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  • All HBS Web  (308)
    • News  (22)
    • Research  (250)
    • Events  (4)
  • Faculty Publications  (230)

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  • All HBS Web  (308)
    • News  (22)
    • Research  (250)
    • Events  (4)
  • Faculty Publications  (230)
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  • 2008
  • Working Paper

On Best-Response Bidding in GSP Auctions

By: Matthew Cary, Aparna Das, Benjamin Edelman, Ioannis Giotis, Kurtis Heimerl, Anna R. Karlin, Claire Mathieu and Michael Schwarz
How should players bid in keyword auctions such as those used by Google, Yahoo! and MSN? We model ad auctions as a dynamic game of incomplete information, so we can study the convergence and robustness properties of various strategies. In particular, we consider... View Details
Keywords: Online Advertising; Auctions; Bids and Bidding; Game Theory; Mathematical Methods; Competitive Strategy
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Cary, Matthew, Aparna Das, Benjamin Edelman, Ioannis Giotis, Kurtis Heimerl, Anna R. Karlin, Claire Mathieu, and Michael Schwarz. "On Best-Response Bidding in GSP Auctions." Harvard Business School Working Paper, No. 08-056, January 2008.
  • September 2019
  • Article

Optimizing Reserves in School Choice: A Dynamic Programming Approach

By: Franklyn Wang, Ravi Jagadeesan and Scott Duke Kominers
We introduce a new model of school choice with reserves in which a social planner is constrained by a limited supply of reserve seats and tries to find an optimal matching according to a social welfare function. We construct the optimal distribution of reserves via a... View Details
Keywords: Matching; Reserves; Dynamic Programming; Marketplace Matching; Mathematical Methods
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Wang, Franklyn, Ravi Jagadeesan, and Scott Duke Kominers. "Optimizing Reserves in School Choice: A Dynamic Programming Approach." Operations Research Letters 47, no. 5 (September 2019): 438–446.
  • 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.
  • November 2007
  • Background Note

Bayesian Estimation & Black-Litterman

By: Joshua D. Coval and Erik Stafford
Describes a practical method for asset allocation that is more robust to estimation errors than the traditional implementation of mean-variance optimization with sample means and covariances. The Bayesian inspired Black-Litterman model is described after introducing... View Details
Keywords: Asset Management; Investment Portfolio; Mathematical Methods
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Coval, Joshua D., and Erik Stafford. "Bayesian Estimation & Black-Litterman." Harvard Business School Background Note 208-085, November 2007.
  • 2007
  • Working Paper

Optimal Reserve Management and Sovereign Debt

By: Laura Alfaro and Fabio Kanczuk
Most models currently used to determine optimal foreign reserve holdings take the level of international debt as given. However, given the sovereign's willingness-to-pay incentive problems, reserve accumulation may reduce sustainable debt levels. In addition, assuming... View Details
Keywords: Sovereign Finance; Borrowing and Debt; Financial Liquidity; International Finance; Emerging Markets; Mathematical Methods
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Alfaro, Laura, and Fabio Kanczuk. "Optimal Reserve Management and Sovereign Debt." NBER Working Paper Series, No. 13216, July 2007.
  • May 2017
  • Article

Agent-based Modeling: A Guide for Social Psychologists

By: Joshua Conrad Jackson, David Rand, Kevin Lewis, Michael I. Norton and Kurt Gray
Agent-based modeling is a longstanding but underused method that allows researchers to simulate artificial worlds for hypothesis testing and theory building. Agent-based models (ABMs) offer unprecedented control and statistical power by allowing researchers to... View Details
Keywords: Social Psychology; Marketing; Mathematical Methods
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Jackson, Joshua Conrad, David Rand, Kevin Lewis, Michael I. Norton, and Kurt Gray. "Agent-based Modeling: A Guide for Social Psychologists." Social Psychological & Personality Science 8, no. 4 (May 2017): 387–395.
  • 2010
  • Working Paper

