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  • All HBS Web  (855)
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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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  • 2019
  • Article

Ridesharing with Driver Location Preferences

By: Duncan Rheingans-Yoo, Scott Duke Kominers, Hongyao Ma and David C. Parkes
We study revenue-optimal pricing and driver compensation in ridesharing platforms when drivers have heterogeneous preferences over locations. If a platform ignores drivers' location preferences, it may make inefficient trip dispatches; moreover, drivers may strategize... View Details
Keywords: Ridesharing; Pricing; Compensation and Benefits; Geographic Location; Market Design; Mathematical Methods
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Rheingans-Yoo, Duncan, Scott Duke Kominers, Hongyao Ma, and David C. Parkes. "Ridesharing with Driver Location Preferences." Proceedings of the International Joint Conference on Artificial Intelligence (2019): 557–564.
  • January 2010
  • Journal Article

A Choice Prediction Competition: Choices from Experience and from Description

By: Ido Erev, Eyal Ert, Alvin E. Roth, Ernan E. Haruvy, Stefan Herzog, Robin Hau, Ralph Hertwig, Terrence Steward, Robert West and Christian Lebiere
Erev, Ert, and Roth organized three choice prediction competitions focused on three related choice tasks: one-shot decisions from description (decisions under risk), one-shot decisions from experience, and repeated decisions from experience. Each competition was based... View Details
Keywords: Experience and Expertise; Decision Choices and Conditions; Forecasting and Prediction; Mathematical Methods; Risk and Uncertainty; Competition
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Erev, Ido, Eyal Ert, Alvin E. Roth, Ernan E. Haruvy, Stefan Herzog, Robin Hau, Ralph Hertwig, Terrence Steward, Robert West, and Christian Lebiere. "A Choice Prediction Competition: Choices from Experience and from Description." Special Issue on Decisions from Experience. Journal of Behavioral Decision Making 23, no. 1 (January 2010).
  • November 2006
  • Background Note

Technical Game Theory Note #1: Solving Bi-matrix Games

By: Dennis A. Yao
Explains how to solve bi-matrix games and introduces the Nash Equilibrium concept. View Details
Keywords: Game Theory; Mathematical Methods; Learning; Balance and Stability; Planning; Strategic Planning; Performance Improvement; Strategy; Games, Gaming, and Gambling
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Yao, Dennis A. "Technical Game Theory Note #1: Solving Bi-matrix Games." Harvard Business School Background Note 707-476, November 2006.
  • 2025
  • Article

Statistical Inference for Heterogeneous Treatment Effects Discovered by Generic Machine Learning in Randomized Experiments

By: Kosuke Imai and Michael Lingzhi Li
Researchers are increasingly turning to machine learning (ML) algorithms to investigate causal heterogeneity in randomized experiments. Despite their promise, ML algorithms may fail to accurately ascertain heterogeneous treatment effects under practical settings with... View Details
Keywords: AI and Machine Learning; Mathematical Methods; Analytics and Data Science
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Imai, Kosuke, and Michael Lingzhi Li. "Statistical Inference for Heterogeneous Treatment Effects Discovered by Generic Machine Learning in Randomized Experiments." Journal of Business & Economic Statistics 43, no. 1 (2025): 256–268.
  • January 2021
  • Article

Using Models to Persuade

By: Joshua Schwartzstein and Adi Sunderam
We present a framework where "model persuaders" influence receivers’ beliefs by proposing models that organize past data to make predictions. Receivers are assumed to find models more compelling when they better explain the data, fixing receivers’ prior beliefs. Model... View Details
Keywords: Model Persuasion; Analytics and Data Science; Forecasting and Prediction; Mathematical Methods; Framework
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Schwartzstein, Joshua, and Adi Sunderam. "Using Models to Persuade." American Economic Review 111, no. 1 (January 2021): 276–323.
  • August 2020 (Revised September 2020)
  • Technical Note

Assessing Prediction Accuracy of Machine Learning Models

By: Michael W. Toffel, Natalie Epstein, Kris Ferreira and Yael Grushka-Cockayne
The note introduces a variety of methods to assess the accuracy of machine learning prediction models. The note begins by briefly introducing machine learning, overfitting, training versus test datasets, and cross validation. The following accuracy metrics and tools... View Details
Keywords: Machine Learning; Statistics; Econometric Analyses; Experimental Methods; Data Analysis; Data Analytics; Forecasting and Prediction; Analytics and Data Science; Analysis; Mathematical Methods
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Toffel, Michael W., Natalie Epstein, Kris Ferreira, and Yael Grushka-Cockayne. "Assessing Prediction Accuracy of Machine Learning Models." Harvard Business School Technical Note 621-045, August 2020. (Revised September 2020.)
  • May 2011
  • Teaching Note

