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  • All HBS Web  (357)
    • News  (43)
    • Research  (280)
    • Events  (2)
  • Faculty Publications  (147)

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  • All HBS Web  (357)
    • News  (43)
    • Research  (280)
    • Events  (2)
  • Faculty Publications  (147)
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  • 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).
  • 1988
  • Chapter

The Expected Utility of Playing a Game

By: A. E. Roth
Keywords: Game Theory; Games, Gaming, and Gambling; Motivation and Incentives
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Roth, A. E. "The Expected Utility of Playing a Game." In The Shapley Value: Essays in Honor of Lloyd S. Shapley, edited by A. E. Roth, 51–70. Cambridge University Press, 1988.
  • 2007
  • Working Paper

Correlated Equilibrium and Nash Equilibrium as an Observer's Assessment of the Game

By: John Hillas, Elon Kohlberg and John W. Pratt
Noncooperative games are examined from the point of view of an outside observer who believes that the players are rational and that they know at least as much as the observer. The observer is assumed to be able to observe many instances of the play of the game; these... View Details
Keywords: Decision Choices and Conditions; Game Theory; Cooperation
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Hillas, John, Elon Kohlberg, and John W. Pratt. "Correlated Equilibrium and Nash Equilibrium as an Observer's Assessment of the Game." Harvard Business School Working Paper, No. 08-005, July 2007.
  • Article

Statistical Physics of Human Cooperation

By: Matjaž Perc, Jillian J. Jordan, David G. Rand, Zhen Wang, Stefano Boccaletti and Attila Szolnoki
Extensive cooperation among unrelated individuals is unique to humans, who often sacrifice personal benefits for the common good and work together to achieve what they are unable to execute alone. The evolutionary success of our species is indeed due, to a large... View Details
Keywords: Human Cooperation; Evolutionary Game Theory; Public Goods; Reward; Punishment; Tolerance; Self-organization; Pattern Formation; Cooperation; Behavior; Game Theory
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Perc, Matjaž, Jillian J. Jordan, David G. Rand, Zhen Wang, Stefano Boccaletti, and Attila Szolnoki. "Statistical Physics of Human Cooperation." Physics Reports 687 (May 8, 2017): 1–51.
  • 1977
  • Chapter

A Fixed Point Approach to Stability in Cooperative Games

By: A. E. Roth
Keywords: Game Theory; Balance and Stability; Cooperation
Citation
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Roth, A. E. "A Fixed Point Approach to Stability in Cooperative Games." In Fixed Points: Algorithms and Applications, edited by S. Karamardian, 165–180. Academic Press, 1977.
  • 14 Jun 2007
  • Working Paper Summaries

Evolution Analysis of Large-Scale Software Systems Using Design Structure Matrices and Design Rule Theory

Keywords: by Matthew J. LaMantia, Yuanfang Cai, Alan D. MacCormack & John Rusnak; Video Game; Video Game
  • July– September 2002
  • Article

Predictive Value and the Usefulness of Game Theoretic Models

By: Ido Erev, Alvin E. Roth, Robert L. Slonim and Greg Barron
Keywords: Value; Games, Gaming, and Gambling; Theory
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Erev, Ido, Alvin E. Roth, Robert L. Slonim, and Greg Barron. "Predictive Value and the Usefulness of Game Theoretic Models." International Journal of Forecasting 18, no. 3 (July– September 2002): 359–368.
  • 2020
  • Working Paper

To Infinity and Beyond: Scaling Economic Theories via Logical Compactness

By: Yannai A. Gonczarowski, Scott Duke Kominers and Ran I. Shorrer
Many economic-theoretic models incorporate finiteness assumptions that, while introduced for simplicity, play a real role in the analysis. Such assumptions introduce a conceptual problem, as results that rely on finiteness are often implicitly nonrobust; for example,... View Details
Keywords: Markets; Analysis; Game Theory
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Gonczarowski, Yannai A., Scott Duke Kominers, and Ran I. Shorrer. "To Infinity and Beyond: Scaling Economic Theories via Logical Compactness." Harvard Business School Working Paper, No. 19-127, June 2019. (Revised November 2020.)
  • 1978
  • Chapter

