The principal problem in algorithmic mechanism design is in merging the incentive constraints imposed by selfish behavior with the algorithmic constraints imposed by computational intractability. This field is motivated by the observation that the preeminent approach for designing incentive compatible mechanisms, namely that of Vickrey, Clarke, and Groves; and the central approach for circumventing computational obstacles, that of approximation algorithms, are fundamentally incompatible: natural applications of the VCG approach to an approximation algorithm fails to yield an incentive compatible mechanism. We consider relaxing the desideratum of (ex post) incentive compatibility (IC) to Bayesian incentive compatibility (BIC), where truthtelling is a Bayes-Nash equilibrium (the standard notion of incentive compatibility in economics). For welfare maximization in single-parameter agent settings, we give a general black-box reduction that turns any approximation algorithm into a Bayesian incentive compatible mechanism with essentially the same 1 approximation factor. In other words, for a large relevant class of problems and slight relaxation of the standard (in computer science) solution concept, we completely solve the central problem in algorithm mechanism design. 1 More specifically, we obtain an FPTAS: for any ǫ we take a β-approximation algorithm and give a BIC (1 + ǫ)β-approximation mechanism. This (1 + ǫ) factor arises from statistical methods that seem necessary for a black-box reduction.
REF and Hartline et al. [2011] provide a general approach, for both single-dimensional and multidimensional domains, for converting any approximation algorithm into a BIC mechanism with the same approximation guarantee on welfare.
Bayesian Algorithmic Mechanism Design
Computer Science