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  • All HBS Web  (858)
    • News  (79)
    • Research  (639)
    • Events  (14)
    • Multimedia  (4)
  • Faculty Publications  (635)
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  • December 2001 (Revised April 2003)
  • Case

Delays at Logan Airport

By: V.G. Narayanan and George Batta
Logan Airport is facing mounting delays for flights landings and takeoffs, especially in inclement weather. An additional runway and peak-period pricing are two alternatives being considered. View Details
Keywords: Price; Problems and Challenges; Decision Making; Mathematical Methods; Air Transportation Industry; Service Industry; Boston
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Narayanan, V.G., and George Batta. "Delays at Logan Airport." Harvard Business School Case 102-011, December 2001. (Revised April 2003.)
  • June 2008
  • Article

Minimally Acceptable Altruism and the Ultimatum Game

By: Julio J. Rotemberg
I suppose that people react with anger when others show themselves not to be minimally altruistic. With heterogeneous agents, this can account for the experimental results of ultimatum and dictator games. Moreover, it can account for the surprisingly large fraction of... View Details
Keywords: Philanthropy and Charitable Giving; Game Theory; Mathematical Methods
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Rotemberg, Julio J. "Minimally Acceptable Altruism and the Ultimatum Game." Journal of Economic Behavior & Organization 66, nos. 3-4 (June 2008).
  • 06 Apr 2020
  • Working Paper Summaries

A General Theory of Identification

Keywords: by Iavor Bojinov and Guillaume Basse
  • 2006
  • Book

Service Productivity Management: Improving Service Performance Using Data Envelopment Analysis

By: H. David Sherman and Joe Zhu
Here is an in-depth guide to the most powerful available benchmarking technique for improving service organization performance—Data Envelopment Analysis (DEA). The book outlines DEA as a benchmarking technique, identifies high cost service units, isolates specific... View Details
Keywords: Data Envelopment Analysis; Economics; Operations; Mathematical Methods
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Sherman, H. David, and Joe Zhu. Service Productivity Management: Improving Service Performance Using Data Envelopment Analysis. Boston, MA: Springer, 2006.
  • 1991
  • Chapter

An Economic Approach to the Study of Bargaining

By: A. E. Roth
Keywords: Negotiation; Economics; Mathematical Methods
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Roth, A. E. "An Economic Approach to the Study of Bargaining." In Handbook of Negotiation Research. Vol. 3, edited by M. H. Bazerman, R. J. Lewicki, and B. H. Sheppard, 35–67. Research on Negotiation in Organizations. JAI Press, 1991.
  • July 1982 (Revised March 1984)
  • Background Note

Why Preference Curves are Useful for Risky Decisions

By: David E. Bell
Keywords: Mathematical Methods; Decision Making
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Bell, David E. "Why Preference Curves are Useful for Risky Decisions." Harvard Business School Background Note 183-030, July 1982. (Revised March 1984.)
  • 18 Nov 2016
  • Conference Presentation

Rawlsian Fairness for Machine Learning

By: Matthew Joseph, Michael J. Kearns, Jamie Morgenstern, Seth Neel and Aaron Leon Roth
Motivated by concerns that automated decision-making procedures can unintentionally lead to discriminatory behavior, we study a technical definition of fairness modeled after John Rawls' notion of "fair equality of opportunity". In the context of a simple model of... View Details
Keywords: Machine Learning; Algorithms; Fairness; Decision Making; Mathematical Methods
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Joseph, Matthew, Michael J. Kearns, Jamie Morgenstern, Seth Neel, and Aaron Leon Roth. "Rawlsian Fairness for Machine Learning." Paper presented at the 3rd Workshop on Fairness, Accountability, and Transparency in Machine Learning, Special Interest Group on Knowledge Discovery and Data Mining (SIGKDD), November 18, 2016.
  • 2008
  • Chapter

Assessing Creativity and Its Antecedents: An Exploration of the Componential Theory of Creativity