Power and Position: The Utility of Playing a Simple Game

By: A. E. Roth
Keywords: Power and Influence; Status and Position; Game Theory; Games, Gaming, and Gambling
Citation
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Roth, A. E. "Power and Position: The Utility of Playing a Simple Game." In Game Theory and Political Science, edited by P. C. Ordeshook. New York: New York University Press, 1978.
  • Article

Third-Party Punishment as a Costly Signal of High Continuation Probabilities in Repeated Games

By: Jillian J. Jordan and David G. Rand
Why do individuals pay costs to punish selfish behavior, even as third-party observers? A large body of research suggests that reputation plays an important role in motivating such third-party punishment (TPP). Here we focus on a recently proposed reputation-based... View Details
Keywords: Direct Reciprocity; Evolution; Dispersal; Cooperation; Trust; Reputation; Game Theory
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Jordan, Jillian J., and David G. Rand. "Third-Party Punishment as a Costly Signal of High Continuation Probabilities in Repeated Games." Journal of Theoretical Biology 421 (May 21, 2017): 189–202.
  • July 2002
  • Article

The Economist As Engineer: Game Theory, Experimental Economics and Computation As Tools of Design Economics

By: Alvin E Roth
Keywords: Game Theory; Economics; Mathematical Methods; Design
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Roth, Alvin E. "The Economist As Engineer: Game Theory, Experimental Economics and Computation As Tools of Design Economics." Econometrica 70, no. 4 (July 2002): 1341–1378.
  • June 2025
  • Article

Collusion in Brokered Markets

By: John William Hatfield, Scott Duke Kominers and Richard Lowery
High commissions in the U.S. residential real estate agency market present a puzzle for economic theory because brokerage is not a concentrated industry. We model brokered markets as a game in which agents post prices for customers and then choose which other agents to... View Details
Keywords: Real Estate Agents; Real Estate; Realtors; Broker Networks; Brokerage; Brokerage Commissions; "Brokerage Industry; Brokered Markets; Brokering; Brokers; Industrial Organization; Repeated Game Framework; "Repeated Games"; Collusion; Antitrust; Microeconomics; Market Design; Theory; Game Theory; Real Estate Industry
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Hatfield, John William, Scott Duke Kominers, and Richard Lowery. "Collusion in Brokered Markets." Journal of Finance 80, no. 3 (June 2025): 1417–1462.
  • Article

Analyzing Scrip Systems

By: Kris Johnson, David Simchi-Levi and Peng Sun
Scrip systems provide a nonmonetary trade economy for exchange of resources. We model a scrip system as a stochastic game and study system design issues on selection rules to match potential trade partners over time. We show the optimality of one particular rule in... View Details
Keywords: "Repeated Games"; Stochastic Trust Game; Dynamic Program; P2P Lending; Scrip Systems; Artificial Currency; Non-monetary Trade Economies; Marketplace Matching; Currency; Operations; Game Theory
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Johnson, Kris, David Simchi-Levi, and Peng Sun. "Analyzing Scrip Systems." Operations Research 62, no. 3 (May–June 2014): 524–534.
  • November 2006 (Revised November 2009)
  • Course Overview Note

Introduction to Competitive Dynamics: Strategy and Tactics

By: Dennis A. Yao
Provides an overview of the course Competitive Dynamics: Strategy and Tactics and discusses challenges facing those who wish to use game theory to assist in strategic and tactical decision making. View Details
Keywords: Decision Choices and Conditions; Game Theory; Competitive Strategy; Competitive Advantage
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Yao, Dennis A. "Introduction to Competitive Dynamics: Strategy and Tactics." Harvard Business School Course Overview Note 707-475, November 2006. (Revised November 2009.)
  • Research Summary

