• Corpus ID: 251040207

Greedy Allocations and Equitable Matchings

  title={Greedy Allocations and Equitable Matchings},
  author={Quitz'e Valenzuela-Stookey},
I study multi-item allocation problems when agents have capacity constraints. I first provide an approximate extension to the multi-item setting of Border’s characterization of realizable interim allocations. I identify necessary conditions for interim realizability, and show that these conditions are sufficient for realizability when the interim allocation in question is scaled by 12 . I then characterize a subset of the realizable polytope which contains all such scaled allocations. This… 

Figures from this paper



Designing Random Allocation Mechanisms: Theory and Applications

Randomization is commonplace in everyday resource allocation. We generalize the theory of randomized assignment to accommodate multi-unit allocations and various real-world constraints, such as

A Constructive Approach to Reduced-Form Auctions with Applications to Multi-Item Mechanism Design

A constructive proof of Border's theorem and its generalization to reduced-form auctions with asymmetric bidders and polynomial-time algorithms for computing the revenue-optimal auction are provided.

A Geometric Approach to Mechanism Design

We develop a novel geometric approach to mechanism design using an important result in convex analysis: the duality between a closed convex set and its support function. By deriving the support

Generalized Reduced-Form Auctions: A Network-Flow Approach

We develop a network-flow approach for characterizing interim-allocation rules that can be implemented by ex post allocations. Our method can be used to characterize feasible interim allocations in

Public Projects, Boolean Functions, and the Borders of Border's Theorem

This paper identifies a complexity-theoretic barrier that indicates, assuming standard complexity class separations, that Border's theorem cannot be extended significantly beyond the state-of-the-art.

Matching "versus" mechanism design

The relationship and tradeoffs between these two approaches to mechanism design and applied matching are discussed.

Truthful Mechanisms for Matching and Clustering in an Ordinal World

The results are the first non-trivial truthful approximation algorithms for these problems, and indicate that in many situations, the can design robust algorithms even when the agents may lie and only provide ordinal information instead of precise utilities.

Optimal Auctions with Risk Averse Buyers

THIS PAPER STUDIES AUCTIONS designed to maximize the expected revenue of a seller facing risk averse bidders with unknown preferences.2 Although we concentrate on auctions where a seller sells a

Stable Matching in Large Economies

We study stability of two‐sided many‐to‐one matching in which firms' preferences for workers may exhibit complementarities. Although such preferences are known to jeopardize stability in a finite

Extreme Points and Majorization: Economic Applications

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