Extreme Points and Majorization: Economic Applications

Kleiner, Andreas; Moldovanu, Benny; Strack, Philipp

doi:10.2139/ssrn.3551258

Cited by 29 publications

(45 citation statements)

References 31 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The form of the solution is consistent with the recent findings of Kleiner et al (2020) who derive general properties of extreme points that emerge as solutions to problems of the form considered in the lemma. The maximization problem in Lemma 2 can also be seen analogous to a Bayesian persuasion problem in which the designer's preferences over posterior beliefs depend only on the posterior mean (see Kolotilin, 2018, andMartini, 2019) with a key difference: The MPS condition is flipped, requiring the solution Φ to be a meanpreserving spread (rather than a mean-preserving contraction) of the prior Φ 0 .…”

supporting

confidence: 87%

Redistributive Allocation Mechanisms

Akbarpour

Dworczak²,

Kominers

2020

SSRN Journal

View full text Add to dashboard Cite

Many scarce public resources are allocated below market-clearing prices (and sometimes for free). Such "non-market" mechanisms necessarily sacrifice some surplus, yet they can potentially improve equity by increasing the rents enjoyed by agents with low willingness to pay. In this paper, we develop a model of mechanism design with redistributive concerns. Agents are characterized by a privately observed willingness to pay for quality, and a publicly observed label. A market designer controls allocation and pricing of a set of objects of heterogeneous quality, and maximizes a linear combination of revenue and total surplus| with Pareto weights that depend both on observed and unobserved agent characteristics. We derive structural insights about the form of the optimal mechanism and describe how social preferences influence the use of non-market mechanisms.

show abstract

supporting

confidence: 87%

Redistributive Allocation Mechanisms

Akbarpour

Dworczak²,

Kominers

2020

SSRN Journal

View full text Add to dashboard Cite

show abstract

“…11 In the Supplemental Material (Kleiner, Moldovanu, and Strack (2021)), we also briefly discuss applications to decision making under uncertainty. …”

mentioning

confidence: 99%

Extreme Points and Majorization: Economic Applications

Kleiner

Moldovanu

Strack

2021

ECTA

Self Cite

View full text Add to dashboard Cite

We characterize the set of extreme points of monotonic functions that are either majorized by a given function f or themselves majorize f and show that these extreme points play a crucial role in many economic design problems. Our main results show that each extreme point is uniquely characterized by a countable collection of intervals. Outside these intervals the extreme point equals the original function f and inside the function is constant. Further consistency conditions need to be satisfied pinning down the value of an extreme point in each interval where it is constant. We apply these insights to a varied set of economic problems: equivalence and optimality of mechanisms for auctions and (matching) contests, Bayesian persuasion, optimal delegation, and decision making under uncertainty.

show abstract

“…Kolotilin and Zapechelnyuk (2018) establish an equivalence result between Bayesian persuasion and delegation and show how the former can be used to improve upon results on the latter. Kleiner et al (2020) explain how the same mathematical technique can be applied to several different economic problems, including auction and contest design, Bayesian persuasion, delegation, and decision making under uncertainty.…”

mentioning

confidence: 99%