Please use this identifier to cite or link to this item: http://hdl.handle.net/10419/150114
Authors: 
Di Tillio, Alfredo
Year of Publication: 
2008
Citation: 
[Journal:] Theoretical Economics [ISSN:] 1555-7561 [Volume:] 3 [Year:] 2008 [Issue:] 3 [Pages:] 287-323
Abstract: 
This paper extends Savage's subjective approach to probability and utility from decision problems under exogenous uncertainty to choice in strategic environments. Interactive uncertainty is modeled both explicitly, using hierarchies of preference relations, the analogue of beliefs hierarchies, and implicitly, using preference structures, the analogue of type spaces a la Harsanyi, and it is shown that the two approaches are equivalent. Preference structures can be seen as those sets of hierarchies arising when certain restrictions on preferences, along with the players' common certainty of the restrictions, are imposed. Preferences are a priori assumed to satisfy only very mild properties (reflexivity, transitivity, and monotone continuity). Thus, the results provide a framework for the analysis of behavior in games under essentially any axiomatic structure. An explicit characterization is given for Savage's axioms, and it is shown that a hierarchy of relatively simple preference relations uniquely identifies the decision maker's utilities and beliefs of all orders. Connections with the literature on beliefs hierarchies and correlated equilibria are discussed.
Subjects: 
Subjective probability
preference hierarchies
type spaces
beliefs hierarchies
common belief
expected utility
incomplete information
correlated equilibria
JEL: 
C70
D80
D81
D82
D83
Creative Commons License: 
https://creativecommons.org/licenses/by-nc/3.0
Document Type: 
Article

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