As common and effective ways of selecting suppliers in procurement, auction and bargaining both have their supports in the current theory, from the perspective of the purchaser. By using the classical multidimensional auction model in and multidimensional asymmetric Nash bargaining model, to compare the expected revenue of auction with the earnings of bargaining, it is found that the boundary of the two mechanisms relates to the power of bargaining and the number of bidders. By dividing the interval of them, the boundary conditions of auction and bargaining and their respective appropriate ranges are also found.