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

  • Souza, Filipe
  • Rêgo, Leandro
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    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.

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    File URL: http://mpra.ub.uni-muenchen.de/43408/1/MPRA_paper_43408.pdf
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    Paper provided by University Library of Munich, Germany in its series MPRA Paper with number 43408.

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    Date of creation: 20 Nov 2012
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    Handle: RePEc:pra:mprapa:43408
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    1. Vitaly Pruzhansky, 2011. "Some interesting properties of maximin strategies," International Journal of Game Theory, Springer, vol. 40(2), pages 351-365, May.
    2. AUMANN, Robert J., . "Subjectivity and correlation in randomized strategies," CORE Discussion Papers RP -167, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    3. Robert J. Aumann, 2010. "Correlated Equilibrium as an expression of Bayesian Rationality," Levine's Working Paper Archive 661465000000000377, David K. Levine.
    4. Martin J Osborne & Ariel Rubinstein, 2009. "A Course in Game Theory," Levine's Bibliography 814577000000000225, UCLA Department of Economics.
    5. Robert J. Leonard, 1993. "From Von Neumann to Nash: Economics, Game Theory and Social Process," Cahiers de recherche du Département des sciences économiques, UQAM 9313, Université du Québec à Montréal, Département des sciences économiques.
    6. R. J. Aumann & M. Maschler, 1972. "Some Thoughts on the Minimax Principle," Management Science, INFORMS, vol. 18(5-Part-2), pages 54-63, January.
    7. Robert J. Leonard, 1993. "Reason, Ethics and Rigour: Morgenstern, Menger, and Mathematical Economics, 1928 - 1944," Cahiers de recherche du Département des sciences économiques, UQAM 9403, Université du Québec à Montréal, Département des sciences économiques.
    8. 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, June.
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