Conditional belief types
We study type spaces where a player's type at a state is a conditional probability on the space. We axiomatize these spaces using conditional belief operators, examining three additional axioms of increasing strength. First, introspection, which requires the agent to be unconditionally certain of her beliefs. Second, echo, according to which the unconditional beliefs implied by the condition must be held given the condition. Third, determination, which says that the conditional beliefs are the unconditional beliefs that are conditionally certain. Echo implies that conditioning on an event is the same as conditioning on the event being certain, which formalizes the standard informal interpretation of conditional probability. The game-theoretic application of our model, discussed within an example, sheds light on a number of issues in the analysis of extensive form games. Type spaces are closely related to the sphere models of counterfactual conditionals and to models of hypothetical knowledge.
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- Samet, Dov, 1998.
"Common Priors and Separation of Convex Sets,"
Games and Economic Behavior,
Elsevier, vol. 24(1-2), pages 172-174, July.
- Dov Samet, 1997. "Common Priors and Separation of Convex Sets," Game Theory and Information 9701002, EconWPA.
- Monderer, Dov & Samet, Dov & Shapley, Lloyd S, 1992. "Weighted Values and the Core," International Journal of Game Theory, Springer;Game Theory Society, vol. 21(1), pages 27-39.
- Joseph Y. Halpern, 1999. "Hypothetical knowledge and counterfactual reasoning," International Journal of Game Theory, Springer;Game Theory Society, vol. 28(3), pages 315-330.
- Samet, Dov, 2000. "Quantified Beliefs and Believed Quantities," Journal of Economic Theory, Elsevier, vol. 95(2), pages 169-185, December.
- Dov Samet, 1998. "Quantified beliefs and believed quantities," Game Theory and Information 9805003, EconWPA.
- Samet, Dov, 1996. "Hypothetical Knowledge and Games with Perfect Information," Games and Economic Behavior, Elsevier, vol. 17(2), pages 230-251, December.
- Dov Samet, 1994. "Hypothetical Knowledge and Games with Perfect Information," Game Theory and Information 9408001, EconWPA, revised 17 Aug 1994.
- Feinberg, Yossi, 2005. "Subjective reasoning--dynamic games," Games and Economic Behavior, Elsevier, vol. 52(1), pages 54-93, July.
- Lawrence Blume & Adam Brandenburger & Eddie Dekel, 2014. "Lexicographic Probabilities and Choice Under Uncertainty," World Scientific Book Chapters,in: The Language of Game Theory Putting Epistemics into the Mathematics of Games, chapter 6, pages 137-160 World Scientific Publishing Co. Pte. Ltd..
- Blume, Lawrence & Brandenburger, Adam & Dekel, Eddie, 1991. "Lexicographic Probabilities and Choice under Uncertainty," Econometrica, Econometric Society, vol. 59(1), pages 61-79, January.
- Heifetz, Aviad & Mongin, Philippe, 2001. "Probability Logic for Type Spaces," Games and Economic Behavior, Elsevier, vol. 35(1-2), pages 31-53, April.
- Heifetz, A. & Mongin, P., 1998. "Probability Logic for Type Spaces," Papers 9825, Paris X - Nanterre, U.F.R. de Sc. Ec. Gest. Maths Infor..
- A. Heifetz & Ph. Mongin, 1998. "Probability logic for type spaces," THEMA Working Papers 98-25, THEMA (THéorie Economique, Modélisation et Applications), Université de Cergy-Pontoise.
- Halpern, Joseph Y., 2010. "Lexicographic probability, conditional probability, and nonstandard probability," Games and Economic Behavior, Elsevier, vol. 68(1), pages 155-179, January.
- Samet, Dov, 1999. "Bayesianism without learning," Research in Economics, Elsevier, vol. 53(2), pages 227-242, June.
- Myerson, Roger B, 1986. "Multistage Games with Communication," Econometrica, Econometric Society, vol. 54(2), pages 323-358, March.
- Roger B. Myerson, 1984. "Multistage Games with Communication," Discussion Papers 590, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
- Roger B. Myerson, 1986. "Axiomatic Foundations of Bayesian Decision Theory," Discussion Papers 671, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
- Battigalli, Pierpaolo & Siniscalchi, Marciano, 1999. "Hierarchies of Conditional Beliefs and Interactive Epistemology in Dynamic Games," Journal of Economic Theory, Elsevier, vol. 88(1), pages 188-230, September.
- Pierpaolo Battigalli, "undated". "Hierarchies of Conditional Beliefs and Interactive Epistemology in Dynamic Games," Working Papers 111, IGIER (Innocenzo Gasparini Institute for Economic Research), Bocconi University.
- John C. Harsanyi, 1967. "Games with Incomplete Information Played by "Bayesian" Players, I-III Part I. The Basic Model," Management Science, INFORMS, vol. 14(3), pages 159-182, November.
- Battigalli, Pierpaolo & Siniscalchi, Marciano, 2002. "Strong Belief and Forward Induction Reasoning," Journal of Economic Theory, Elsevier, vol. 106(2), pages 356-391, October.
- Samet, Dov, 1998. "Iterated Expectations and Common Priors," Games and Economic Behavior, Elsevier, vol. 24(1-2), pages 131-141, July. Full references (including those not matched with items on IDEAS)
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