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Pairwise epistemic conditions for correlated rationalizability

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  • Tsakas, Elias

Abstract

We provide a foundation for correlated rationalizability by means of pairwise epistemic conditions imposed only on some pairs of players. Indeed, we show that pairwise mutual belief, for some pairs of players, of (i) the game payoffs, (ii) rationality, and (iii) deeming possible only strategy profiles that receive positive probability by the actual conjectures suffice for correlated rationalizability when there is a common prior. Moreover, we show that our epistemic conditions do not require nor imply mutual belief of rationality. Finally, we discuss the relationship between correlated rationalizability and Nash equilibrium on the basis of the respective pairwise epistemic conditions for each of the two concepts.

Suggested Citation

  • Tsakas, Elias, 2013. "Pairwise epistemic conditions for correlated rationalizability," Mathematical Social Sciences, Elsevier, vol. 66(3), pages 379-384.
    • Handle: RePEc:eee:matsoc:v:66:y:2013:i:3:p:379-384
    DOI: 10.1016/j.mathsocsci.2013.08.003
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    1. Tan, Tommy Chin-Chiu & da Costa Werlang, Sergio Ribeiro, 1988. "The Bayesian foundations of solution concepts of games," Journal of Economic Theory, Elsevier, vol. 45(2), pages 370-391, August.
    2. Perea,Andrés, 2012. "Epistemic Game Theory," Cambridge Books, Cambridge University Press, number 9781107401396, September.
    3. Adam Brandenburger & Eddie Dekel, 2014. "Rationalizability and Correlated Equilibria," World Scientific Book Chapters, in: The Language of Game Theory Putting Epistemics into the Mathematics of Games, chapter 3, pages 43-57, World Scientific Publishing Co. Pte. Ltd..
    4. Bernheim, B Douglas, 1984. "Rationalizable Strategic Behavior," Econometrica, Econometric Society, vol. 52(4), pages 1007-1028, July.
    5. Perea,Andrés, 2012. "Epistemic Game Theory," Cambridge Books, Cambridge University Press, number 9781107008915, September.
    6. Robert Aumann & Adam Brandenburger, 2014. "Epistemic Conditions for Nash Equilibrium," World Scientific Book Chapters, in: The Language of Game Theory Putting Epistemics into the Mathematics of Games, chapter 5, pages 113-136, World Scientific Publishing Co. Pte. Ltd..
    7. Bach, Christian W. & Tsakas, Elias, 2014. "Pairwise epistemic conditions for Nash equilibrium," Games and Economic Behavior, Elsevier, vol. 85(C), pages 48-59.
    8. Pearce, David G, 1984. "Rationalizable Strategic Behavior and the Problem of Perfection," Econometrica, Econometric Society, vol. 52(4), pages 1029-1050, July.
    9. Zambrano, Eduardo, 2008. "Epistemic conditions for rationalizability," Games and Economic Behavior, Elsevier, vol. 63(1), pages 395-405, May.
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