While I wholeheartedly agree with TheSaint321's answer, here is a different take on the question. We could think of a Becker DeGroot Marschak mechanism as a 1 player 2nd price auction. That is, say we want the player to truthfully reveal her value, $v$, of an object. We know the value is between 0 and 10. We could her to report her value $\hat v$, then randomly draw a number, $x$ from a continuous distribution between 0 and 10. If $x > \hat v$, she gets gets nothing. If her $\hat v \geq x$, she gets the object and pays a cost $x$.
It is pretty easy to show that this is strategically equivalent to a 2nd price auction with 2 players where the 2nd player has a valuation according to the induced distribution. For this reason, it is incentive compatible for the (single, real) player to report her true value. Note however, that is is not an efficient auction, since the player with the highest bid (trivially the only player) does not always get the object.