Rationalizability in continuous games
Define a continuous game to be one in which every player's strategy set is a Polish space, and the payoff function of each player is bounded and continuous. We prove that in this class of games the process of sequentially eliminating "never-best-reply" strategies terminates before or at the first uncountable ordinal, and this bound is tight. Also, we examine the connection between this process and common belief of rationality in the universal type space of Mertens and Zamir (1985).
References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- Morris, Stephen & Dekel, Eddie & Fudenberg, Drew, 2007.
"Interim Correlated Rationalizability,"
3196333, Harvard University Department of Economics.
- D. B. Bernheim, 2010.
"Rationalizable Strategic Behavior,"
Levine's Working Paper Archive
514, David K. Levine.
- Adam Brandenburger & Eddie Dekel, 2014.
"Rationalizability and Correlated Equilibria,"
World Scientific Book Chapters,
in: The Language of Game Theory Putting Epistemics into the Mathematics of Games, chapter 3, pages 43-57
World Scientific Publishing Co. Pte. Ltd..
- Pearce, David G, 1984. "Rationalizable Strategic Behavior and the Problem of Perfection," Econometrica, Econometric Society, vol. 52(4), pages 1029-1050, July.
- Lipman Barton L., 1994. "A Note on the Implications of Common Knowledge of Rationality," Games and Economic Behavior, Elsevier, vol. 6(1), pages 114-129, January.
- D. Pearce, 2010. "Rationalizable Strategic Behavior and the Problem of Perfection," Levine's Working Paper Archive 523, David K. Levine.
- Brandenburger, Adam & Friedenberg, Amanda, 2008.
"Intrinsic correlation in games,"
Journal of Economic Theory,
Elsevier, vol. 141(1), pages 28-67, July.
- Brandenburger Adam & Dekel Eddie, 1993.
"Hierarchies of Beliefs and Common Knowledge,"
Journal of Economic Theory,
Elsevier, vol. 59(1), pages 189-198, February.
- Battigalli Pierpaolo & Siniscalchi Marciano, 2003.
"Rationalization and Incomplete Information,"
The B.E. Journal of Theoretical Economics,
De Gruyter, vol. 3(1), pages 1-46, June.
- Friedenberg, Amanda, 2010. "When do type structures contain all hierarchies of beliefs?," Games and Economic Behavior, Elsevier, vol. 68(1), pages 108-129, January.
- Apt Krzysztof R., 2007. "The Many Faces of Rationalizability," The B.E. Journal of Theoretical Economics, De Gruyter, vol. 7(1), pages 1-39, May.
When requesting a correction, please mention this item's handle: RePEc:eee:mateco:v:46:y:2010:i:5:p:912-924. See general information about how to correct material in RePEc.
If references are entirely missing, you can add them using this form.