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The context of the game

Amanda Friedenberg () and Martin Meier ()
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Amanda Friedenberg: Arizona State University
Martin Meier: Institut für Höhere Studien

Economic Theory, 2017, vol. 63, issue 2, 347-386

Abstract: Abstract We study games of incomplete information and argue that it is important to correctly specify the “context” within which hierarchies of beliefs lie. We consider a situation where the players understand more than the analyst: It is transparent to the players—but not to the analyst—that certain hierarchies of beliefs are precluded. In particular, the players’ type structure can be viewed as a strict subset of the analyst’s type structure. How does this affect a Bayesian equilibrium analysis? One natural conjecture is that this doesn’t change the analysis—i.e., every equilibrium of the players’ type structure can be associated with an equilibrium of the analyst’s type structure. We show that this conjecture is wrong. Bayesian equilibrium may fail an Extension Property. This can occur even in the case where the game is finite and the analyst uses the so-called universal structure (to analyze the game)—and, even, if the associated Bayesian game has an equilibrium. We go on to explore specific situations in which the Extension Property is satisfied.

Keywords: Bayesian games; Universal type structure; Robustness; Hierarchies of beliefs; Context (search for similar items in EconPapers)
JEL-codes: D80 D82 C72 C70 (search for similar items in EconPapers)
Date: 2017
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