Conditional belief types |
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| Affiliation: | 1. IGIER and Department of Economics, Università Bocconi, Italy;2. Computer Science Department, Cornell University, USA;3. Faculty of Management, Tel Aviv University, Israel;1. University of Heidelberg, Germany;2. University of Amsterdam and Tinbergen Institute, The Netherlands;1. University of Cologne, Department of Economics, Albertus-Magnus Platz, D-50923 Cologne, Germany;2. Department of Economics, University of Essex, Wivenhoe Park, Colchester CO4 3SQ, United Kingdom;1. ICREA, Universitat Pompeu Fabra and Barcelona GSE, Spain;2. Universitat Autonoma de Barcelona and Barcelona GSE, Spain;3. University of Michigan, United States;1. Department of Government, University of Essex, Wivenhoe Park, Colchester CO4 3SQ, United Kingdom;2. Faculty of Engineering, Information and Systems, University of Tsukuba, 1-1-1 Tennodai, Tsukuba, Ibaraki 305-8573, Japan;3. WZB Berlin Social Science Center, Reichpietschufer 50, D-10785 Berlin, Germany;4. Department of Economics, University of Heidelberg, Bergheimer Str. 58, 69115 Heidelberg, Germany |
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| Abstract: | 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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| Keywords: | Conditional probability Type spaces Hypothetical knowledge Counterfactuals |
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