Extreme Points and Majorization: Economic Applications

52 Pages Posted: 3 Apr 2020 Last revised: 6 Apr 2020

See all articles by Andreas Kleiner

Andreas Kleiner

Arizona State University (ASU)

Benny Moldovanu

University of Bonn - Chair of Economic Theory II; Centre for Economic Policy Research (CEPR)

Philipp Strack

Yale, Department of Economics

Date Written: March 12, 2020

Abstract

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

Kleiner, Andreas and Moldovanu, Benny and Strack, Philipp, Extreme Points and Majorization: Economic Applications (March 12, 2020). Available at SSRN: https://ssrn.com/abstract=3551258 or http://dx.doi.org/10.2139/ssrn.3551258

Andreas Kleiner

Arizona State University (ASU) ( email )

Farmer Building 440G PO Box 872011
Tempe, AZ 85287
United States

Benny Moldovanu

University of Bonn - Chair of Economic Theory II ( email )

Lennestrasse 37
53113 Bonn
Germany
+49 228 736395 (Phone)
+49 228 737940 (Fax)

Centre for Economic Policy Research (CEPR)

London
United Kingdom

Philipp Strack (Contact Author)

Yale, Department of Economics ( email )

28 Hillhouse Ave
New Haven, CT 06520-8268
United States

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