2011/08/18 by Brendan Pass, Pass, Brendan
Decision Sciences · Economics, Econometrics and Finance · Mathematics · #49N30 #90C25 #91B24 #Analysis of PDEs (math.AP) #Auction Theory and Applications #Economic theories and models #FOS: Mathematics #Game Theory and Applications #Game Theory and Voting Systems #Optimization and Control (math.OC) #math.AP #math.OC #msc:49N30 #msc:90C25 #msc:91B24
paper · pdf · doi:10.48550/arxiv.1108.3798
arxiv created 2011/08/18 · openalex publication_date 2011/08/18 · arxiv updated 2011/08/19 · openalex created_date 2022/10/05 · openalex updated_date 2026/07/28
We study the principal-agent problem. We show that b-convexity of the space of products, a condition which appears in a recent paper by Figalli, Kim and McCann \citefkm, is necessary to formulate the problem as a maximization over a convex set. We then show that when the dimension m of the space of types is larger than the dimension n of the space of products, this condition implies that the extra dimensions do not encode independent economic information. When m is smaller than n, we show that under b-convexity of the space of products, it is always optimal for the principal to offer goods only from a certain prescribed subset. We show that this is equivalent to offering an m-dimensional space of goods.