Iterated dominance revisited

Amanda Friedenberg () and H. Jerome Keisler ()
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Amanda Friedenberg: University of Arizona
H. Jerome Keisler: University of Wisconsin-Madison

Economic Theory, 2021, vol. 72, issue 2, No 1, 377-421

Abstract: Abstract Epistemic justifications of solution concepts often refer to type structures that are sufficiently rich. One important notion of richness is that of a complete type structure, i.e., a type structure that induces all possible beliefs about types. For instance, it is often said that, in a complete type structure, the set of strategies consistent with rationality and common belief of rationality are the set of strategies that survive iterated dominance. This paper shows that this classic result is false, absent certain topological conditions on the type structure. In particular, it provides an example of a finite game and a complete type structure in which there is no state consistent with rationality and common belief of rationality. This arises because the complete type structure does not induce all hierarchies of beliefs—despite inducing all beliefs about types. This raises the question: Which beliefs does a complete type structure induce? We provide several positive results that speak to that question. However, we also show that, within ZFC, one cannot show that a complete structure induces all second-order beliefs.

Keywords: Iterated dominance; Rationalizability; Rationality and common belief of rationality; Type structures; Epistemic game theory (search for similar items in EconPapers)
JEL-codes: C70 C72 C79 D81 D89 (search for similar items in EconPapers)
Date: 2021
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Citations: View citations in EconPapers (6)

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DOI: 10.1007/s00199-020-01275-z

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