  We present different versions of a conjecture which would express that first
price mechanisms never work very badly in a very general class of problems. The
definitions include most of the problems where there is a principal (seller)
who has the right to exclude others from the game. The exact definitions are
motivated by the "first price mechanism" in E Cs: "Efficient Teamwork", but the
conjecture is relevant for most auction problems, e.g. for combinatorial
auctions.
