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SUMMARY:The Economics of Convex Function Intervals
DTSTART;TZID=Europe/London:20260612T110000
DTEND;TZID=Europe/London:20260612T121500
DTSTAMP:20260512T062407Z
UID:09e0e299-6219-f111-8342-7c1e522d9057
CREATED:20260306T140242Z
DESCRIPTION:We introduce convex function intervals (CFIs): families of con
 vex functions satisfying given level and slope constraints. CFIs naturally
  arise as constraint sets in economic design\, including problems with typ
 e-dependent participation constraints and two-sided (weak) majorization co
 nstraints. Our main results include: (i) a geometric characterization of t
 he extreme points of CFIs\; (ii) sufficient optimality conditions for line
 ar programs over CFIs\; and (iii) methods for nested optimization on their
  lower level boundary that can be applied\, e.g.\, to the optimal design o
 f outside options. We apply these results to four settings: screening and 
 delegation problems with type-dependent outside options\, contest design w
 ith limited disposal\, and mean-based persuasion with informativeness cons
 traints. We draw several novel economic implications using our tools. For 
 instance\, we show that better outside options lead to larger delegation s
 ets\, and that posted price mechanisms can be suboptimal in the canonical 
 monopolistic screening problem with nontrivial\, type-dependent participat
 ion constraints.
LAST-MODIFIED:20260424T150612Z
LOCATION:Manor Road Building - Seminar Room G\, Seminar Room G Manor Road 
 Building Manor Road Oxford Oxfordshire OX1 3UQ United Kingdom
SPEAKER:Lina Uhe (University of Bonn)
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