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  • All HBS Web  (855)
    • News  (79)
    • Research  (639)
    • Events  (14)
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Show Results For

  • All HBS Web  (855)
    • News  (79)
    • Research  (639)
    • Events  (14)
    • Multimedia  (4)
  • Faculty Publications  (632)
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  • Article

Matching in Networks with Bilateral Contracts: Corrigendum

By: John William Hatfield, Ravi Jagadeesan and Scott Duke Kominers
Hatfield and Kominers (2012) introduced a model of matching in networks with bilateral contracts and showed that stable outcomes exist in supply chains when firms' preferences over contracts are fully substitutable. Hatfield and Kominers (2012) also asserted that in... View Details
Keywords: Matching With Contracts; Substitutability; Mathematical Methods
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Hatfield, John William, Ravi Jagadeesan, and Scott Duke Kominers. "Matching in Networks with Bilateral Contracts: Corrigendum." American Economic Journal: Microeconomics 12, no. 3 (August 2020): 277–285.
  • 1981
  • Chapter

A Degeneracy Exploiting LU Factorization for the Simplex Method

By: André Perold
Keywords: Mathematical Methods
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Perold, André. "A Degeneracy Exploiting LU Factorization for the Simplex Method." In Large Scale Linear Programming, edited by G. B. Dantzig, M. A. H. Dempster, and Markku Kallio. Laxenburg, Austria: International Institute for Applied Systems Analysis (IIASA), 1981.
  • 2015
  • Working Paper

Configurations of Extremal Type II Codes

By: Noam D. Elkies and Scott Duke Kominers
We prove configuration results for extremal Type II codes, analogous to the configuration results of Ozeki and of the second author for extremal Type II lattices. Specifically, we show that for n∈{8,24,32,48,56,72,96} every extremal Type II code of length n is... View Details
Keywords: Mathematical Methods
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Elkies, Noam D., and Scott Duke Kominers. "Configurations of Extremal Type II Codes." Working Paper, March 2015.
  • February 1991 (Revised February 1993)
  • Background Note

Regression Analysis

By: David E. Bell
Provides a relatively simple introduction to multivariate regression analysis. View Details
Keywords: Mathematical Methods
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Bell, David E. "Regression Analysis." Harvard Business School Background Note 191-117, February 1991. (Revised February 1993.)
  • Article

Configurations of Rank-40r Extremal Even Unimodular Lattices (r=1,2,3)

By: Scott Duke Kominers and Zachary Abel
We show that if L is an extremal even unimodular lattice of rank 40r with r=1,2,3 then L is generated by its vectors of norms 4r and 4r+2. Our result is an extension of Ozeki's result for the case r=1. View Details
Keywords: Mathematical Methods
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Kominers, Scott Duke, and Zachary Abel. "Configurations of Rank-40r Extremal Even Unimodular Lattices (r=1,2,3)." Journal de Théorie des Nombres de Bordeaux 20, no. 2 (2008): 365–371.
  • August 2005 (Revised April 2008)
  • Teaching Note

Store24 (B): Statistics Review with Data Desk (TN)

By: Frances X. Frei
Presents an overview of the statistical analysis covered in the case discussion. View Details
Keywords: Mathematical Methods; Retail Industry
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Frei, Frances X. "Store24 (B): Statistics Review with Data Desk (TN)." Harvard Business School Teaching Note 606-037, August 2005. (Revised April 2008.)
  • fall 1992
  • Article

Exploring the Limits of the Technology S-curve, Part 1: Component Technologies

By: Clayton M. Christensen
Keywords: Technology; Mathematical Methods
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Christensen, Clayton M. "Exploring the Limits of the Technology S-curve, Part 1: Component Technologies." Production and Operations Management 1 (fall 1992): 334–357.
  • 20 Mar 2001 - 21 Mar 2001
  • Conference Presentation

