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Publications

Publications

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  • All HBS Web  (839)
    • News  (79)
    • Research  (641)
    • Events  (14)
    • Multimedia  (4)
  • Faculty Publications  (635)

Show Results For

  • All HBS Web  (839)
    • News  (79)
    • Research  (641)
    • Events  (14)
    • Multimedia  (4)
  • Faculty Publications  (635)
← Page 26 of 839 Results →
  • 2013
  • Working Paper

Competing Ad Auctions

By: Itai Ashlagi, Benjamin Edelman and Hoan Soo Lee
We present a two-stage model of competing ad auctions. Search engines attract users via Cournot-style competition. Meanwhile, each advertiser must pay a participation cost to use each ad platform, and advertiser entry strategies are derived using symmetric Bayes-Nash... View Details
Keywords: Online Advertising; Auctions; Market Participation; Market Platforms; Mathematical Methods; Competition
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Ashlagi, Itai, Benjamin Edelman, and Hoan Soo Lee. "Competing Ad Auctions." Harvard Business School Working Paper, No. 10-055, January 2010. (Revised May 2010, February 2011, September 2013.)
  • 2009
  • Working Paper

Farsighted Stability for Roommate Markets

By: Bettina-Elisabeth Klaus, Flip Klijn and Markus Walzl
Using a bi-choice graph technique (Klaus and Klijn, 2009), we show that a matching for a roommate market indirectly dominates another matching if and only if no blocking pair of the former is matched in the latter (Proposition 1). Using this characterization of... View Details
Keywords: Two-Sided Platforms; Marketplace Matching; Mathematical Methods; Balance and Stability
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Klaus, Bettina-Elisabeth, Flip Klijn, and Markus Walzl. "Farsighted Stability for Roommate Markets." Harvard Business School Working Paper, No. 09-135, May 2009.
  • October 2004 (Revised May 2006)
  • Case

Wells REIT II

By: Arthur I Segel and Dwight Angelini
Dr. Richard Planter, a dentist, asks his financial adviser, Michael Saris, to review an offering memorandum for a new, private real estate investment trust. After reviewing the documents, Saris needs to develop an analytical framework and provide concrete advice... View Details
Keywords: Finance; Investment; Framework; Private Ownership; Mathematical Methods; Real Estate Industry
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Segel, Arthur I., and Dwight Angelini. "Wells REIT II." Harvard Business School Case 205-019, October 2004. (Revised May 2006.)
  • Article

Diverging Trends in Macro and Micro Volatility

By: Diego Comin and Sunil Mulani
This paper documents the diverging trends in volatility of the growth rate of sales at the aggregate and firm level. We establish that the upward trend in micro volatility is not simply driven by a compositional bias in the sample studied. We argue that this new fact... View Details
Keywords: Volatility; Mathematical Methods; Theory; Sales; Growth and Development
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Comin, Diego, and Sunil Mulani. "Diverging Trends in Macro and Micro Volatility." Review of Economics and Statistics 88, no. 2 (May 2006).
  • 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).
  • Profile

Aspa Lekka

people for immediate help." Aspa, perhaps drawing upon her mathematics perspective, sees HBS as having a multiplier effect. "There’s so much opportunity for us. HBS opens your vision and view. If, before HBS, I had seen '100’ as... View Details
Keywords: Consulting
  • Student-Profile

Do Yoon Kim

I was born in Seoul, South Korea and spent most of my life there. For my undergraduate degree, I went to Northwestern and majored in Math, Economics, and Mathematical Methods in the Social Sciences (MMSS). Since my sophomore year at... View Details
  • 2024
  • Working Paper

Fiscal Policy under Convex Supply Curves

By: Shlok Goyal, Avi Lipton and Borui Niklas Zhu
Recent empirical evidence suggests that supply curves are convex. Supply curve convexity is at odds with conventional Phillips curves, which rely on an infinitely elastic underlying supply curve. This paper explores the effect of supply curve convexity on the... View Details
Keywords: Fiscal Stimulus; Fiscal Policy; Inflation; Inflation and Deflation; Macroeconomics; Policy; Mathematical Methods; United States
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Goyal, Shlok, Avi Lipton, and Borui Niklas Zhu. "Fiscal Policy under Convex Supply Curves." Working Paper, August 2024.
  • 2009
  • Working Paper

Patent Policy, Patent Pools, and the Accumulation of Claims in Sequential Innovation

