An algorithmic characterization of multi-dimensional mechanisms

We obtain a characterization of feasible, Bayesian, multi-item multi-bidder mechanisms with independent, additive bidders as distributions over hierarchical mechanisms. Combined with cyclic-monotonicity our results provide a complete characterization of feasible, Bayesian Incentive Compatible mechanisms for this setting. Our characterization is enabled by a novel, constructive proof of Border’s theorem [5], and a new generalization of this theorem to independent (but not necessarily identically distributed) bidders, improving upon the results of [6, 12]. For a single item and independent (but not necessarily identically distributed) bidders, we show that any feasible reduced form auction can be implemented as a distribution over hierarchical mechanisms. We also give a polynomial-time algorithm for determining feasibility of a reduced form auction, or providing a separation hyperplane from the set of feasible reduced forms. To complete the picture, we provide polynomialtime algorithm...

• Type: Journal
• Year: 2012
• Where: STOC
• Authors: Yang Cai, Constantinos Daskalakis, S. Matthew Weinberg
• Keywords: Algorithms, Constructive Proof, Polynomial Time Algorithm, STOC 2012, Time Polynomial