Subjective Expected Utility in Games

IGIER Working Paper No. 311

52 Pages Posted: 27 Oct 2009

See all articles by Alfredo Di Tillio

Alfredo Di Tillio

Bocconi University - Department of Economics

Date Written: October 27, 2009


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 à 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.

Suggested Citation

Di Tillio, Alfredo, Subjective Expected Utility in Games (October 27, 2009). IGIER Working Paper No. 311, Available at SSRN: or

Alfredo Di Tillio (Contact Author)

Bocconi University - Department of Economics ( email )



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