According to this paper, "every submodular function can be represented as a maximum of additive valuations." It gives an algebraic description as well, but I'm having trouble seeing the high level idea.
Is there a simple geometric intuition for this fact? Is there an obvious economic application to explain why valuations susceptible to diminishing marginal utility relate to valuations with constant marginal utility? Or is this similar to the main idea of Fourier Series, in that you can build one type of function out of another, in a way that is not at all a priori obvious?
Is there a simple geometric intuition for this fact? Is there an obvious economic application to explain why valuations susceptible to diminishing marginal utility relate to valuations with constant marginal utility? Or is this similar to the main idea of Fourier Series, in that you can build one type of function out of another, in a way that is not at all a priori obvious?