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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 present paper presents a more complete theory that expands their solution. Speci cally, 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 justi cation 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.

Suggested Citation

  • Adam Kalai & Ehud Kalai, 2011. "Cooperation in Strategic Games Revisited," Discussion Papers 1512, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    • Handle: RePEc:nwu:cmsems:1512
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    References listed on IDEAS

    as
    1. de Clippel, Geoffroy & Minelli, Enrico, 2004. "Two-person bargaining with verifiable information," Journal of Mathematical Economics, Elsevier, vol. 40(7), pages 799-813, November.
    2. Bernard de Meyer & Ehud Lehrer & Dinah Rosenberg, 2009. "Evaluating information in zero-sum games with incomplete information on both sides," Post-Print halshs-00390625, HAL.
    3. Thomson,William & Lensberg,Terje, 2006. "Axiomatic Theory of Bargaining with a Variable Number of Agents," Cambridge Books, Cambridge University Press, number 9780521027038, November.
    4. Bernard de Meyer & Ehud Lehrer & Dinah Rosenberg, 2009. "Evaluating information in zero-sum games with incomplete information on both sides," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-00390625, HAL.
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    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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