Extreme Points and Majorization: Economic Applications
52 Pages Posted: 3 Apr 2020 Last revised: 6 Apr 2020
Date Written: March 12, 2020
We characterize the set of extreme points of monotone functions that are either majorized by a given function f or themselves majorize f. Any feasible element in a majorization set can be expressed as an integral with respect to a measure supported on the extreme points of that set. We show that these extreme points play a crucial rule in mechanism design, Bayesian persuasion, optimal delegation and many other models of decision making with expected and non-expected utility. Our main results show that each extreme point is uniquely characterized by a countable collection of intervals. Outside these intervals the extreme point equals the original function f and inside the function is constant. Further consistency conditions need to be satisfied pinning down the value of the extreme points in each interval where it is constant. Finally, we apply these insights to a varied set of economic problems.
Keywords: Majorization, Extreme Points, Bayesian Persuation, Border's Theorem
Suggested Citation: Suggested Citation