Auctions without Common Knowledge

This paper proves that the revenue equivalence theorem ceases to hold for auctions without common knowledge about the agents' prior beliefs. That is, different auction forms yield different expected revenue. To prove this, an auction game is converted to a Bayesian decision problem with an infinite hierarchy of beliefs. A general solution for such Bayesian decision problems is proposed. The solution is a generalization of the standard Bayesian solution and coincides with it for finite belief trees and for trees representing common knowledge. It is shown how the solution generalizes the frequently used technique of backward induction for infinite belief trees. The solution can be applied to any game with infinite belief trees. Computation of the solution does not rely on approximating the infinite trees with finite ones. The method can be used, for example, to analyze the expected revenue of alternative auction forms. ... Read complete abstract on page 2.