By: T. M. Amabile and Jennifer Mueller
Keywords: Creativity; Mathematical Methods; Theory
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Amabile, T. M., and Jennifer Mueller. "Assessing Creativity and Its Antecedents: An Exploration of the Componential Theory of Creativity." In Handbook of Organizational Creativity, edited by Jing Zhou and Christina E. Shalley. Lawrence Erlbaum Associates, 2008.
  • March 1999 (Revised December 2001)
  • Background Note

Analyzing Consumer Preferences

By: Robert J. Dolan
Presents a non-traditional description of the conjoint analysis methodology. Discusses the process by which a study is done and cites areas of application. View Details
Keywords: Marketing; Mathematical Methods; Product Marketing
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Dolan, Robert J. "Analyzing Consumer Preferences." Harvard Business School Background Note 599-112, March 1999. (Revised December 2001.)
  • Forthcoming
  • Article

Sticky Capital Controls

By: Miguel Acosta-Henao, Laura Alfaro and Andrés Fernández
There is much ongoing debate on the merits of capital controls as effective policy instruments. The differing perspectives are due in part to a lack of empirical studies that look at the intensive margin of controls, which in turn has prevented a quantitative... View Details
Keywords: Capital Controls; Macroprudential Policies; Stickiness; Intensive; (S, S) Costs; Capital; Management; Macroeconomics; Governance Controls; Mathematical Methods
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Acosta-Henao, Miguel, Laura Alfaro, and Andrés Fernández. "Sticky Capital Controls." Journal of International Economics (forthcoming).
  • July 2012
  • Article

Discrete Choice Cannot Generate Demand That Is Additively Separable in Own Price

By: Sonia Jaffe and Scott Duke Kominers
We show that in a unit demand discrete choice framework with at least three goods, demand cannot be additively separable in own price. This result sharpens the analogous result of Jaffe and Weyl (2010) in the case of linear demand and has implications for testing of... View Details
Keywords: Discrete Choice; Unit Demand; Separable Demand; Linear Demand; Demand and Consumers; Market Design; Mathematical Methods; Economics
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Jaffe, Sonia, and Scott Duke Kominers. "Discrete Choice Cannot Generate Demand That Is Additively Separable in Own Price." Economics Letters 116, no. 1 (July 2012): 129–132.
  • 2004
  • Chapter

The Harrod-Domar Model

By: Diego Comin
Keywords: Mathematical Methods; Economic Growth; Development Economics; Capital
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Comin, Diego. "The Harrod-Domar Model." In An Eponymous Dictionary of Economics, edited by C. R. Braun and Julio Segura. Edward Elgar Publishing, 2004.
  • 1970
  • Chapter

The Time Series Behavior of Earnings: Discussion

By: Michael Jensen
Keywords: Business Earnings; Mathematical Methods
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Jensen, Michael. "The Time Series Behavior of Earnings: Discussion." In Empirical Research in Accounting: Selected Studies. University of Chicago, Institute of Professional Accounting, 1970.
  • 2025
  • Working Paper

Evaluations Amid Measurement Error: Determining the Optimal Timing for Workplace Interventions

By: Matthew DosSantos DiSorbo, Iavor I. Bojinov and Fiammetta Menchetti
Researchers have embraced factorial experiments to simultaneously evaluate multiple treatments, each with different levels. Typically, in large-scale factorial experiments, the primary objective is identifying the treatment with the largest causal effect, especially... View Details
Keywords: Factorial Designs; Fisher Randomizations; Rank Estimators; Employer Interventions; Causal Inference; Mathematical Methods; Performance Improvement
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DosSantos DiSorbo, Matthew, Iavor I. Bojinov, and Fiammetta Menchetti. "Evaluations Amid Measurement Error: Determining the Optimal Timing for Workplace Interventions." Harvard Business School Working Paper, No. 24-075, June 2024. (Revised May 2025.)
  • September 2021
  • Article

Diagnostic Bubbles

By: Pedro Bordalo, Nicola Gennaioli, Spencer Yongwook Kwon and Andrei Shleifer
We introduce diagnostic expectations into a standard setting of price formation in which investors learn about the fundamental value of an asset and trade it. We study the interaction of diagnostic expectations with two well-known mechanisms: learning from prices and... View Details
Keywords: Bubble; Speculation; Diagnostic Expectations; Price Bubble; Mathematical Methods
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Bordalo, Pedro, Nicola Gennaioli, Spencer Yongwook Kwon, and Andrei Shleifer. "Diagnostic Bubbles." Journal of Financial Economics 141, no. 3 (September 2021).
  • 14 Aug 2017
  • Conference Presentation