Substitution Patterns of the Random Coefficients Logit

By: Thomas J. Steenburgh and Andrew Ainslie
Previous research suggests that the random coefficients logit is a highly flexible model that overcomes the problems of the homogeneous logit by allowing for differences in tastes across individuals. The purpose of this paper is to show that this is not true. We prove... View Details
Keywords: Decision Choices and Conditions; Mathematical Methods; Behavior; Prejudice and Bias
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Steenburgh, Thomas J., and Andrew Ainslie. "Substitution Patterns of the Random Coefficients Logit." Harvard Business School Working Paper, No. 10-053, January 2010.
  • May–June 2018
  • Article

Data Uncertainty in Markov Chains: Application to Cost-Effectiveness Analyses of Medical Innovations

By: Joel Goh, Mohsen Bayati, Stefanos A. Zenios, Sundeep Singh and David Moore
Cost-effectiveness studies of medical innovations often suffer from data inadequacy. When Markov chains are used as a modeling framework for such studies, this data inadequacy can manifest itself as imprecision in the elements of the transition matrix. In this paper,... View Details
Keywords: Markov Chains; Cost Effectiveness; Medical Innovations; Colorectal Cancer; Health Care and Treatment; Cost vs Benefits; Innovation and Invention; Mathematical Methods; Health Industry
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Goh, Joel, Mohsen Bayati, Stefanos A. Zenios, Sundeep Singh, and David Moore. "Data Uncertainty in Markov Chains: Application to Cost-Effectiveness Analyses of Medical Innovations." Operations Research 66, no. 3 (May–June 2018): 697–715. (Winner, 2014 INFORMS Health Applications Society Pierskalla Award & Finalist, 2014 INFORMS George E. Nicholson student paper competition.)
  • 2020
  • Working Paper

Overcoming the Cold Start Problem of CRM Using a Probabilistic Machine Learning Approach

By: Eva Ascarza
The success of Customer Relationship Management (CRM) programs ultimately depends on the firm's ability to understand consumers' preferences and precisely capture how these preferences may differ across customers. Only by understanding customer heterogeneity, firms can... View Details
Keywords: Customer Management; Targeting; Deep Exponential Families; Probabilistic Machine Learning; Cold Start Problem; Customer Relationship Management; Customer Value and Value Chain; Consumer Behavior; Analytics and Data Science; Mathematical Methods; Retail Industry
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Padilla, Nicolas, and Eva Ascarza. "Overcoming the Cold Start Problem of CRM Using a Probabilistic Machine Learning Approach." Harvard Business School Working Paper, No. 19-091, February 2019. (Revised May 2020. Accepted at the Journal of Marketing Research.)
  • May 2020
  • Article

Identifying Sources of Inefficiency in Health Care

By: Amitabh Chandra and Douglas O. Staiger
In medicine, the reasons for variation in treatment rates across hospitals serving similar patients are not well understood. Some interpret this variation as unwarranted and push standardization of care as a way of reducing allocative inefficiency. However, an... View Details
Keywords: Health Care and Treatment; Performance Efficiency; Performance Productivity; Mathematical Methods
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Chandra, Amitabh, and Douglas O. Staiger. "Identifying Sources of Inefficiency in Health Care." Quarterly Journal of Economics 135, no. 2 (May 2020): 785–843.
  • 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.
  • 2010
  • Working Paper

Do Bonuses Enhance Sales Productivity? A Dynamic Structural Analysis of Bonus-Based Compensation Plans

By: Doug J. Chung, Thomas J. Steenburgh and K. Sudhir
We estimate a dynamic structural model of sales force response to a bonus based compensation plan. The paper has two main methodological innovations: First, we implement empirically the method proposed by Arcidiacono and Miller (2010) to accommodate unobserved latent... View Details
Keywords: Compensation and Benefits; Performance Productivity; Mathematical Methods; Salesforce Management; Motivation and Incentives
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Chung, Doug J., Thomas J. Steenburgh, and K. Sudhir. "Do Bonuses Enhance Sales Productivity? A Dynamic Structural Analysis of Bonus-Based Compensation Plans." Harvard Business School Working Paper, No. 11-041, October 2010.
  • 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.
  • Article

Moment-to-moment Optimal Branding in TV Commercials: Preventing Avoidance by Pulsing

