Cited By
View all- Bach CCabessa J(2011)Agreeing to disagree with limit knowledgeProceedings of the Third international conference on Logic, rationality, and interaction10.5555/2050423.2050426(51-60)Online publication date: 10-Oct-2011
Limit knowledge of rationality
Pages 34 - 40
Abstract
Epistemic game theory scrutinizes the relationship between knowledge, belief and choice of rational players. Here, the relationship between common knowledge and the limit of higher-order mutual knowledge is studied from a topological point of view. More precisely, the new epistemic operator limit knowledge defined as the topological limit of higher-order mutual knowledge is introduced. We then show that limit knowledge of the specific event rationality can be used for epistemic-topological characterizations of solution concepts in games. As a first step towards this scheme, we construct a game where limit knowledge of rationality appears to be a cogent strict refinement of common knowledge of rationality in terms of solution concepts. More generally, it is shown that for any given game and epistemic model of it satisfying some specific condition, every possible epistemic hypothesis as well as as every solution concept can be characterized by limit knowledge of rationality for some appropriate topology.
References
[1]
R. J. Aumann (1976). Agreeing to Disagree. Annals of Statistics 4, 1236--1239.
[2]
R. J. Aumann (1987). Correlated Equilibrium as an Expression of Bayesian Rationality. Econometrica 55, 1--18.
[3]
R. J. Aumann (1995). Backward Induction and Common Knowledge of Rationality. Games and Economic Behavior 8, 6--19.
[4]
R. J. Aumann (1996). Reply to Binmore. Games and Economic Behavior 17, 138--146.
[5]
R. J. Aumann (1999a). Interactive Epistemology I: Knowledge. International Journal of Game Theory 28, 263--300.
[6]
R. J. Aumann (1999b). Interactive Epistemology II: Probability. International Journal of Game Theory 28, 301--314.
[7]
R. J. Aumann (2005). Musings on Information and Knowledge. Econ Journal Watch 2, 88--96.
[8]
R. J. Aumann and A. Brandenburger (1995). Epistemic Conditions for Nash Equilibrium. Econometrica 63, 1161--1180.
[9]
J. Barwise (1988). Three Views of Common Knowledge. In M. Y. Vardi (ed.), Theoretical Aspects of Reasoning about Knowledge. Proceedings of the Second Conference (TARK 1988), 227--243. Morgan Kaufmann.
[10]
J. van Benthem and D. Sarenac (2005). The Geometry of Knowledge. In J.-Y. Béziau et al. (ed.), Aspects of Universal Logic, 1--31. Centre de Recherches Sémiologiques, Université de Neuchâtel.
[11]
M. Dufwenberg and M. Stegeman (2002). Existence and Uniqueness of Maximal Reductions under Iterated Strict Dominance. Econometrica 70, 2007--2023.
[12]
B. L. Lipman (1994). A Note on the Implications of Common Knowledge of Rationality. Journal of Economic Theory 45, 370--391.
[13]
T. C. C. Tan and S. R. C. Werlang (1988). The Bayesian Foundation of Solution Concepts of Games. Journal of Economic Theory 45, 370--391.
[14]
D. K. Lewis (1969). Convention. Harvard University Press.
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Association for Computing Machinery
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Published: 06 July 2009
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TARK '09
TARK '09: The 11th conference on Theoretical aspects of rationality and knowledge
July 6 - 8, 2009
California
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TARK '09 Paper Acceptance Rate 29 of 77 submissions, 38%;
Overall Acceptance Rate 61 of 177 submissions, 34%
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View all- Bach CCabessa J(2011)Agreeing to disagree with limit knowledgeProceedings of the Third international conference on Logic, rationality, and interaction10.5555/2050423.2050426(51-60)Online publication date: 10-Oct-2011
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