FOUNDATIONS OF BUSINESS STRATEGY

Pankaj Ghemawat is involved in an ongoing stream of research and course development on the foundations of business strategy. Recent work has included the application of game theory to business strategy, as reported in the book Games Businesses Play, and the... View Details
  • Article

Howard Raiffa: The Art, Science, and Humanity of a Legendary Negotiation Analyst

By: James K. Sebenius
Rightly known as the “father of negotiation analysis,” Howard Raiffa was my thesis advisor, colleague, and friend for over 30 years. The bulk of this article develops an account of his intellectual trajectory from game theory to statistical decision theory to decision... View Details
Keywords: Negotiation Analysis; Bargaining; Howard Raiffa; Negotiation; Personal Development and Career
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Sebenius, James K. "Howard Raiffa: The Art, Science, and Humanity of a Legendary Negotiation Analyst." Negotiation Journal 33, no. 4 (October 2017): 283–307.
  • March 2023
  • Article

Not from Concentrate: Collusion in Collaborative Industries

By: Jordan M. Barry, John William Hatfield, Scott Duke Kominers and Richard Lowery
The chief principle of antitrust law and theory is that reducing market concentration—having more, smaller firms instead of fewer, bigger ones—reduces anticompetitive behavior. We demonstrate that this principle is fundamentally incomplete.

In many... View Details
Keywords: Antitrust; Antitrust Law; Antitrust Theory; Law And Economics; Collusion; Collaboration; Collaborative Industries; Regulation; "Repeated Games"; IPOs; Initial Public Offerings; Underwriters; Real Estate; Real Estate Agents; Realtors; Syndicated Markets; Syndication; Brokers; Market Concentration; Competition; Law; Economics; Collaborative Innovation and Invention; Governing Rules, Regulations, and Reforms; Game Theory; Initial Public Offering
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Barry, Jordan M., John William Hatfield, Scott Duke Kominers, and Richard Lowery. "Not from Concentrate: Collusion in Collaborative Industries." Iowa Law Review 108, no. 3 (March 2023): 1089–1148.
  • 2016
  • Book

Competing Against Luck: The Story of Innovation and Customer Choice

By: Clayton M. Christensen, Taddy Hall, Karen Dillon and David S. Duncan
The foremost authority on innovation and growth presents a path-breaking book every company needs to transform innovation from a game of chance to one in which they develop products and services that customers want to buy and are willing to purchase at a premium price.... View Details
Keywords: Disruptive Innovation; Consumer Behavior
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Christensen, Clayton M., Taddy Hall, Karen Dillon, and David S. Duncan. Competing Against Luck: The Story of Innovation and Customer Choice. New York: Harper Business, 2016.
  • 26 Mar 2024
  • Research & Ideas

How Humans Outshine AI in Adapting to Change

that required increasingly more flexible self-orienting. Like a simplified version of a four-player scenario of the classic video game Mario Kart, each game included four “possible selves,” which were... View Details
Keywords: by Rachel Layne; Technology; Information Technology
  • August 2010 (Revised October 2012)
  • Exercise

To Catch a Vandal: A Power & Influence Exercise

By: Amy J.C. Cuddy, Ruwan Tharindu Gunatilake and Meredith Hodges
This exercise is based on the "Mafia" game created by psychologist Dimma Davidoff, and is designed to give students a broad introduction to multiple theories of influence and to challenge their instincts about which techniques are the most powerful and how they may be... View Details
Keywords: Nonverbal Communication; Knowledge Use and Leverage; Management Analysis, Tools, and Techniques; Management Skills; Groups and Teams; Power and Influence; Trust
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Cuddy, Amy J.C., Ruwan Tharindu Gunatilake, and Meredith Hodges. "To Catch a Vandal: A Power & Influence Exercise." Harvard Business School Exercise 911-013, August 2010. (Revised October 2012.)
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