We investigate the algorithmic performance of Vickrey-Clarke-Groves mechanisms in the single item case. We provide a formal definition of a Vickrey algorithm for this framework, and give a number of examples of Vickrey algorithms. We consider three performance criteria, one corresponding to a Pareto criterion, one corresponding to worst case analysis, and a third criterion related to first-order stochastic dominance. We show that Pareto optimal Vickrey algorithms do not exist and that worst case analysis is of no use in discriminating between Vickrey algorithms. For the case of two bidders, we show the bisection auction to be optimal according to the third criterion. The bisection auction i