By: Thales S. Teixeira, Michel Wedel and Rik Pieters
We develop a conceptual framework for understanding the impact that branding activity (the audio-visual representation of brands) and consumers' dispersion of attention have on their moment-to-moment avoidance decisions during television advertising. It formalizes this... View Details
Keywords: Advertising; Decision Choices and Conditions; Television Entertainment; Brands and Branding; Consumer Behavior; Mathematical Methods
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Teixeira, Thales S., Michel Wedel, and Rik Pieters. "Moment-to-moment Optimal Branding in TV Commercials: Preventing Avoidance by Pulsing." Marketing Science 29, no. 5 (September–October 2010): 783–804. (Lead Article.)
  • 2017
  • Working Paper

Identifying Sources of Inefficiency in Health Care

By: Amitabh Chandra and Douglas O. Staiger
In medicine, the reasons for variation in treatment rates across hospitals serving similar patients are not well understood. Some interpret this variation as unwarranted and push standardization of care as a way of reducing allocative inefficiency. However, an... View Details
Keywords: Health Care and Treatment; Performance Efficiency; Performance Productivity; Mathematical Methods
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Chandra, Amitabh, and Douglas O. Staiger. "Identifying Sources of Inefficiency in Health Care." NBER Working Paper Series, No. 24035, November 2017.
  • May–June 2025
  • Article

Branch-and-Price for Prescriptive Contagion Analytics

By: Alexandre Jacquillat, Michael Lingzhi Li, Martin Ramé and Kai Wang
Contagion models are ubiquitous in epidemiology, social sciences, engineering, and management. This paper formulates a prescriptive contagion analytics model where a decision maker allocates shared resources across multiple segments of a population, each governed by... View Details
Keywords: COVID-19; Mathematical Methods
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Jacquillat, Alexandre, Michael Lingzhi Li, Martin Ramé, and Kai Wang. "Branch-and-Price for Prescriptive Contagion Analytics." Operations Research 73, no. 3 (May–June 2025): 1558–1580.
  • 2011
  • Working Paper

Free to Punish? The American Dream and the Harsh Treatment of Criminals

By: Rafael Di Tella and Juan Dubra
We describe the evolution of selective aspects of punishment in the U.S. over the period 1980-2004. We note that imprisonment increased around 1980, a period that coincides with the "Reagan revolution" in economic matters. We build an economic model where beliefs about... View Details
Keywords: Crime and Corruption; Economy; Moral Sensibility; Mathematical Methods; Opportunities; Behavior; United States
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Di Tella, Rafael, and Juan Dubra. "Free to Punish? The American Dream and the Harsh Treatment of Criminals." NBER Working Paper Series, No. 17309, August 2011.
  • 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).
  • 2011
  • Chapter

An Exploration of the Japanese Slowdown during the 1990s

By: Diego A. Comin
Why was the 1990s a lost decade for Japan? How is it possible that the Japanese economy stagnated for a decade if none of the shocks that arguably hit the economy seemed to have persisted for much more than three years or so? In this paper I show that the endogenous... View Details
Keywords: Economic Slowdown and Stagnation; Performance Productivity; Mathematical Methods; Research and Development; Technology Adoption; Japan
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Comin, Diego A. "An Exploration of the Japanese Slowdown during the 1990s." In Japan's Bubble, Deflation, and Long-term Stagnation, edited by Koichi Hamada, Anil Kashyap, and David Weinstein. MIT Press, 2011.
  • 2022
  • Working Paper

The Disagreement Problem in Explainable Machine Learning: A Practitioner's Perspective

By: Satyapriya Krishna, Tessa Han, Alex Gu, Javin Pombra, Shahin Jabbari, Steven Wu and Himabindu Lakkaraju
As various post hoc explanation methods are increasingly being leveraged to explain complex models in high-stakes settings, it becomes critical to develop a deeper understanding of if and when the explanations output by these methods disagree with each other, and how... View Details
Keywords: AI and Machine Learning; Analytics and Data Science; Mathematical Methods
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Krishna, Satyapriya, Tessa Han, Alex Gu, Javin Pombra, Shahin Jabbari, Steven Wu, and Himabindu Lakkaraju. "The Disagreement Problem in Explainable Machine Learning: A Practitioner's Perspective." Working Paper, 2022.
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