The Knightian Truthfulness of Classical Mechanisms

We study mechanisms where a player’s strategy is one of his possible (payoff) types and at least one player is Knightian, that is, cannot distinguish which element of a “candidate set” with multiple types is his true type. We call such a mechanism Knightian truthful if, in all its rational plays, every player reports his own true type, if he knows it exactly, and a type in his candidate set, if he is Knightian. We argue that Knightian truthfulness is a very desirable property. In particular, it is crucial for guaranteeing social welfare in auctions. We analyze two celebrated mechanisms, the Vickrey mechanism and the general VCG, and prove that the first is Knightian truthful, but not the second. This difference is reflected in their social welfare performance in the presence of Knightian players. We prove that the Vickrey mechanism always guarantees a very high fraction of the maximum possible social welfare in multi-unit auctions, but that in unrestricted multi-good auctions the general VCG only guarantees an abysmally low fraction of the maximum possible social welfare.