Keisler, H. Jerome and Lee, Byung Soo (2011): Common assumption of rationality.
Download (475Kb) | Preview
In this paper, we provide an epistemic characterization of iterated admissibility (IA), i.e., iterated elimination of weakly dominated strategies. We show that rationality and common assumption of rationality (RCAR) in complete lexicographic type structures implies IA, and that there exist such structures in which RCAR can be satisfied. Our result is unexpected in light of a negative result in Brandenburger, Friedenberg, and Keisler (2008) (BFK) that shows the impossibility of RCAR in complete continuous structures. We also show that every complete structure with RCAR has the same types and beliefs as some complete continuous structure. This enables us to reconcile and interpret the difference between our results and BFK’s. Finally, we extend BFK’s framework to obtain a single structure that contains a complete structure with an RCAR state for every game. This gives a game-independent epistemic condition for IA.
|Item Type:||MPRA Paper|
|Original Title:||Common assumption of rationality|
|English Title:||Common Assumption of Rationality|
|Keywords:||Epistemic game theory; rationality; admissibility; iterated weak dominance; assumption; completeness; Borel Isomorphism Theorem; o-minimality|
|Subjects:||D - Microeconomics > D8 - Information, Knowledge, and Uncertainty > D80 - General
C - Mathematical and Quantitative Methods > C7 - Game Theory and Bargaining Theory > C72 - Noncooperative Games
|Depositing User:||Byung Soo Lee|
|Date Deposited:||01. Nov 2011 23:32|
|Last Modified:||14. Feb 2013 07:39|
Kenneth J. Arrow. Alternative approaches to the theory of choice in risk-taking situations. Econometrica, 19(4):404–437, 1951.
Robert Aumann. Agreeing to disagree. Annals of Statistics, 4(6):1236–1239, 1976.
Paulo Barelli and Spyros Galanis. Admissibility and event-rationality. mimeo, 2010.
Pierpaolo Battigalli. Strategic rationality orderings and the best rationalization principle. Games and Economic Behavior, 13(2):178–200, 1996.
B. Douglas Bernheim. Rationalizable strategic behavior. Econometrica, 52(4):1007–1028, 1984.
Lawrence Blume, Adam Brandenburger, and Eddie Dekel. Lexicographic probabilities and choice under uncertainty. Econometrica, 59(1):61–79, 1991a.
Lawrence Blume, Adam Brandenburger, and Eddie Dekel. Lexicographic probabilities and equilibrium refinements. Econometrica, 59(1):81–98, 1991b.
Adam Brandenburger and Eddie Dekel. Rationalizability and correlated equilibria. Econometrica, 55(6):1391–1402, 1987a.
Adam Brandenburger and Eddie Dekel. Common knowledge with probability 1. Journal of Mathematical Economics, 16(3):237–245, 1987b.
Adam Brandenburger, Amanda Friedenberg, and H. Jerome Keisler. Admissibility in games. Econometrica, 76(2):307–352, 2008.
Amanda Friedenberg. When do type structures contain all hierarchies of beliefs? Games and Economic Behavior, 68(1):108–129, 2010.
Robert M. Hardt. Semi-algebraic local-triviality in semi-algebraic mappings. American Journal of Mathematics, 102(2):291–302, 1980.
John C. Harsanyi. Games with incomplete information played by “Bayesian” players, I-III. part I. the basic model. Management Science, 14(3):159–182, 1967.
Alexander S. Kechris. Classical Descriptive Set Theory. Springer-Verlag, New York, 1995.
David Lewis. Convention: A Philosophical Study. Harvard University Press, 1969.
R. Duncan Luce and Howard Raiffa. Games and Decisions. Wiley, New York, NY, 1957.
Dov Monderer and Dov Samet. Approximating common knowledge with common beliefs. Games and Economic Behavior, 1(2):170–190, 1989.
David G. Pearce. Rationalizable strategic behavior and the problem of perfection. Econometrica, 52(4):1029–1050, 1984.
Larry Samuelson. Dominated strategies and common knowledge. Games and Economic Behavior, 4(2):284–313, 1992.
Leonard J. Savage. The Foundations of Statistics. Dover, New York, NY, 1954.
Dale O. Stahl. Lexicographic rationalizability and iterated admissibility. Economic Letters, 47(2):155–159, 1995.
Tommy Chin-Chiu Tan and Sérgio Werlang. The Bayesian foundations of solution concepts of games. Journal of Economic Theory, 45(2):370–391, 1988.
Alfred Tarski. A Decision Method for Elementary Algebra and Geometry. RAND Corporation, Berkeley and Los Angeles, second edition, 1951.
Lau van den Dries. Tame Topology and O-minimal Structures. Number 248 in London Mathematical Society Lecture Note Series. Cambridge University Press, 1998.
John von Neumann and Oskar Morgenstern. Theory of Games and Economic Behavior. Princeton University Press, Princeton, NJ, 1944.
Abraham Wald. Contributions to the theory of statistical estimation and testing hypotheses. The Annals of Mathematical Statistics, 10(4):239–326, 1939.
Chih-Chun Yang. Epistemic foundations of admissibility. mimeo, 2010.