A Convex Framework for Fair Regression

By: Richard Berk, Hoda Heidari, Shahin Jabbari, Matthew Joseph, Michael J. Kearns, Jamie Morgenstern, Seth Neel and Aaron Roth
We introduce a flexible family of fairness regularizers for (linear and logistic) regression problems. These regularizers all enjoy convexity, permitting fast optimization, and they span the range from notions of group fairness to strong individual fairness. By varying... View Details
Keywords: Regression Models; Machine Learning; Fairness; Framework; Mathematical Methods
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Berk, Richard, Hoda Heidari, Shahin Jabbari, Matthew Joseph, Michael J. Kearns, Jamie Morgenstern, Seth Neel, and Aaron Roth. "A Convex Framework for Fair Regression." Paper presented at the 4th Workshop on Fairness, Accountability, and Transparency in Machine Learning, Special Interest Group on Knowledge Discovery and Data Mining (SIGKDD), August 14, 2017.
  • Article

A Prescriptive Analytics Framework for Optimal Policy Deployment Using Heterogeneous Treatment Effects

By: Edward McFowland III, Sandeep Gangarapu, Ravi Bapna and Tianshu Sun
We define a prescriptive analytics framework that addresses the needs of a constrained decision-maker facing, ex ante, unknown costs and benefits of multiple policy levers. The framework is general in nature and can be deployed in any utility maximizing context, public... View Details
Keywords: Prescriptive Analytics; Heterogeneous Treatment Effects; Optimization; Observed Rank Utility Condition (OUR); Between-treatment Heterogeneity; Machine Learning; Decision Making; Analysis; Mathematical Methods
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McFowland III, Edward, Sandeep Gangarapu, Ravi Bapna, and Tianshu Sun. "A Prescriptive Analytics Framework for Optimal Policy Deployment Using Heterogeneous Treatment Effects." MIS Quarterly 45, no. 4 (December 2021): 1807–1832.
  • 1995
  • Chapter

Dynamic General Equilibrium Models with Imperfectly Competitive Product Markets

By: Julio J. Rotemberg and Michael Woodford
Keywords: Mathematical Methods; Competition; Markets
Citation
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Rotemberg, Julio J., and Michael Woodford. "Dynamic General Equilibrium Models with Imperfectly Competitive Product Markets." In Frontiers of Business Cycle Research, edited by Thomas Cooley. Princeton, NJ: Princeton University Press, 1995.
  • December 2019
  • Article

Costly Concessions: An Empirical Framework for Matching with Imperfectly Transferable Utility

By: Alfred Galichon, Scott Duke Kominers and Simon Weber
We introduce an empirical framework for models of matching with imperfectly transferable utility and unobserved heterogeneity in tastes. Our framework allows us to characterize matching equilibrium in a flexible way that includes as special cases the classic fully- and... View Details
Keywords: Sorting; Matching; Marriage Market; Intrahousehold Allocation; Imperfectly Transferable Utility; Marketplace Matching; Mathematical Methods
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Galichon, Alfred, Scott Duke Kominers, and Simon Weber. "Costly Concessions: An Empirical Framework for Matching with Imperfectly Transferable Utility." Journal of Political Economy 127, no. 6 (December 2019): 2875–2925.
  • Article

Games of Threats

By: Elon Kohlberg and Abraham Neyman
A game of threats on a finite set of players, N, is a function d that assigns a real number to any coalition, S ⊆ N, such that d(S) = -d(N\S). A game of threats is not necessarily a coalitional game as it may fail to satisfy the condition d(Ø) = 0. We show that analogs... View Details
Keywords: Shapley Value; Coalitional Game; Game Theory; Mathematical Methods
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Kohlberg, Elon, and Abraham Neyman. "Games of Threats." Games and Economic Behavior 108 (March 2018): 139–145.
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