By: Gaston Llanes and Stefano Trento
We present a dynamic model where the accumulation of patents generates an increasing number of claims on sequential innovation. We study the equilibrium innovation activity under three regimes: patents, no-patents and patent pools. Patent pools increase the probability... View Details
Keywords: Innovation and Invention; Patents; Rights; Mathematical Methods
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Llanes, Gaston, and Stefano Trento. "Patent Policy, Patent Pools, and the Accumulation of Claims in Sequential Innovation." Harvard Business School Working Paper, No. 10-005, July 2009.
  • Article

Eliminating Unintended Bias in Personalized Policies Using Bias-Eliminating Adapted Trees (BEAT)

By: Eva Ascarza and Ayelet Israeli

An inherent risk of algorithmic personalization is disproportionate targeting of individuals from certain groups (or demographic characteristics such as gender or race), even when the decision maker does not intend to discriminate based on those “protected”... View Details

Keywords: Algorithm Bias; Personalization; Targeting; Generalized Random Forests (GRF); Discrimination; Customization and Personalization; Decision Making; Fairness; Mathematical Methods
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Ascarza, Eva, and Ayelet Israeli. "Eliminating Unintended Bias in Personalized Policies Using Bias-Eliminating Adapted Trees (BEAT)." e2115126119. Proceedings of the National Academy of Sciences 119, no. 11 (March 8, 2022).
  • January 2006
  • Tutorial

Cost-Volume Profit Models

By: David F. Hawkins, V.G. Narayanan, Jacob Cohen and Michele Jurgens
Covers fixed, variable, and semivariable costs and their role in building and interpreting cost-volume-profit models. Introduces the cost-volume and contribution-volume-profit models and identifies some of their uses and limitations. Teaches how to use the... View Details
Keywords: Volume; Cost; Profit; Mathematical Methods
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"Cost-Volume Profit Models." Harvard Business School Tutorial 105-705, January 2006.
  • 2007
  • Working Paper

Mental Accounting and Small Windfalls: Evidence from an Online Grocer

By: Katherine L. Milkman, John Beshears, Todd Rogers and Max H. Bazerman
We study the effect of small windfalls on consumer spending decisions by examining the purchasing behavior of a sample of online grocery shoppers over the course of a year. We compare the purchases customers make when redeeming a $10-off coupon they received from their... View Details
Keywords: Spending; Consumer Behavior; Mathematical Methods; Food and Beverage Industry; Retail Industry
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Milkman, Katherine L., John Beshears, Todd Rogers, and Max H. Bazerman. "Mental Accounting and Small Windfalls: Evidence from an Online Grocer." Harvard Business School Working Paper, No. 08-024, September 2007. (Revised March 2008.)
  • 01 Mar 2016
  • News

Faculty Q&A: Price Check

How did you come to focus on algorithmic pricing? In my doctoral work at MIT, I was studying optimization, probability, and machine learning, which are essentially mathematical tools that enable us to use data to make better decisions.... View Details
Keywords: Julia Hanna; Nonstore Retailers; Retail Trade
  • Web

Harvard Business School

being named a Fellow of the American Academy of Arts and Sciences and receiving the Robert F. Greenhill Award for outstanding service to HBS. Dr. Cash earned a bachelor's degree in mathematics from Texas Christian University, where his... View Details
  • Working Paper

Group Fairness in Dynamic Refugee Assignment

By: Daniel Freund, Thodoris Lykouris, Elisabeth Paulson, Bradley Sturt and Wentao Weng
Ensuring that refugees and asylum seekers thrive (e.g., find employment) in their host countries is a profound humanitarian goal, and a primary driver of employment is the geographic location within a host country to which the refugee or asylum seeker is... View Details
Keywords: Refugees; Geographic Location; Mathematical Methods; Employment; Fairness
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Freund, Daniel, Thodoris Lykouris, Elisabeth Paulson, Bradley Sturt, and Wentao Weng. "Group Fairness in Dynamic Refugee Assignment." Harvard Business School Working Paper, No. 23-047, February 2023.
  • August 2003 (Revised May 2009)
  • Background Note

Basic Venture Capital Formula, The

By: William A. Sahlman and Matthew Willis
Briefly summarizes the process that venture capitalists use to analyze high-risk, long-term investments. Contains information on methods that can be used to calculate valuation, share price, percent ownership, implied valuation, dilution, and option pools. View Details
Keywords: Venture Capital; Risk Management; Mathematical Methods; Valuation
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Sahlman, William A., and Matthew Willis. "Basic Venture Capital Formula, The." Harvard Business School Background Note 804-042, August 2003. (Revised May 2009.)
  • 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

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." Art. 104104. Journal of International Economics 157 (September 2025).
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