Skip to main content

Lund University Publications

LUND UNIVERSITY LIBRARIES

Essays on Matching

Kratz, Jörgen LU (2018) In Lund Economic Studies
Abstract
This thesis makes a contribution to matching theory and mechanism design. It consists of four self-contained papers focusing on kidney exchange, object allocation and partnership formation.

The first paper, Pairwise Kidney Exchange over the Blood Group Barrier, investigates how the use of immunosuppressive drugs can be implemented within kidney exchange programs. Thanks to advances in medicine, immunosuppressive drugs can be used to enable some kidney transplants that were previously infeasible due to blood group incompatibilities. We introduce
a class of Pareto efficient matchings and provide a method for finding such matchings. We show that introducing immunosuppressive drugs would have a larger impact on the number of... (More)
This thesis makes a contribution to matching theory and mechanism design. It consists of four self-contained papers focusing on kidney exchange, object allocation and partnership formation.

The first paper, Pairwise Kidney Exchange over the Blood Group Barrier, investigates how the use of immunosuppressive drugs can be implemented within kidney exchange programs. Thanks to advances in medicine, immunosuppressive drugs can be used to enable some kidney transplants that were previously infeasible due to blood group incompatibilities. We introduce
a class of Pareto efficient matchings and provide a method for finding such matchings. We show that introducing immunosuppressive drugs would have a larger impact on the number of transplants than three-way exchanges and altruistic participation in a simulation study.

The second paper, Triage in Kidney Exchange, considers a problem where there is a planner in charge of designing a kidney exchange program. The planner sorts patients into “priority groups” based on how urgent their conditions are. I define a class of matchings that are Pareto efficient regardless of how patients are sorted into priority groups or how the planner chooses to design the kidney exchange program. Such matchings can be found using integer programming
and include a number of well studied subclasses of matchings as special cases.

The third paper, Overlapping Multiple Object Assignments, deals with an object allocation problem where agents are assigned bundles of objects. The assignments are allowed to overlap in the sense that multiple agents can be assigned the same object as long as the agents are “compatible”. This object allocation problem is closely related to zoning, where a city is divided into, e.g., industrial, commercial and residential districts. The main result shows that a rule assigning bundles of objects to agents is group-strategyproof, Pareto efficient and satisfies a third property called compatibility-monotonicity if and only if it belongs to a class of rules called compatibility-sorting sequential dictatorships.

The fourth paper, A Method for Finding the Maximal Set in Excess Demand, provides a slight amendment to a method used to find an equilibrium (whenever it exists) in the partnership formation problem. Using a computationally simple method for finding a particular set of agents, we show that an equilibrium payoff vector can be found in polynomial time. (Less)
Please use this url to cite or link to this publication:
author
supervisor
opponent
  • Associate Professor Rodríguez-Álvarez, Carmelo, Universidad Complutense de Madrid
organization
publishing date
type
Thesis
publication status
published
subject
in
Lund Economic Studies
issue
209
pages
176 pages
publisher
Media-Tryck, Lund University, Sweden
defense location
Holger Crafoord Centre EC3:210
defense date
2018-05-21 14:15:00
ISSN
0460-0029
ISBN
978-91-7753-640-6
978-91-7753-639-0
language
English
LU publication?
yes
id
fce69c5d-3658-4ec5-8442-91f9e18a0545
date added to LUP
2018-04-23 22:57:39
date last changed
2018-11-21 21:39:29
@phdthesis{fce69c5d-3658-4ec5-8442-91f9e18a0545,
  abstract     = {This thesis makes a contribution to matching theory and mechanism design. It consists of four self-contained papers focusing on kidney exchange, object allocation and partnership formation. <br/><br/>The first paper, Pairwise Kidney Exchange over the Blood Group Barrier, investigates how the use of immunosuppressive drugs can be implemented within kidney exchange programs. Thanks to advances in medicine, immunosuppressive drugs can be used to enable some kidney transplants that were previously infeasible due to blood group incompatibilities. We introduce<br/>a class of Pareto efficient matchings and provide a method for finding such matchings. We show that introducing immunosuppressive drugs would have a larger impact on the number of transplants than three-way exchanges and altruistic participation in a simulation study.<br/><br/>The second paper, Triage in Kidney Exchange, considers a problem where there is a planner in charge of designing a kidney exchange program. The planner sorts patients into “priority groups” based on how urgent their conditions are. I define a class of matchings that are Pareto efficient regardless of how patients are sorted into priority groups or how the planner chooses to design the kidney exchange program. Such matchings can be found using integer programming<br/>and include a number of well studied subclasses of matchings as special cases. <br/><br/>The third paper, Overlapping Multiple Object Assignments, deals with an object allocation problem where agents are assigned bundles of objects. The assignments are allowed to overlap in the sense that multiple agents can be assigned the same object as long as the agents are “compatible”. This object allocation problem is closely related to zoning, where a city is divided into, e.g., industrial, commercial and residential districts. The main result shows that a rule assigning bundles of objects to agents is group-strategyproof, Pareto efficient and satisfies a third property called compatibility-monotonicity if and only if it belongs to a class of rules called compatibility-sorting sequential dictatorships. <br/><br/>The fourth paper, A Method for Finding the Maximal Set in Excess Demand, provides a slight amendment to a method used to find an equilibrium (whenever it exists) in the partnership formation problem. Using a computationally simple method for finding a particular set of agents, we show that an equilibrium payoff vector can be found in polynomial time.},
  author       = {Kratz, Jörgen},
  isbn         = {978-91-7753-640-6},
  issn         = {0460-0029},
  language     = {eng},
  month        = {04},
  number       = {209},
  publisher    = {Media-Tryck, Lund University, Sweden},
  school       = {Lund University},
  series       = {Lund Economic Studies},
  title        = {Essays on Matching},
  year         = {2018},
}