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      Mathematical MethodsRemove Mathematical Methods →

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      • November–December 2018
      • Article

      Online Network Revenue Management Using Thompson Sampling

      By: Kris J. Ferreira, David Simchi-Levi and He Wang
      We consider a network revenue management problem where an online retailer aims to maximize revenue from multiple products with limited inventory constraints. As common in practice, the retailer does not know the consumer's purchase probability at each price and must... View Details
      Keywords: Online Marketing; Revenue Management; Revenue; Management; Marketing; Internet and the Web; Price; Mathematical Methods
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      Ferreira, Kris J., David Simchi-Levi, and He Wang. "Online Network Revenue Management Using Thompson Sampling." Operations Research 66, no. 6 (November–December 2018): 1586–1602.
      • November 2018
      • Case

      Sportradar (A): From Data to Storytelling

      By: Ramon Casadesus-Masanell, Karen Elterman and Oliver Gassmann
      In 2013, the Swiss sports data company Sportradar debated whether to expand from its core business of data provision to bookmakers into sports media products. Sports data was becoming a commodity, and in the future, sports leagues might reduce their dependence on... View Details
      Keywords: Sports Data; Data; Sport; Sportradar; Football; Soccer; Gambling; Betting; Betting Markets; Statistics; Odds; Live Data; Bookmakers; Betradar; Visualization; Integrity; Monitoring; Gaming; Streaming; 2013; St.Gallen; Algorithm; Mathematical Modeling; Carsten Koerl; Betandwin; Bwin; Wagering; Probability; Sports; Analytics and Data Science; Mathematical Methods; Games, Gaming, and Gambling; Transition; Strategy; Media; Sports Industry; Technology Industry; Information Technology Industry; Media and Broadcasting Industry; Europe; Switzerland; Asia; Austria; Germany; England
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      Casadesus-Masanell, Ramon, Karen Elterman, and Oliver Gassmann. "Sportradar (A): From Data to Storytelling." Harvard Business School Case 719-429, November 2018.
      • 2018
      • Working Paper

      Full Substitutability

      By: John William Hatfield, Scott Duke Kominers, Alexandru Nichifor, Michael Ostrovsky and Alexander Westkamp
      Various forms of substitutability are essential for establishing the existence of equilibria and other useful properties in diverse settings such as matching, auctions, and exchange economies with indivisible goods. We extend earlier models’ definitions of... View Details
      Keywords: Substitutability; Mathematical Methods; Auctions; Market Design
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      Hatfield, John William, Scott Duke Kominers, Alexandru Nichifor, Michael Ostrovsky, and Alexander Westkamp. "Full Substitutability." Harvard Business School Working Paper, No. 19-016.
      • 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
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      Ma, Jonathan, and Scott Duke Kominers. "Bundling Incentives in (Many-to-Many) Matching with Contracts." Harvard Business School Working Paper, No. 19-011, August 2018.
      • August 2018
      • Article

      Extrapolation and Bubbles

      By: Nicholas Barberis, Robin Greenwood, Lawrence Jin and Andrei Shleifer
      We present an extrapolative model of bubbles. In the model, many investors form their demand for a risky asset by weighing two signals: an average of the asset’s past price changes and the asset’s degree of overvaluation. The two signals are in conflict, and investors... View Details
      Keywords: Bubble; Extrapolation; Volume; Price Bubble; Mathematical Methods
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      Barberis, Nicholas, Robin Greenwood, Lawrence Jin, and Andrei Shleifer. "Extrapolation and Bubbles." Journal of Financial Economics 129, no. 2 (August 2018): 203–227.
      • May 2018
      • Article

      Selection and Market Reallocation: Productivity Gains from Multinational Production

      By: Laura Alfaro and Maggie X. Chen
      Assessing the productivity gains from multinational production has been a vital topic of economic research and policy debate. Positive aggregate productivity gains are often attributed to within-firm productivity improvement; however, an alternative, less emphasized... View Details
      Keywords: Productivity Gains; Multinational Production; Selection; Market Reallocation; And Within-firm Productivity; Multinational Firms and Management; Production; Performance Productivity; Competition; Mathematical Methods
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      Alfaro, Laura, and Maggie X. Chen. "Selection and Market Reallocation: Productivity Gains from Multinational Production." American Economic Journal: Economic Policy 10, no. 2 (May 2018): 1–38. (Also NBER Working Paper 18207. See Harvard Business School Working Paper, No. 12–111, 2015 for longer version.)
      • November 2021
      • Article

      Gaussian Process Subset Scanning for Anomalous Pattern Detection in Non-iid Data

      By: William Herlands, Edward McFowland III, Andrew Gordon Wilson and Daniel B. Neill
      Identifying anomalous patterns in real-world data is essential for understanding where, when, and how systems deviate from their expected dynamics. Yet methods that separately consider the anomalousness of each individual data point have low detection power for subtle,... View Details
      Keywords: Pattern Detection; Subset Scanning; Gaussian Processes; Mathematical Methods
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      Herlands, William, Edward McFowland III, Andrew Gordon Wilson, and Daniel B. Neill. "Gaussian Process Subset Scanning for Anomalous Pattern Detection in Non-iid Data." Proceedings of Machine Learning Research (PMLR) 84 (2018): 425–434. (Also presented at the 21st International Conference on Artificial Intelligence and Statistics (AISTATS), 2018.)
      • 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.
      • January 2018
      • Background Note

