Publications

September 2010 (Revised January 2012)
Case

OPOWER: Increasing Energy Efficiency through Normative Influence (A)

By: Amy J.C. Cuddy, Kyle Todd Doherty and Maarten W. Bos

The case profiles OPOWER, an energy efficiency software company that applies Cialdini's principles of social influence to successfully encourage consumers to reduce their energy usage. OPOWER was co-founded in 2008 by two young Harvard graduates, Dan Yates and Alex... View Details

Keywords: Mathematical Methods; Applications and Software; Attitudes; Entrepreneurship; Energy Conservation; Power and Influence; Growth and Development Strategy; Energy Industry; United States

16 Dec 2021
Blog Post

African American Student Union Spotlight on STEM

as a STEM student, and how did you overcome it? I don't come from a finance background, and it often shows when I'm going through cases or engaging in the classroom. The jargon and concepts are new, but I find solace in breaking things down to fundamental View Details

04 Feb 2010
What Do You Think?

What’s the Best Way to Make Careful Decisions?

for a more careful approach, suggesting that we place too much emphasis on intuition and personal experience as opposed to the "wisdom of crowds," mathematical models, and systematically-collected data. He argues that... View Details

Keywords: by James Heskett

17 Dec 2007
Research & Ideas

The Rise of Medical Tourism

the U.S. medical profession are still large. In India, the same depth of pool of engineering and mathematical talent for software, offshoring, and outsourcing is there for medicine, too. In the 1950s and '60s, the Indian government... View Details

Keywords: by Martha Lagace; Health; Medical Devices & Supplies

September 2010 (Revised December 2010)
Case

Compass Maritime Services, LLC: Valuing Ships

By: Benjamin C. Esty and Albert W. Sheen

Tom Roberts, a founding partner of Compass Maritime Services, a New Jersey-based shipping research and consulting firm, has been asked by a new potential customer in May 2008 for advice on purchasing a capesize bulk carrier. After identifying a suitable ship with his... View Details

Keywords: Decision Choices and Conditions; Judgments; Price; Management Analysis, Tools, and Techniques; Negotiation Offer; Mathematical Methods; Ship Transportation; Valuation; Consulting Industry; Shipping Industry

30 Jun 2021
In Practice

The Harvard Business School Faculty Summer Reader 2021

What’s on HBS faculty members’ reading list for summer 2021? Which books are most meaningful to them and why? Below, faculty share their top picks, ranging from biographies and memoirs to their colleagues’ latest works. Julia Austin: Social justice and the Obamas I... View Details

Keywords: by Kathryn Haviland

Web

Frequently Asked Questions | HBS Online

prediction, causality, visualization, data wrangling, privacy, and ethics—but does so without coding or mathematical application. The course is intended for organizational leaders and managers to be prepared to act on data analysis and to... View Details

03 May 2010
Research & Ideas

What Is the Future of MBA Education?

situations into mathematical models. The percentage of MBAs that we hire will go down in the next ten years. A director of a leading consulting firm made much the same point: We now hire a very large number of non-MBAs into our Associate... View Details

Keywords: by Martha Lagace; Education

Student-Profile

Sagar Saxena

While applying for graduate programs, Sagar Saxena (he/him) was unsure about whether he had the right background to pursue a PhD in Business Economics at HBS because he had not taken graduate-level courses in mathematics or economics.... View Details

01 Mar 2009
News

The Case for Studying Financial History

guide than certain other disciplines that are sometimes regarded as more rigorous, like economics, for example. Economists with their more mathematical approach to social science conspicuously failed to anticipate this crisis, whereas a... View Details

Keywords: Roger Thompson; federal bailouts; Finance; Administration of Economic Programs; Government

1972
Chapter

Random Walks and Technical Theories: Some Additional Evidence

By: George A. Benington and Michael C. Jensen

Keywords: Mathematical Methods

SSRN

1979
Article

An Extension and Simple Proof of a Constrained Lattice Fix-Point Theorem

By: C. Blair and A. E. Roth

Keywords: Mathematical Methods

Find at Harvard

January 1975
Article

A Lattice Fixed-Point Theorem with Constraints

By: A. E. Roth

Keywords: Mathematical Methods

Find at Harvard

September–October 2023
Article

Interpretable Matrix Completion: A Discrete Optimization Approach

By: Dimitris Bertsimas and Michael Lingzhi Li

We consider the problem of matrix completion on an n × m matrix. We introduce the problem of interpretable matrix completion that aims to provide meaningful insights for the low-rank matrix using side information. We show that the problem can be... View Details

Keywords: Mathematical Methods

2022
Article

Exploring Counterfactual Explanations Through the Lens of Adversarial Examples: A Theoretical and Empirical Analysis.

By: Martin Pawelczyk, Chirag Agarwal, Shalmali Joshi, Sohini Upadhyay and Himabindu Lakkaraju

As machine learning (ML) models become more widely deployed in high-stakes applications, counterfactual explanations have emerged as key tools for providing actionable model explanations in practice. Despite the growing popularity of counterfactual explanations, a... View Details

Keywords: Machine Learning Models; Counterfactual Explanations; Adversarial Examples; Mathematical Methods

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November 2021
Article

Panel Experiments and Dynamic Causal Effects: A Finite Population Perspective

By: Iavor Bojinov, Ashesh Rambachan and Neil Shephard

In panel experiments, we randomly assign units to different interventions, measuring their outcomes, and repeating the procedure in several periods. Using the potential outcomes framework, we define finite population dynamic causal effects that capture the relative... View Details

Keywords: Panel Data; Dynamic Causal Effects; Potential Outcomes; Finite Population; Nonparametric; Mathematical Methods

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2018
Working Paper

Bundling Incentives in (Many-to-Many) Matching with Contracts

By: Jonathan Ma and Scott Duke Kominers

In many-to-many matching with contracts, the way in which contracts are specified can affect the set of stable equilibrium outcomes. Consequently, agents may be incentivized to modify the set of contracts upfront. We consider one simple way in which agents may do so:... View Details

Keywords: Matching With Contracts; Contract Design; Bundling-proofness; Substitutability; Mathematical Methods

SSRN

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2011
Chapter

Fundamental Data Anomalies

By: Ian D. Gow

Keywords: Mathematical Methods; Data and Data Sets

November 1990 (Revised November 1992)
Background Note

Note on Linear Programming

Gives an elementary introduction to formulating linear programming models and interpreting linear programmings output. Other aspects of linear programming are discussed briefly. View Details

Keywords: Mathematical Methods