The Extreme Points of Mean-Preserving Contractions

Andreas Kleiner (), Benny Moldovanu (), Philipp Strack () and Mark Whitmeyer ()

CRC TR 224 Discussion Paper Series from University of Bonn and University of Mannheim, Germany

Abstract: We study multidimensional mean-preserving contractions (MPC) and their ex treme points. Proposition 1 focuses on extreme MPCs of a measure µ: each finitely supported extreme MPC ν induces a partition of X, the domain of µ, into convex sets such that the support of ν on each element of the partition is an affinely indepen dent set, and such that the restriction of ν on each element of the partition is itself an MPC of the restriction of the prior µ on that element. We apply our results to several questions concerning moment persuasion and categorization. In particular, we prove that categories and prototypes (key elements typically assumed to be exogenous in the classical literature on categorization) can endogenously emerge as outcomes of optimization when the decision maker faces limits on the amount of information that she can either acquire or process.

Keywords: mean-preserving contractions; convex order; extreme points; Bayesian per suasion; information design; categorization (search for similar items in EconPapers)
JEL-codes: C02 D82 D83 (search for similar items in EconPapers)
Pages: 36
Date: 2026-09
New Economics Papers: this item is included in nep-des
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