Extreme Points and Majorization: Economic Applications

Research Seminars

The paper presented in this Virtual Market Design Seminar characterizes the set of extreme points of monotonic functions that are either majorized by a given function f or themselves majorize f and show that these extreme points play a crucial role in many economic design problems. The 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 an extreme point in each interval where it is constant. Finally, the authors apply these insights to a varied set of economic problems: equivalence and optimality of mechanisms for auctions and (matching) contests, Bayesian persuasion, optimal delegation, and decision making under uncertainty.

The seminar series is jointly organized by ZEW, the University Paris 2 Panthéon-Assas, the Karlsruhe Institute of Technology (KIT), and the Universities of Bonn and Mannheim. Additional information on the Virtual MD Seminar Series.