The Morrison Company (Brief Case)

By: Steven C. Wheelwright and Paul Meyers
Teaching Note for 4564. View Details
Keywords: Quantitative Analysis; Technology; Operations Management; Product Lines; Manufacturing; Capacity Planning; Production Planning; Information Technology; Production; Mathematical Methods; Performance Capacity; Product Development; Planning; Manufacturing Industry
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Wheelwright, Steven C., and Paul Meyers. "The Morrison Company (Brief Case)." Harvard Business School Teaching Note 114-565, May 2011.
  • October 2011
  • Article

The Surprising Power of Age-Dependent Taxes

By: Matthew C. Weinzierl
This article provides a new, empirically driven application of the dynamic Mirrleesian framework by studying a feasible and potentially powerful tax reform: age-dependent labor income taxation. I show analytically how age dependence improves policy on both the... View Details
Keywords: Taxation; Policy; Age; Income; Mathematical Methods; Welfare; United States
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Weinzierl, Matthew C. "The Surprising Power of Age-Dependent Taxes." Review of Economic Studies 78, no. 4 (October 2011): 1490–1518. (Also Harvard Business School Working Paper, No. 11-114, May 2011.)
  • 2011
  • Working Paper

Better-reply Dynamics in Deferred Acceptance Games

In this paper we address the question of learning in a two-sided matching mechanism that utilizes the deferred acceptance algorithm. We consider a repeated matching game where at each period agents observe their match and have the opportunity to revise their strategy... View Details
Keywords: Learning; Marketplace Matching; Outcome or Result; Game Theory; Mathematical Methods; Strategy
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Haeringer, Guillaume, and Hanna Halaburda. "Better-reply Dynamics in Deferred Acceptance Games." Harvard Business School Working Paper, No. 11-126, June 2011.
  • April 2011
  • Teaching Note

Neck & Neck: Leveraging the Club Neck Information (TN)

Teaching Note for 111112. View Details
Keywords: Budgets and Budgeting; Knowledge Use and Leverage; Profit; Planning; Advertising Campaigns; Mathematical Methods; Apparel and Accessories Industry; Retail Industry
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Martinez-Jerez, Francisco de Asis, Jasmijn Bol, and Christopher Ittner. "Neck & Neck: Leveraging the Club Neck Information (TN)." Harvard Business School Teaching Note 111-112, April 2011.
  • Article

An Exploration of Optimal Stabilization Policy

By: N. Gregory Mankiw and Matthew C. Weinzierl
This paper examines the optimal response of monetary and fiscal policy to a decline in aggregate demand. The theoretical framework is a two-period general equilibrium model in which prices are sticky in the short-run and flexible in the long-run. Policy is evaluated by... View Details
Keywords: Fiscal Policy; Monetary Policy; Economic Models; Aggregate Demand; Demand and Consumers; Money; Mathematical Methods; Taxation; Spending; Policy; Welfare; Household; Economic Slowdown and Stagnation
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Mankiw, N. Gregory, and Matthew C. Weinzierl. "An Exploration of Optimal Stabilization Policy." Brookings Papers on Economic Activity (Spring 2011). (Also Harvard Business School Working Paper, No. 11-113, May 2011 and NBER Working Paper Series, No. 17029, May 2011.)
  • 2022
  • Article

Which Explanation Should I Choose? A Function Approximation Perspective to Characterizing Post hoc Explanations

By: Tessa Han, Suraj Srinivas and Himabindu Lakkaraju
A critical problem in the field of post hoc explainability is the lack of a common foundational goal among methods. For example, some methods are motivated by function approximation, some by game theoretic notions, and some by obtaining clean visualizations. This... View Details
Keywords: Mathematical Methods; Decision Choices and Conditions; Analytics and Data Science
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Han, Tessa, Suraj Srinivas, and Himabindu Lakkaraju. "Which Explanation Should I Choose? A Function Approximation Perspective to Characterizing Post hoc Explanations." Advances in Neural Information Processing Systems (NeurIPS) (2022). (Best Paper Award, International Conference on Machine Learning (ICML) Workshop on Interpretable ML in Healthcare.)
  • 2022
  • Article

Fairness via Explanation Quality: Evaluating Disparities in the Quality of Post hoc Explanations

By: Jessica Dai, Sohini Upadhyay, Ulrich Aivodji, Stephen Bach and Himabindu Lakkaraju
As post hoc explanation methods are increasingly being leveraged to explain complex models in high-stakes settings, it becomes critical to ensure that the quality of the resulting explanations is consistently high across all subgroups of a population. For instance, it... View Details
Keywords: Prejudice and Bias; Mathematical Methods; Research; Analytics and Data Science
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Dai, Jessica, Sohini Upadhyay, Ulrich Aivodji, Stephen Bach, and Himabindu Lakkaraju. "Fairness via Explanation Quality: Evaluating Disparities in the Quality of Post hoc Explanations." Proceedings of the AAAI/ACM Conference on Artificial Intelligence, Ethics, and Society (2022): 203–214.
  • August 2019
  • Article

