Subjective Expected Utility in Games
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.
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- Harsanyi, John C., 1994.
"Games with Incomplete Information,"
Nobel Prize in Economics documents
1994-1, Nobel Prize Committee.
- Monderer, Dov & Samet, Dov, 1989. "Approximating common knowledge with common beliefs," Games and Economic Behavior, Elsevier, vol. 1(2), pages 170-190, June.
- Battigalli, Pierpaolo & Siniscalchi, Marciano, 2002. "Strong Belief and Forward Induction Reasoning," Journal of Economic Theory, Elsevier, vol. 106(2), pages 356-391, October.
- FORGES , Françoise, 1993.
"Five Legitimate Definitions of Correlated Equilibrium in Games with Incomplete Information,"
CORE Discussion Papers
1993009, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
- FORGES, Françoise, . "Five legitimate definitions of correlated equilibrium in games with incomplete informations," CORE Discussion Papers RP -1071, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
- R. Aumann, 2010.
"Correlated Equilibrium as an expression of Bayesian Rationality,"
513, UCLA Department of Economics.
- Aumann, Robert J, 1987. "Correlated Equilibrium as an Expression of Bayesian Rationality," Econometrica, Econometric Society, vol. 55(1), pages 1-18, January.
- Robert J. Aumann, 2010. "Correlated Equilibrium as an expression of Bayesian Rationality," Levine's Working Paper Archive 661465000000000377, David K. Levine.
- Adam Brandenburger & Amanda Friedenberg & H. Jerome Keisler, 2008. "Admissibility in Games," Econometrica, Econometric Society, vol. 76(2), pages 307-352, 03.
- Battigalli, Pierpaolo & Bonanno, Giacomo, 1999. "Editors' note," Research in Economics, Elsevier, vol. 53(3), pages 243-246, September.
- Joseph B. Kadane & Patrick D. Larkey, 1982. "Subjective Probability and the Theory of Games," Management Science, INFORMS, vol. 28(2), pages 113-120, February.
- Aviad Heifetz & Dov Samet, 1996.
"Topology-Free Typology of Beliefs,"
Game Theory and Information
9609002, EconWPA, revised 17 Sep 1996.
- Aumann, Robert J., 1974.
"Subjectivity and correlation in randomized strategies,"
Journal of Mathematical Economics,
Elsevier, vol. 1(1), pages 67-96, March.
- R. Aumann, 2010. "Subjectivity and Correlation in Randomized Strategies," Levine's Working Paper Archive 389, David K. Levine.
- AUMANN, Robert J., . "Subjectivity and correlation in randomized strategies," CORE Discussion Papers RP -167, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
- Brandenburger Adam & Dekel Eddie, 1993. "Hierarchies of Beliefs and Common Knowledge," Journal of Economic Theory, Elsevier, vol. 59(1), pages 189-198, February.
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