Constrained Majorization: Applications in Mechanism Design

Abstract

Classical frameworks in mechanism design often specify an objective function and maximize it by choosing allocation. We extend these frameworks by studying mechanisms that maximize an objective function (such as expected revenue) subject to additional constraints (such as a lower bound constraint on efficiency). Building on the findings of Kleiner et al. (2021), the analysis considers mechanisms as extreme points of function spaces. The additional complexity arising due to each additional constraint manifests in the reduced form of the optimal mechanism as at most one jump discontinuity in an “ironed” interval. We apply our results to demonstrate the simplicity of optimal mechanisms in common economic applications such as contract and auction design. We also introduce a regularity condition on the distribution of valuations under which the general structure of optimal mechanisms bears no additional complexity due to the presence of a side constraint in these applications.

Keywords: Mechanism design, Majorization