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Rationalizability and Correlated Equilibria

In: The Language of Game Theory Putting Epistemics into the Mathematics of Games

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  • Adam Brandenburger
  • Eddie Dekel

Abstract

We discuss the unity between the two standard approaches to noncooperative solution concepts for games. The decision-theoretic approach starts from the assumption that the rationality of the players is common knowledge. This leads to the notion of correlated rationalizability. It is shown that correlated rationalizability is equivalent to a posteriori equilibrium — a refinement of subjective correlated equilibrium. Hence a decision-theoretic justification for the equilibrium approach to game theory is provided. An analogous equivalence result is proved between independent rationalizability, which is the appropriate concept if each player believes that the others act independently, and conditionally independent a posteriori equilibrium. A characterization of Nash equilibrium is also provided.

Suggested Citation

  • 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..
  • Handle: RePEc:wsi:wschap:9789814513449_0003
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    Keywords

    Game Theory; Epistemic Game Theory; Foundations; Applied Mathematics; Social Neuroscience; Rationalizability; Nash Equilibrium; Probability; Uncertainty;
    All these keywords.

    JEL classification:

    • C70 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - General
    • C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games

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