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Collaborative Dominance: When Doing Unto Others As You Would Have Them Do Unto You Is Reasonable

Author

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  • Souza, Filipe
  • Rêgo, Leandro

Abstract

In this article, we analyze how reasonable it is to play according to some Nash equilibria if players have a preference for one of their opponents’ strategies. For this, we propose the concepts of collaborative dominance and collaborative equilibrium. First we prove that, when the collaborative equilibrium exists it is always efficient, what can be seen as a focal property. Further we argue that a reason for players choosing not to collaborate is if they are focusing in security instead of efficiency, in which case they would prefer to play maximin strategies. This argument allows us to reduce the hall of reasonable equilibria for games where a collaborative equilibrium exists. Finally, we point out that two-player zero-sum games do not have collaborative equilibrium and, moreover, if there exists a strategy profile formed only by collaboratively dominated actions it is a Nash equilibrium in such kind of game.

Suggested Citation

  • Souza, Filipe & Rêgo, Leandro, 2012. "Collaborative Dominance: When Doing Unto Others As You Would Have Them Do Unto You Is Reasonable," MPRA Paper 43408, University Library of Munich, Germany.
  • Handle: RePEc:pra:mprapa:43408
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    File URL: https://mpra.ub.uni-muenchen.de/43408/1/MPRA_paper_43408.pdf
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    References listed on IDEAS

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    1. John C. Harsanyi & Reinhard Selten, 1988. "A General Theory of Equilibrium Selection in Games," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262582384, January.
    2. R. J. Aumann & M. Maschler, 1972. "Some Thoughts on the Minimax Principle," Management Science, INFORMS, vol. 18(5-Part-2), pages 54-63, January.
    3. Robert J. Leonard, 1995. "From Parlor Games to Social Science: Von Neumann, Morgenstern, and the Creation of Game Theory, 1928-1994," Journal of Economic Literature, American Economic Association, vol. 33(2), pages 730-761, June.
    4. Aumann, Robert J, 1987. "Correlated Equilibrium as an Expression of Bayesian Rationality," Econometrica, Econometric Society, vol. 55(1), pages 1-18, January.
    5. Aumann, Robert J., 1974. "Subjectivity and correlation in randomized strategies," Journal of Mathematical Economics, Elsevier, vol. 1(1), pages 67-96, March.
    6. Vitaly Pruzhansky, 2011. "Some interesting properties of maximin strategies," International Journal of Game Theory, Springer;Game Theory Society, vol. 40(2), pages 351-365, May.
    7. Martin J. Osborne & Ariel Rubinstein, 1994. "A Course in Game Theory," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262650401, January.
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    More about this item

    Keywords

    Nash Equilibrium; Collaborative Dominance; Two-Players Zero-Sum Games;

    JEL classification:

    • C7 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory

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