop efficient algorithms to construct approximately utility maximizing mechanisms for a risk averse seller in the presence of potentially risk-averse buyers in Bayesian single parameter and multi-parameter settings. We model risk aversion by concave utility function. Bayesian mechanism design has usually focused on revenue maximization in a risk-neutral environment, and while some work has regarded buyers' risk aversion, very little of past work addresses the seller's risk aversion. We first consider the problem of designing a DSIC mechanism for a risk-averse seller in the case of multi-unit auctions. We give a poly-time computable pricing mechanism that is a (1−1/e−ε)-approximation to an optimal DSIC mechanism, for any ε0. Our result is based on a novel application of correlation gap bound, that involves splitting and merging of random variables to redistribute probability mass across buyers. This allows us to reduce our problem to that of checking feasibility of a small number of distinct configurations, each of which corresponds to a covering LP. DSIC mechanisms are robust against buyers' risk aversion, but may yield arbitrarily worse utility than the optimal BIC mechanisms, when buyers' utility functions are assumed to be known. For a risk averse seller, we design a truthful-in-expectation mechanism whose utility is a small constant factor approximation to the utilty of the optimal BIC mechanism under two mild assumptions: (a) ex post individual rationality and (b) no positive transfers. Our mechanism simulates several rounds of sequential offers, that are computed using stochastic techniques developed for our DSIC mechanism. We believe that our techniques will be useful for other stochastic optimization problems with concave objective functions.