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- Article
Multilateral Matching
By: John William Hatfield and Scott Duke Kominers
We introduce a matching model in which agents engage in joint ventures via multilateral contracts. This approach allows us to consider production complementarities previously outside the scope of matching theory. We show analogues of the first and second welfare... View Details
Keywords: Matching; Stability; Competitive Equilibrium; Core; Networks; Competition; Joint Ventures; Balance and Stability; Groups and Teams; Entrepreneurship
Hatfield, John William, and Scott Duke Kominers. "Multilateral Matching." Journal of Economic Theory 156 (March 2015): 175–206.
- January 2017
- Article
Contract Design and Stability in Many-to-Many Matching
By: John William Hatfield and Scott Duke Kominers
We develop a model of many-to-many matching with contracts that subsumes as special cases many-to-many matching markets and buyer/seller markets with heterogeneous and indivisible goods. In our setting, substitutable preferences are sufficient to guarantee the... View Details
Keywords: Many-to-Many Matching; Stability; Substitutes; Contract Design; Contracts; Marketplace Matching; Balance and Stability
Hatfield, John William, and Scott Duke Kominers. "Contract Design and Stability in Many-to-Many Matching." Games and Economic Behavior 101 (January 2017): 78–97.
- May 2016
- Article
Matching with Slot-Specific Priorities: Theory
By: Scott Duke Kominers and Tayfun Sönmez
We introduce a two-sided, many-to-one matching with contracts model in which agents with unit demand match to branches that may have multiple slots available to accept contracts. Each slot has its own linear priority order over contracts; a branch chooses contracts by... View Details
Keywords: Matching With Contracts; Stability; Strategy-proofness; School Choice; Affirmative Action; Airline Seat Upgrades; Contracts; Market Design; Marketplace Matching; Balance and Stability
Kominers, Scott Duke, and Tayfun Sönmez. "Matching with Slot-Specific Priorities: Theory." Theoretical Economics 11, no. 2 (May 2016): 683–710.
- Article
On the Correspondence of Contracts to Salaries in (Many-to-Many) Matching
In this note, I extend the work of Echenique (2012) to show that a model of many-to-many matching with contracts may be embedded into a model of many-to-many matching with wage bargaining whenever (1) all agentsʼ preferences are substitutable and (2) the matching with... View Details
Keywords: Many-to-Many Matching; Stability; Substitutes; Contract Design; Unitarity; Market Design; Contracts; Marketplace Matching; Balance and Stability; Economics
Kominers, Scott Duke. "On the Correspondence of Contracts to Salaries in (Many-to-Many) Matching." Games and Economic Behavior 75, no. 2 (July 2012): 984–989.
- March 2010
- Article
Matching with Preferences over Colleagues Solves Classical Matching
In this note, we demonstrate that the problem of "many-to-one matching with (strict) preferences over colleagues" is actually more difficult than the classical many-to-one matching problem, "matching without preferences over colleagues." We give an explicit reduction... View Details
Kominers, Scott Duke. "Matching with Preferences over Colleagues Solves Classical Matching." Games and Economic Behavior 68, no. 2 (March 2010): 773–780.
- Article
Analyzing Scrip Systems
By: Kris Johnson, David Simchi-Levi and Peng Sun
Scrip systems provide a nonmonetary trade economy for exchange of resources. We model a scrip system as a stochastic game and study system design issues on selection rules to match potential trade partners over time. We show the optimality of one particular rule in... View Details
Keywords: ＂Repeated Games＂; Stochastic Trust Game; Dynamic Program; P2P Lending; Scrip Systems; Artificial Currency; Non-monetary Trade Economies; Marketplace Matching; Currency; Operations; Game Theory
Johnson, Kris, David Simchi-Levi, and Peng Sun. "Analyzing Scrip Systems." Operations Research 62, no. 3 (May–June 2014): 524–534.
- 2008
- Working Paper
Stable Many-to-Many Matchings with Contracts
By: Bettina-Elisabeth Klaus and Markus Walzl
We consider several notions of setwise stability for many-to-many matching markets with contracts and provide an analysis of the relations between the resulting sets of stable allocations for general, substitutable, and strongly substitutable preferences. Apart from... View Details
Klaus, Bettina-Elisabeth, and Markus Walzl. "Stable Many-to-Many Matchings with Contracts." Harvard Business School Working Paper, No. 09-046, September 2008.
- 22 May 2007
- Working Paper Summaries
Strategy-Proofness versus Efficiency in Matching with Indifferences: Redesigning the NYC High School Match
- 2021
- Working Paper
Deep Learning for Two-Sided Matching
By: Sai Srivatsa Ravindranatha, Zhe Feng, Shira Li, Jonathan Ma, Scott Duke Kominers and David Parkes
We initiate the use of a multi-layer neural network to model two-sided matching and to explore the design space between strategy-proofness and stability. It is well known that both properties cannot be achieved simultaneously but the efficient frontier in this design... View Details
Keywords: Strategy-proofness; Deep Learning; Two-Sided Platforms; Marketplace Matching; Balance and Stability
Srivatsa Ravindranatha, Sai, Zhe Feng, Shira Li, Jonathan Ma, Scott Duke Kominers, and David Parkes. "Deep Learning for Two-Sided Matching." Working Paper, July 2021.
