ubjective Expected Utility in Games
Number: 311
Year: 2006
Author(s): Alfredo Di Tillio
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
implicitly - using preference structures, the analogue of type spaces 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.
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
implicitly - using preference structures, the analogue of type spaces 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.
Kewords: Subjective probability, Preference hierarchies, Type spaces, Beliefs
hierarchies, Common belief, Expected utility, Incomplete information,
Correlated equilibria