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DTSTAMP:20260909T022646Z
DESCRIPTION:\n	\n		Title: The monopolist's free boundary problem in the plane:
  an excursion into the economic value of private information\n\n		Abstract: 
 The principal-agent problem is an important paradigm in economic theory fo
 r studying the value of private information: the nonlinear pricing problem
  faced by a monopolist is one example\; others include optimal taxation an
 d auction design. For multidimensional spaces of consumers (i.e. agents) a
 nd products\, Rochet and Chone (1998) reformulated this problem as a conca
 ve maximization over the set of convex functions\, by assuming agent prefe
 rences are bilinear in the product and agent parameters. This optimization
  corresponds mathematically to a convexity-constrained obstacle problem. T
 he solution is divided into multiple regions\, according to the rank of th
 e Hessian of the optimizer. Apart from four possible pathologies\, if the 
 monopolists costs grow quadratically with the product type we show that a 
 smooth free boundary delineates the region where it becomes efficient to c
 ustomize products for individual buyers. We give the first complete soluti
 on of the problem on square domains\, and discover new transitions from un
 bunched to targeted and from targeted to blunt bunching as market conditio
 ns become more and more favorable to the seller. Based on work such as htt
 ps://arxiv.org/abs/2412.15505 with Cale Rankin (Monash and University of N
 ew South Wales at Canberra)\, Kelvin Shuangjian Zhang (Fudan University)\,
  and more recently Lucas O'Brien (MIT).\n\n		Université de Montréal\n			CRM\n			Pa
 villon André-Aisenstadt\, 6th floor\, room 6214\n	\n\n
DTSTART:20260320T193000Z
DTEND:20260320T203000Z
SUMMARY:2026 CRM-Fields-PIMS Prize lecture – Robert McCann
URL:https://www.mcgill.ca/mathstat/channels/event/2026-crm-fields-pims-priz
 e-lecture-robert-mccann-371101
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