When and How to Diversify—A Multicategory Utility Model for Personalized Content Recommendation

By: Yicheng Song, Nachiketa Sahoo and Elie Ofek
Sometimes we desire change, a break from the same or an opportunity to fulfill different aspects of our needs. Noting that consumers seek variety, several approaches have been developed to diversify items recommended by personalized recommender systems. However,... View Details
Keywords: Recommender Systems; Personalization; Recommendation Diversity; Variety Seeking; Collaborative Filtering; Consumer Utility Models; Digital Media; Clickstream Analysis; Learning-to-rank; Consumer Behavior; Media; Customization and Personalization; Strategy; Mathematical Methods
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Song, Yicheng, Nachiketa Sahoo, and Elie Ofek. "When and How to Diversify—A Multicategory Utility Model for Personalized Content Recommendation." Management Science 65, no. 8 (August 2019): 3737–3757.
  • 2010
  • Working Paper

Agency Revisited

By: Ramon Casadesus-Masanell and Daniel F. Spulber
The article presents a comprehensive overview of the principal-agent model that emphasizes the role of trust in the agency relationship. The analysis demonstrates that the legal remedy for breach of duty can result in a full-information efficient outcome eliminating... View Details
Keywords: Ethics; Contracts; Agency Theory; Mathematical Methods; Behavior; Trust
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Casadesus-Masanell, Ramon, and Daniel F. Spulber. "Agency Revisited." Harvard Business School Working Paper, No. 10-082, March 2010.
  • June 2009
  • Teaching Note

Stryker Corporation: In-sourcing PCBs (TN)

By: Timothy A. Luehrman
Teaching Note for [207121]. View Details
Keywords: Investment; Capital Budgeting; Valuation; Investment Return; Mathematical Methods; Medical Devices and Supplies Industry
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Luehrman, Timothy A. "Stryker Corporation: In-sourcing PCBs (TN)." Harvard Business School Teaching Note 209-156, June 2009.
  • 2008
  • Working Paper

Allocating Marketing Resources

By: Sunil Gupta and Thomas J. Steenburgh
Marketing is essential for the organic growth of a company. Not surprisingly, firms spend billions of dollars on marketing. Given these large investments, marketing managers have the responsibility to optimally allocate these resources and demonstrate that these... View Details
Keywords: Investment Return; Resource Allocation; Marketing; Demand and Consumers; Mathematical Methods
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Gupta, Sunil, and Thomas J. Steenburgh. "Allocating Marketing Resources." Harvard Business School Working Paper, No. 08-069, February 2008.
  • 2008
  • Chapter

Allocating Marketing Resources

By: Sunil Gupta and Thomas J. Steenburgh

Companies spend billions of dollars on marketing every year because it is essential to organic growth. Given these large investments, marketing managers have the responsibility to optimally allocate resources and to demonstrate that their investments generate... View Details

Keywords: Investment Return; Resource Allocation; Marketing; Demand and Consumers; Mathematical Methods
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Gupta, Sunil, and Thomas J. Steenburgh. "Allocating Marketing Resources." In Marketing Mix Decisions: New Perspectives and Practices, edited by Roger A. Kerin and Rob O'Regan. Chicago, IL: American Marketing Association, 2008.
  • 2008
  • Working Paper

Minimally Altruistic Wages and Unemployment in a Matching Model

By: Julio J. Rotemberg
This paper presents a model in which firms recruit both unemployed and employed workers by posting vacancies. Firms act monopsonistically and set wages to retain their existing workers as well as to attract new ones. The model differs from Burdett and Mortensen (1998)... View Details
Keywords: Retention; Selection and Staffing; Employment; Wages; Mathematical Methods
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Rotemberg, Julio J. "Minimally Altruistic Wages and Unemployment in a Matching Model." NBER Working Paper Series, No. 13755, February 2008.
  • 1980
  • Article

Consumer Impulse Purchase and Credit Card Usage: An Empirical Examination Using the Log Linear Model

By: Rohit Deshpandé and S. Krishnan
Most of the work in impulse purchase behavior has investigated the association of socioeconomic variables and unplanned purchases with equivocal results. This paper examines the interrelationship between impulse purchases, credit card usage, cost of items bought, and... View Details
Keywords: Consumer Behavior; Mathematical Methods; Credit Cards; Income
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Deshpandé, Rohit, and S. Krishnan. "Consumer Impulse Purchase and Credit Card Usage: An Empirical Examination Using the Log Linear Model." Advances in Consumer Research 7 (1980): 792–795.
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