Extreme Points and Majorization: Economic Applications

We characterize the set of extreme points monotonic functions that are either majorized by a given function f or themselves majorize and show these play crucial role in many economic design problems. Our main results each point is uniquely characterized countable collection intervals. Outside intervals equals original inside constant. Further consistency conditions need to be satisfied pinning down value an interval where it apply insights varied problems: equivalence optimality mechanisms for auctions (matching) contests, Bayesian persuasion, optimal delegation, decision making under uncertainty.