Critical types

Jeffrey C. Ely; Marcin Peski

doi:10.1093/restud/rdq035

Critical types

Jeffrey C. Ely^*, Marcin Peski

^*Corresponding author for this work

Economics

Research output: Contribution to journal › Article › peer-review

12 Scopus citations

Abstract

How can we know in advance whether simplifying assumptions about beliefs will make a difference in the conclusions of game-theoretic models? We define critical types to be types whose rationalizable correspondence is sensitive to assumptions about arbitrarily high-order beliefs. We show that a type is critical if and only if it exhibits common belief in some non-trivial event. We use this characterization to show that all types in commonly used type spaces are critical. On the other hand, we show that regular types (types that are not critical) are generic, although perhaps inconvenient to use in applications.

Original language	English (US)
Pages (from-to)	907-937
Number of pages	31
Journal	Review of Economic Studies
Volume	78
Issue number	3
DOIs	https://doi.org/10.1093/restud/rdq035
State	Published - Jul 1 2011

Funding

Acknowledgment. Both authors acknowledge National Science Foundation grant #0958856. We thank Yi-Chun Chen for outstanding research assistance. We are grateful to the editor, Andrea Prat, and three anonymous referees for detailed comments. We also thank Muhamet Yildiz for suggestions that helped improve the exposition. We take all the blame.

Keywords

Higher-order beliefs
Robustness

ASJC Scopus subject areas

Economics and Econometrics

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10.1093/restud/rdq035

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title = "Critical types",

abstract = "How can we know in advance whether simplifying assumptions about beliefs will make a difference in the conclusions of game-theoretic models? We define critical types to be types whose rationalizable correspondence is sensitive to assumptions about arbitrarily high-order beliefs. We show that a type is critical if and only if it exhibits common belief in some non-trivial event. We use this characterization to show that all types in commonly used type spaces are critical. On the other hand, we show that regular types (types that are not critical) are generic, although perhaps inconvenient to use in applications.",

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N2 - How can we know in advance whether simplifying assumptions about beliefs will make a difference in the conclusions of game-theoretic models? We define critical types to be types whose rationalizable correspondence is sensitive to assumptions about arbitrarily high-order beliefs. We show that a type is critical if and only if it exhibits common belief in some non-trivial event. We use this characterization to show that all types in commonly used type spaces are critical. On the other hand, we show that regular types (types that are not critical) are generic, although perhaps inconvenient to use in applications.

AB - How can we know in advance whether simplifying assumptions about beliefs will make a difference in the conclusions of game-theoretic models? We define critical types to be types whose rationalizable correspondence is sensitive to assumptions about arbitrarily high-order beliefs. We show that a type is critical if and only if it exhibits common belief in some non-trivial event. We use this characterization to show that all types in commonly used type spaces are critical. On the other hand, we show that regular types (types that are not critical) are generic, although perhaps inconvenient to use in applications.

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KW - Robustness

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Critical types

Abstract

Funding

Keywords

ASJC Scopus subject areas

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