Artikel
On the structure of rationalizability for arbitrary spaces of uncertainty
Weinstein and Yildiz (Econometrica, 2007) have shown that only very weak predictions are robust to mispecifications of higher order beliefs. Whenever a type has multiple rationalizable actions, any of these actions is uniquely rationalizable for some arbitrarily close type. Hence, refinements of rationalizability are not robust. This negative result is obtained under a richness condition, which essentially means that all common knowledge assumptions on payoffs are relaxed. In many settings this condition entails an unnecessarily demanding robustness test. It is therefore natural to explore the structure of rationalizability when arbitrary common knowledge assumptions are relaxed (i.e., without assuming richness). For arbitrary spaces of uncertainty, and for every player i, I construct a set A_{i}^{∞} of actions that are uniquely rationalizable for some hierarchy of beliefs. The main result shows that for any type t_{i}, and any action a_{i} rationalizable for t_{i}, if a_{i} belongs to A_{i}^{∞} and is justified by conjectures concentrated on A_{-i}^{∞}, then there exists a sequence of types converging to t_{i} for which a_{i} is uniquely rationalizable. This result significantly generalizes Weinstein and Yildiz's. Some of its implications are discussed in the context of auctions, equilibrium refinements and in connection with the literature on global games.
- Language
-
Englisch
- Bibliographic citation
-
Journal: Theoretical Economics ; ISSN: 1555-7561 ; Volume: 8 ; Year: 2013 ; Issue: 2 ; Pages: 405-430 ; New Haven, CT: The Econometric Society
- Classification
-
Wirtschaft
Noncooperative Games
- Subject
-
Rationalizability
incomplete information
uniqueness
robustness
refinements
higher order beliefs
- Event
-
Geistige Schöpfung
- (who)
-
Penta, Antonio
- Event
-
Veröffentlichung
- (who)
-
The Econometric Society
- (where)
-
New Haven, CT
- (when)
-
2013
- DOI
-
doi:10.3982/TE861
- Handle
- Last update
-
10.03.2025, 11:43 AM CET
Data provider
ZBW - Deutsche Zentralbibliothek für Wirtschaftswissenschaften - Leibniz-Informationszentrum Wirtschaft. If you have any questions about the object, please contact the data provider.
Object type
- Artikel
Associated
- Penta, Antonio
- The Econometric Society
Time of origin
- 2013
Other Objects (12)
Spaces of uncertainty
Structure of arbitrary purely inseparable extension fields
Spaces of uncertainty - Berlin revisited
The structure of nuclear Fréchet spaces
Lyapunov Exponents for Linear Delay Equations in arbitrary Phase Spaces
Lyapunov exponents for linear delay equations in arbitrary phase spaces
Approximation and Uncertainty Quantification of Systems with Arbitrary Parameter Distributions Using Weighted Leja Interpolation
Uncertainty relations for general phase spaces
An overview of the structure at infinity of representation spaces
Uncertainty and the Institutional Structure of Capitalist Economies
The arbitrary government of D. Bode
Subgroups of Arbitrary even ordinary depth
Spaces of uncertainty
Structure of arbitrary purely inseparable extension fields
Spaces of uncertainty - Berlin revisited
The structure of nuclear Fréchet spaces
Lyapunov Exponents for Linear Delay Equations in arbitrary Phase Spaces
Lyapunov exponents for linear delay equations in arbitrary phase spaces
Approximation and Uncertainty Quantification of Systems with Arbitrary Parameter Distributions Using Weighted Leja Interpolation
Uncertainty relations for general phase spaces
An overview of the structure at infinity of representation spaces
Uncertainty and the Institutional Structure of Capitalist Economies
The arbitrary government of D. Bode
Subgroups of Arbitrary even ordinary depth
Spaces of uncertainty
Structure of arbitrary purely inseparable extension fields
Spaces of uncertainty - Berlin revisited
The structure of nuclear Fréchet spaces
Lyapunov Exponents for Linear Delay Equations in arbitrary Phase Spaces
Lyapunov exponents for linear delay equations in arbitrary phase spaces
Approximation and Uncertainty Quantification of Systems with Arbitrary Parameter Distributions Using Weighted Leja Interpolation
Uncertainty relations for general phase spaces
An overview of the structure at infinity of representation spaces
Uncertainty and the Institutional Structure of Capitalist Economies
The arbitrary government of D. Bode