QAP: The Quadratic Assignment Procedure

By: William B. Simpson
Keywords: Mathematical Methods
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Simpson, William B. "QAP: The Quadratic Assignment Procedure." Paper presented at the North American Stata Users' Group Meeting, March 20–21, 2001.
  • 2002
  • Case

Qualitative Response Models: Ordinal and Multinomial Models

By: William B. Simpson
Keywords: Mathematical Methods
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Simpson, William B. "Qualitative Response Models: Ordinal and Multinomial Models." 2002. Electronic.
  • 1979
  • Dissertation

Inference in Partially Identified Models

By: Dutch Leonard
Keywords: Mathematical Methods
Citation
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Leonard, Dutch. "Inference in Partially Identified Models." Diss., Harvard University, 1979.
  • Article

Who Will Vote Quadratically? Voter Turnout and Votes Cast Under Quadratic Voting

By: Louis Kaplow and Scott Duke Kominers
Who will vote quadratically in large-N elections under quadratic voting (QV)? First, who will vote? Although the core QV literature assumes that everyone votes, turnout is endogenous. Drawing on other work, we consider the representativeness of endogenously... View Details
Keywords: Voting Turnout; Paradox Of Voting; Quadratic Voting; Pivotality; Elections; Voting; Political Elections; Mathematical Methods
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Kaplow, Louis, and Scott Duke Kominers. "Who Will Vote Quadratically? Voter Turnout and Votes Cast Under Quadratic Voting." Special Issue on Quadratic Voting and the Public Good. Public Choice 172, nos. 1-2 (July 2017): 125–149.
  • May 2000
  • Article

Maxmin Expected Utility over Savage Acts with a Set of Priors

By: Ramon Casadesus-Masanell, Peter Klibanoff and Emre Ozdenoren
This paper provides an axiomatic foundation for a maxmin expected utility over a set of priors (MMEU) decision rule in an environment where the elements of choice are Savage acts. This characterization complements the original axiomatizations of MMEU developed in a... View Details
Keywords: Uncertainty Aversion; Ambiguity; Expected Utility; Set Of Priors; Knightian Uncertainty; Decision Making; Game Theory; Risk and Uncertainty; Mathematical Methods
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Casadesus-Masanell, Ramon, Peter Klibanoff, and Emre Ozdenoren. "Maxmin Expected Utility over Savage Acts with a Set of Priors." Journal of Economic Theory 92, no. 1 (May 2000): 35–65.
  • September 2025
  • Article

Using Satellites and Phones to Evaluate and Promote Agricultural Technology Adoption: Evidence from Smallholder Farms in India

By: Shawn Cole, Tomoko Harigaya, Grady Killeen and Aparna Krishna
This paper evaluates a low-cost, customized soil nutrient management advisory service in India. As a methodological contribution, we examine whether and in which settings satellite measurements may be effective at estimating both agricultural yields and treatment... View Details
Keywords: Measurement and Metrics; Mathematical Methods; Analytics and Data Science; Agriculture and Agribusiness Industry; India
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Cole, Shawn, Tomoko Harigaya, Grady Killeen, and Aparna Krishna. "Using Satellites and Phones to Evaluate and Promote Agricultural Technology Adoption: Evidence from Smallholder Farms in India." Journal of Development Economics 176 (September 2025).
  • 2024
  • Working Paper

What Is Newsworthy? Theory and Evidence

By: Luis Armona, Matthew Gentzkow, Emir Kamenica and Jesse M. Shapiro
We study newsworthiness in theory and practice. We focus on situations in which a news outlet observes the realization of a state of the world and must decide whether to report the realization to a consumer who pays an opportunity cost to consume the report. The... View Details
Keywords: News; Mathematical Methods; Prejudice and Bias; Media and Broadcasting Industry
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Armona, Luis, Matthew Gentzkow, Emir Kamenica, and Jesse M. Shapiro. "What Is Newsworthy? Theory and Evidence." NBER Working Paper Series, No. 32512, May 2024.
  • August 2022
  • Article

