Rationalizability and Correlated Equilibria

Adam Brandenburger and Eddie Dekel

Chapter 3 in The Language of Game Theory:Putting Epistemics into the Mathematics of Games, 2014, pp 43-57 from World Scientific Publishing Co. Pte. Ltd.

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.

Keywords: Game Theory; Epistemic Game Theory; Foundations; Applied Mathematics; Social Neuroscience; Rationalizability; Nash Equilibrium; Probability; Uncertainty (search for similar items in EconPapers)
Date: 2014
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Journal Article: Rationalizability and Correlated Equilibria (1987)
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