      Math Tools for Strategists

      By: Tarun Khanna and Jan W. Rivkin
      Great strategists rely heavily on numbers as they go about their work. This note offers an overview of the highbrow and lowbrow quantitative tools that individuals commonly encounter during strategy courses and in actual strategy work. The note focuses especially on... View Details
      Keywords: Mathematical Methods; Strategy
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      Khanna, Tarun, and Jan W. Rivkin. "Math Tools for Strategists." Harvard Business School Background Note 718-477, January 2018.
      • Article

      Mitigating Bias in Adaptive Data Gathering via Differential Privacy

      By: Seth Neel and Aaron Leon Roth
      Data that is gathered adaptively—via bandit algorithms, for example—exhibits bias. This is true both when gathering simple numeric valued data—the empirical means kept track of by stochastic bandit algorithms are biased downwards—and when gathering more complicated... View Details
      Keywords: Bandit Algorithms; Bias; Analytics and Data Science; Mathematical Methods; Theory
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      Neel, Seth, and Aaron Leon Roth. "Mitigating Bias in Adaptive Data Gathering via Differential Privacy." Proceedings of the International Conference on Machine Learning (ICML) 35th (2018).
      • Article

      Preventing Fairness Gerrymandering: Auditing and Learning for Subgroup Fairness

      By: Michael J Kearns, Seth Neel, Aaron Leon Roth and Zhiwei Steven Wu
      The most prevalent notions of fairness in machine learning are statistical definitions: they fix a small collection of pre-defined groups, and then ask for parity of some statistic of the classifier (like classification rate or false positive rate) across these groups.... View Details
      Keywords: Machine Learning; Algorithms; Fairness; Mathematical Methods
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      Kearns, Michael J., Seth Neel, Aaron Leon Roth, and Zhiwei Steven Wu. "Preventing Fairness Gerrymandering: Auditing and Learning for Subgroup Fairness." Proceedings of the International Conference on Machine Learning (ICML) 35th (2018).
      • 2017
      • Working Paper

      Investment Timing with Costly Search for Financing

      By: Samuel Antill
      I develop a dynamic model of investment timing in which firms must first choose when to search for external financing. Search is costly and the arrival of investors is uncertain, leading to delay in financing and investment. Depending on parameters, my model can... View Details
      Keywords: Real Options; Search And Bargaining; Time-varying Financial Conditions; Investment; Venture Capital; Mathematical Methods
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      Antill, Samuel. "Investment Timing with Costly Search for Financing." Working Paper, December 2017.
      • 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.
      • 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

      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.
      • 2019
      • Chapter

      Quantitative and Qualitative Methods in Organizational Research

      By: Amy C. Edmondson and Tiona Zuzul
      Selecting the appropriate method for a given research question is an essential skill for organizational researchers. High-quality research involves a good fit between the methods used and the nature of the contribution to the literature. This article describes a... View Details
      Keywords: Mathematical Methods; Organizations
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      Edmondson, Amy C., and Tiona Zuzul. "Quantitative and Qualitative Methods in Organizational Research." In The Palgrave Encyclopedia of Strategic Management. Continuously updated edition, edited by Mie Augier and David J. Teece. Palgrave Macmillan, 2017. Electronic. (Pre-published, October 2013.)
      • 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.
      • May 2017
      • Article

      Stable and Strategy-Proof Matching with Flexible Allotments

      By: John William Hatfield, Scott Duke Kominers and Alexander Westkamp
      We introduce a framework of matching with flexible allotments that can be used to model firms with cross-division hiring restrictions. Our framework also allows us to nest some prior models of matching with distributional constraints. Building upon our recent work on... View Details
      Keywords: Balance and Stability; Mathematical Methods
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      Hatfield, John William, Scott Duke Kominers, and Alexander Westkamp. "Stable and Strategy-Proof Matching with Flexible Allotments." American Economic Review 107, no. 5 (May 2017): 214–219.
      • March 2017 (Revised March 2022)
      • Case

      Flashion: Art vs. Science in Fashion Retailing

      By: Kris Ferreira and Karim R. Lakhani
      Kate Wilson, retail analytics manager at Flashion, a fashion flash-sale site, is tasked with developing analytics to optimize pricing for first-exposure products on the site. Many in the industry have relied on years of experience and intuition to determine pricing—can... View Details
      Keywords: Analytics; Pricing; Data; Service Operations; Forecasting and Prediction; Internet and the Web; Technology Adoption; Mathematical Methods; Decision Making; E-commerce; Retail Industry; Fashion Industry; United States
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      Ferreira, Kris, and Karim R. Lakhani. "Flashion: Art vs. Science in Fashion Retailing." Harvard Business School Case 617-059, March 2017. (Revised March 2022.)
      • 2017
      • Working Paper

      Minimizing Justified Envy in School Choice: The Design of New Orleans' OneApp

      By: Atila Abdulkadiroglu, Yeon-Koo Che, Parag A. Pathak, Alvin E. Roth and Oliver Tercieux
      In 2012, New Orleans Recovery School District (RSD) became the first U.S. district to unify charter and traditional public school admissions in a single-offer assignment mechanism known as OneApp. The RSD also became the first district to use a mechanism based on Top... View Details
      Keywords: Education; Decision Choices and Conditions; Marketplace Matching; Mathematical Methods; Design
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      Abdulkadiroglu, Atila, Yeon-Koo Che, Parag A. Pathak, Alvin E. Roth, and Oliver Tercieux. "Minimizing Justified Envy in School Choice: The Design of New Orleans' OneApp." NBER Working Paper Series, No. 23265, March 2017.
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