Contract Duration and the Costs of Market Transactions

By: Alexander MacKay
The optimal duration of a supply contract balances the costs of reselecting a supplier against the costs of being matched to an inefficient supplier when the contract lasts too long. I develop a structural model of contract duration that captures this tradeoff and... View Details
Keywords: Supply Contracts; Intermediate Goods; Switching Costs; Vertical Relationships; Transaction Costs; Contract Duration; Identification; Supply Chain; Cost; Contracts; Auctions; Mathematical Methods
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MacKay, Alexander. "Contract Duration and the Costs of Market Transactions." American Economic Journal: Microeconomics 14, no. 3 (August 2022): 164–212.
  • 2012
  • Chapter

Knowledge-based Innovation: Emergence and Embedding of New Practice Areas in Management Consulting Firms

By: Heidi K. Gardner, N. Anand and Tim Morris
How do innovative knowledge-based structures emerge and become embedded in organizations? We drew on theories of knowledge-intensive firms, communities of practice, and professional service firms to analyze multiple cases of new practice area creation in management... View Details
Keywords: Competency and Skills; Innovation and Invention; Knowledge; Organizations; Practice; Mathematical Methods; Consulting Industry
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Gardner, Heidi K., N. Anand, and Tim Morris. "Knowledge-based Innovation: Emergence and Embedding of New Practice Areas in Management Consulting Firms." In Management Consulting, edited by Stephanos Avakian and Timothy Clark. Cheltenham: Edward Elgar Publishing, 2012.
  • 2009
  • Working Paper

Smith and Rawls Share a Room: Stability and Medians

By: Bettina-Elisabeth Klaus and Flip Klijn
We consider one-to-one, one-sided matching (roommate) problems in which agents can either be matched as pairs or remain single. We introduce a so-called bi-choice graph for each pair of stable matchings and characterize its structure. Exploiting this structure we... View Details
Keywords: Fairness; One-Sided Platforms; Two-Sided Platforms; Marketplace Matching; Mathematical Methods; Balance and Stability
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Klaus, Bettina-Elisabeth, and Flip Klijn. "Smith and Rawls Share a Room: Stability and Medians." Harvard Business School Working Paper, No. 09-111, March 2009.
  • 2008
  • Chapter

Matching and Market Design

By: Muriel Niederle, Alvin E. Roth and Tayfun Sonmez
Matching is the part of economics concerned with who transacts with whom and how. Models of matching, starting with the Gale-Shapley deferred acceptance algorithm, have been particularly useful in studying labour markets and in helping design clearinghouses to fix... View Details
Keywords: Market Design; Marketplace Matching; Outcome or Result; Mathematical Methods
Citation
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Niederle, Muriel, Alvin E. Roth, and Tayfun Sonmez. "Matching and Market Design." In The New Palgrave Dictionary of Economics. 2nd ed. Edited by Steven Derlauf and Larry Blume. Hampshire, U.K.: Palgrave Macmillan, 2008.
  • January 2003 (Revised February 2011)
  • Tool

Business Analysis and Valuation Model (Version 5)

By: Paul M. Healy, Krishna G. Palepu and Jonathan Barnett
Once you enter company financial statements, this software enables you to standardize them to a common format, make any needed adjustments to the company's accounting, and make assumptions about the company's future performance. The model then provides financial ratios... View Details
Keywords: Financial Statements; Standards; Mathematical Methods; Valuation
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"Business Analysis and Valuation Model (Version 5)." Harvard Business School Tool 103-701, January 2003. (Revised February 2011.)
  • Article

The Shapley Value as a von Neumann-Morgenstern Utility

By: A. E. Roth
Keywords: Value; Mathematical Methods
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Roth, A. E. "The Shapley Value as a von Neumann-Morgenstern Utility." Econometrica 45, no. 3 (April 1977): 657–664.
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