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Cooperation in Strategic Games Revisited

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  • Adam Kalai
  • Ehud Kalai

Abstract

For two-person complete-information strategic games with transferable utility, all major variable-threat bargaining and arbitration solutions coincide. This confluence of solutions by luminaries such as Nash, Harsanyi, Raiffa, and Selten, is more than mere coincidence. Staying in the class of two-person games with transferable unility, the article presents a more complete theory that expands their solution. Specifically, it presents: (1) a decomposition of a game into cooperative and competitive components, (2) an intuitive and computable closed-form formula for the solution, (3) an axiomatic justification of the solution, and (4) a generalization of the solution to games with private signals, along with an arbitration scheme that implements it. The objective is to restart research on cooperative solutions to strategic games and their applications. JEL Codes: C71, C72, C78. Copyright 2013, Oxford University Press.

Suggested Citation

  • Adam Kalai & Ehud Kalai, 2013. "Cooperation in Strategic Games Revisited," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 128(2), pages 917-966.
    • Handle: RePEc:oup:qjecon:v:128:y:2013:i:2:p:917-966
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    File URL: http://hdl.handle.net/10.1093/qje/qjs074
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    Cited by:

    1. M. G. Fiestras-Janeiro & I. García-Jurado & A. Meca & M. A. Mosquera, 2020. "On benefits of cooperation under strategic power," Annals of Operations Research, Springer, vol. 288(1), pages 285-306, May.
    2. Joseph Abdou & Nikolaos Pnevmatikos & Marco Scarsini & Xavier Venel, 2022. "Decomposition of Games: Some Strategic Considerations," Mathematics of Operations Research, INFORMS, vol. 47(1), pages 176-208, February.
    3. Geoffroy de Clippel & Jack Fanning & Kareen Rozen, 2022. "Bargaining over Contingent Contracts under Incomplete Information," American Economic Review, American Economic Association, vol. 112(5), pages 1522-1554, May.
    4. Thomas Demuynck & Christian Seel & Giang Tran, 2022. "An Index of Competitiveness and Cooperativeness for Normal-Form Games," American Economic Journal: Microeconomics, American Economic Association, vol. 14(2), pages 215-239, May.
    5. Roberto Serrano, 2020. "Sixty-Seven Years of the Nash Program: Time for Retirement?," Working Papers 2020-20, Brown University, Department of Economics.
    6. Daniel G. Arce, 2018. "On the cooperative and competitive aspects of strategic monitoring," Rationality and Society, , vol. 30(3), pages 377-390, August.
    7. Santiago Guisasola & Donald Saari, 2020. "With Potential Games, Which Outcome Is Better?," Games, MDPI, vol. 11(3), pages 1-20, August.
    8. Kiho Yoon, 2020. "Bilateral trading with contingent contracts," International Journal of Game Theory, Springer;Game Theory Society, vol. 49(2), pages 445-461, June.
    9. Gallin, Joshua & Verbrugge, Randal J., 2019. "A theory of sticky rents: Search and bargaining with incomplete information," Journal of Economic Theory, Elsevier, vol. 183(C), pages 478-519.
    10. David Gaddis Ross, 2018. "Using cooperative game theory to contribute to strategy research," Strategic Management Journal, Wiley Blackwell, vol. 39(11), pages 2859-2876, November.
    11. Salamanca, Andrés, 2020. "On the values of Bayesian cooperative games with sidepayments," Mathematical Social Sciences, Elsevier, vol. 108(C), pages 38-49.
    12. Mikael Böörs & Tobias Wängberg & Tom Everitt & Marcus Hutter, 2022. "Classification by decomposition: a novel approach to classification of symmetric $$2\times 2$$ 2 × 2 games," Theory and Decision, Springer, vol. 93(3), pages 463-508, October.
    13. Stefan Penczynski & Stefania Sitzia & Jiwei Zheng, 2023. "Decomposed games, focal points, and the framing of collective and individual interests," Working Paper series, University of East Anglia, Centre for Behavioural and Experimental Social Science (CBESS) 20-04, School of Economics, University of East Anglia, Norwich, UK..
    14. Shiran Rachmilevitch, 2022. "Pre-bargaining Investment Implies a Pareto Ranking of Bargaining Solutions," Group Decision and Negotiation, Springer, vol. 31(4), pages 769-787, August.
    15. Ryan Kendall, 2022. "Decomposing coordination failure in stag hunt games," Experimental Economics, Springer;Economic Science Association, vol. 25(4), pages 1109-1145, September.
    16. Stefan Penczynski & Stefania Sitzia & Jiwei Zheng, 2020. "Compound games, focal points, and the framing of collective and individual interests," Working Papers 305138214, Lancaster University Management School, Economics Department.
    17. Roberto Serrano, 2021. "Sixty-seven years of the Nash program: time for retirement?," SERIEs: Journal of the Spanish Economic Association, Springer;Spanish Economic Association, vol. 12(1), pages 35-48, March.
    18. Olivier GOSSNER & Jean-François MERTENS, 2020. "The Value of Information in Zero-Sum Games," Working Papers 2020-19, Center for Research in Economics and Statistics.
    19. Guennady Ougolnitsky & Alexey Korolev, 2023. "Game-Theoretic Models of Coopetition in Cournot Oligopoly," Stats, MDPI, vol. 6(2), pages 1-20, May.

    More about this item

    JEL classification:

    • C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games
    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • C78 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Bargaining Theory; Matching Theory

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