Selfconfirming Equilibrium and Uncertainty
We propose to bring together two conceptually complementary ideas: (1) selfconfi?rming equilibrium (SCE): at a rest point of learning dynamics in a game played recurrently, agents best respond to confi?rmed beliefs, i.e. beliefs consistent with the evidence they accumulate, and (2) ambiguity aversion: agents, coeteris paribus, prefer to bet on events with known rather than unknown probabilities, more generally, agents distinguish objective from subjective uncertainty, which is captured by their ambiguity attitudes. Using as a workhorse the ?smooth ambiguity model of Klibanoff, Marinacci and Mukerji (2005), we provide a de?nition of "smooth SCE" which generalizes the traditional concept of Fudenberg and Levine (1993a,b), called Bayesian SCE, and admits Waldean (maxmin) SCE as a limit case. We show that the set of equilibria expands as ambiguity aversion increases. The intuition is simple: by playing the same "status-quo" strategy in a stable state an agent learns the implied objective probabilities of payoffs, but alternative strategies yield payoffs with unknown probabilities; keeping beliefs ?fixed, increased aversion to ambiguity makes such strategies less appealing. We rely on this core intuition to show that different notions of equilibrium are nested in a simple way, from ?ner to coarser: Nash, Bayesian SCE, Smooth SCE and Waldean SCE. We also prove some equivalence results, under special assumptions about the information structure.
|Date of creation:||2011|
|Date of revision:|
|Contact details of provider:|| Postal: via Rontgen, 1 - 20136 Milano (Italy)|
Web page: http://www.igier.unibocconi.it/
|Order Information:|| Web: http://www.igier.unibocconi.it/en/papers/index.htm Email: |
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.:
- Simone Cerreia-Vioglio & Fabio Maccheroni & Massimo Marinacci & Luigi Montrucchio, 2011.
"Ambiguity and Robust Statistics,"
382, IGIER (Innocenzo Gasparini Institute for Economic Research), Bocconi University.
- Ignacio Esponda, 2008. "Behavioral Equilibrium in Economies with Adverse Selection," American Economic Review, American Economic Association, vol. 98(4), pages 1269-91, September.
- Azrieli, Yaron, 2009. "Categorizing others in a large game," Games and Economic Behavior, Elsevier, vol. 67(2), pages 351-362, November.
- Peter Klibanoff & Massimo Marinacci & Sujoy Mukerji, 2002.
"A smooth model of decision making under ambiguity,"
ICER Working Papers - Applied Mathematics Series
11-2003, ICER - International Centre for Economic Research, revised Apr 2003.
- Drew Fudenberg & David K. Levine, 1998.
"The Theory of Learning in Games,"
MIT Press Books,
The MIT Press,
edition 1, volume 1, number 0262061945, December.
- Martin J Osborne & Ariel Rubinstein, 2009.
"A Course in Game Theory,"
814577000000000225, UCLA Department of Economics.
- Lehrer, Ehud & Teper, Roee, 2011. "Justifiable preferences," Journal of Economic Theory, Elsevier, vol. 146(2), pages 762-774, March.
- Drew Fudenberg & David K Levine, 2005.
"Superstition and Rational Learning,"
Levine's Working Paper Archive
618897000000000731, David K. Levine.
- Drew Fudenberg & David K. Levine, 2006. "Superstition and Rational Learning," Harvard Institute of Economic Research Working Papers 2114, Harvard - Institute of Economic Research.
- Levine, David & Fudenberg, Drew, 2006. "Superstition and Rational Learning," Scholarly Articles 3196330, Harvard University Department of Economics.
- Simone Cerreia-Vioglio & Fabio Maccheroni & Massimo Marinacci & Luigi Montrucchio, 2011. "Classical Subjective Expected Utility," Working Papers 400, IGIER (Innocenzo Gasparini Institute for Economic Research), Bocconi University.
- Esponda, Ignacio, 2013. "Rationalizable conjectural equilibrium: A framework for robust predictions," Theoretical Economics, Econometric Society, vol. 8(2), May.
When requesting a correction, please mention this item's handle: RePEc:igi:igierp:428. 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: ()
If references are entirely missing, you can add them using this form.