  We develop a novel framework to construct and analyze finite valued,
multidimensional mechanisms using tropical convex geometry. We geometrically
characterize incentive compatibility using cells in the tropical convex hull of
the type set. These cells are the sets of incentive compatible payments and
form tropical simplices, spanned by generating payments whose number equals the
dimension of the simplex. The analysis of the collection of incentive
compatible mechanisms via tropical simplices and their generating payments
facilitates the use of geometric techniques. We use this view to derive a new
geometric characterization of revenue equivalence but also show how to handle
multidimensional mechanisms in the absence of revenue equivalence.