- December 2009
- Article
Strategy-proofness versus Efficiency in Matching with Indifferences: Redesigning the NYC High School Match
By: Atila Abdulkadiroglu, Parag A. Pathak and Alvin E. Roth
The design of the New York City (NYC) High School match involved tradeoffs among efficiency, stability, and strategy-proofness that raise new theoretical questions. We analyze a model with indifferences—ties—in school preferences. Simulations with field data and the... View Details
Keywords: Decision Choices and Conditions; Secondary Education; Marketplace Matching; Performance Efficiency; Mathematical Methods; Motivation and Incentives; Strategy; Balance and Stability
Abdulkadiroglu, Atila, Parag A. Pathak, and Alvin E. Roth. "Strategy-proofness versus Efficiency in Matching with Indifferences: Redesigning the NYC High School Match." American Economic Review 99, no. 5 (December 2009). (AER links to access the Appendix and Downloadable Data Set.)
- May 2017
- Article
Stable and Strategy-Proof Matching with Flexible Allotments
By: John William Hatfield, Scott Duke Kominers and Alexander Westkamp
We introduce a framework of matching with flexible allotments that can be used to model firms with cross-division hiring restrictions. Our framework also allows us to nest some prior models of matching with distributional constraints. Building upon our recent work on... View Details
Hatfield, John William, Scott Duke Kominers, and Alexander Westkamp. "Stable and Strategy-Proof Matching with Flexible Allotments." American Economic Review 107, no. 5 (May 2017): 214–219.
- 01 Dec 2020
- News
Finding The Right Patient-Provider Match
—GRAHAM GARDNER (MBA 2007) “We don’t define what is right for the patients. Our job is to get the data to help you find the best match for you.” —GRAHAM GARDNER (MBA 2007) “I saw that major health systems... View Details
Keywords: Susan Young
- 2008
- Working Paper
Stability and Nash Implementation in Matching Markets with Couples
By: Claus-Jochen Haake and Bettina-Elisabeth Klaus
We consider two-sided matching markets with couples. First, we extend a result by Klaus and Klijn (2005, Theorem 3.3) and show that for any weakly responsive couples market there always exists a "double stable" matching, i.e., a matching that is stable for the couples... View Details
Haake, Claus-Jochen, and Bettina-Elisabeth Klaus. "Stability and Nash Implementation in Matching Markets with Couples." Harvard Business School Working Paper, No. 09-017, August 2008.
- 2013
- Article
Matching with Couples: Stability and Incentives in Large Markets
By: Fuhito Kojima, Parag A. Pathak and Alvin E. Roth
Accommodating couples has been a long-standing issue in the design of centralized labor market clearinghouses for doctors and psychologists, because couples view pairs of jobs as complements. A stable matching may not exist when couples are present. This article's main... View Details
Keywords: Market Design; Marketplace Matching; Balance and Stability; Jobs and Positions; Family and Family Relationships; Health Care and Treatment; Employment Industry; Health Industry
Kojima, Fuhito, Parag A. Pathak, and Alvin E. Roth. "Matching with Couples: Stability and Incentives in Large Markets." Quarterly Journal of Economics 128, no. 4 (November 2013): 1585–1632.
- 16 Nov 2010
- Lessons from the Classroom
Data.gov: Matching Government Data with Rapid Innovation
participants wondered what the endeavor interrupted in local agencies as it began to fulfill its mandate of gathering data. "I don't believe there were no ripple effects," said one executive. Public trust and consistency of data architecture: Does government... View Details
- May 1997
- Teaching Note
Module Overview: Coordinating and Managing Supply Chains: Matching Supply and Demand TN
By: Ananth Raman
Prepares students to configure operating and distribution systems to provide product (or service) supply to match customer demand. Begins by introducing students to the supply-demand mismatch problem, documenting its significance in many companies, and suggesting ways... View Details
- 2014
- Working Paper
Hidden Substitutes
By: John William Hatfield and Scott Duke Kominers
In this paper, we show that preferences exhibiting some forms of complementarity
in fact have an underlying substitutable structure. Specifically, we show that some
preferences that are not substitutable in the setting of many-to-one matching with
contracts become... View Details
Keywords: Many-to-One Matching; Many-to-Many Matching; Stability; Substitutes; Matching With Contracts; Slot-Specific Priorities; Sherlock; Market Design; Contracts; Marketplace Matching; Balance and Stability
Hatfield, John William, and Scott Duke Kominers. "Hidden Substitutes." Working Paper, September 2014.
- November 2019
- Other Article
Corrigendum to "Multilateral Matching"
By: Keisuke Bando, Toshiyuki Hirai, John William Hatfield and Scott Duke Kominers
We identify an error in the claim by Hatfield and Kominers (2015) that every stable outcome in the setting of multilateral matching with contracts is efficient. We then show that the result can be recovered under a suitable differentiability condition. View Details
Keywords: Matching; Stability; Competitive Equilibrium; Networks; Joint Ventures; Balance and Stability
Bando, Keisuke, Toshiyuki Hirai, John William Hatfield, and Scott Duke Kominers. Corrigendum to "Multilateral Matching". Art. 104933. Journal of Economic Theory 184 (November 2019).
- 09 Oct 2019
- News