An Epistemic Rationale for Order-Independence
The issue of the order-dependence of iterative deletion processes is well-known in the game theory community, and meanwhile conditions on the dominance concept underlying these processes have been detected which ensure order-independence (see e.g. the criteria of Gilboa et al., 1990 and Apt, 2011). While this kind of research deals with the technical issue, whether certain iterative deletion processes are order-independent, or not, our focus is on the normative issue, whether there are good reasons for employing order-independent iterative deletion processes on strategic games. We tackle this question from an epistemic perspective and attempt to figure out, whether order-independence contains some specific epistemic meaning. It turns out that, under fairly general preconditions on the choice rules underlying the iterative deletion processes, the order-independence of these deletion processes coincides with the epistemic characterization of their solutions by the common belief of choice-rule following behavior. The presumably most challenging precondition of this coincidence is the property of the independence of irrelevant acts. We also examine the consequences of two weakenings of this property on our epistemic motivation for order-independence. Although the coincidence mentioned above breaks down for both weakenings, still there exist interesting links between the order-independence of iterative deletion processes and the common belief of following the choice rules, on which these processes are based.
|Date of creation:||20 Mar 2012|
|Contact details of provider:|| Postal: Carl-Zeiss-Strasse 3, 07743 JENA|
Phone: +049 3641/ 9 43000
Fax: +049 3641/ 9 43000
Web page: http://www.jenecon.de
More information through EDIRC
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.:
- Krzysztof R. Apt & Jonathan A. Zvesper, 2010. "The Role of Monotonicity in the Epistemic Analysis of Strategic Games," Games, MDPI, Open Access Journal, vol. 1(4), pages 381-381, October.
- Ronald Fagin & Joseph Y. Halpern & Yoram Moses & Moshe Y. Vardi, 2003. "Reasoning About Knowledge," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262562006.
- Leslie M. Marx & Jeroen M. Swinkels, 1996.
"Order Independence for Iterated Weak Dominance,"
1066R, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
- Marx, Leslie M. & Swinkels, Jeroen M., 1997. "Order Independence for Iterated Weak Dominance," Games and Economic Behavior, Elsevier, vol. 18(2), pages 219-245, February.
- Marx, Leslie M. & Swinkels, Jeroen M., 2000. "Order Independence for Iterated Weak Dominance," Games and Economic Behavior, Elsevier, vol. 31(2), pages 324-329, May.
- Halpern, Joseph Y. & Pass, Rafael, 2012. "Iterated regret minimization: A new solution concept," Games and Economic Behavior, Elsevier, vol. 74(1), pages 184-207.
- D. B. Bernheim, 2010.
"Rationalizable Strategic Behavior,"
Levine's Working Paper Archive
661465000000000381, David K. Levine.
- Yi-Chun Chen & Ngo Van Long & Xiao Luo, 2007.
"Iterated Strict Dominance in General Games,"
CIRANO Working Papers
- Pearce, David G, 1984. "Rationalizable Strategic Behavior and the Problem of Perfection," Econometrica, Econometric Society, vol. 52(4), pages 1029-1050, July.
- Martin J. Osborne & Ariel Rubinstein, 1994.
"A Course in Game Theory,"
MIT Press Books,
The MIT Press,
edition 1, volume 1, number 0262650401.
- Itzhak Gilboa & E. Kalai & E. Zemel, 1990. "On the order of eliminating dominated strategies," Post-Print hal-00481648, HAL.
When requesting a correction, please mention this item's handle: RePEc:jrp:jrpwrp:2012-010. See general information about how to correct material in RePEc.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Markus Pasche)
If references are entirely missing, you can add them using this form.