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Selfconfirming Equilibrium and Uncertainty

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  • Pierpaolo Battigalli
  • Simone Cerreia-Vioglio
  • Fabio Maccheroni
  • Massimo Marinacci

Abstract

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.

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Bibliographic Info

Paper provided by IGIER (Innocenzo Gasparini Institute for Economic Research), Bocconi University in its series Working Papers with number 428.

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Date of creation: 2011
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Handle: RePEc:igi:igierp:428

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References

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  1. Ignacio Esponda, 2008. "Behavioral Equilibrium in Economies with Adverse Selection," American Economic Review, American Economic Association, vol. 98(4), pages 1269-91, September.
  2. Drew Fudenberg & David K. Levine, 1996. "The Theory of Learning in Games," Levine's Working Paper Archive 624, David K. Levine.
  3. Levine, David & Fudenberg, Drew, 2006. "Superstition and Rational Learning," Scholarly Articles 3196330, Harvard University Department of Economics.
  4. Sujoy Mukerji & Peter Klibanoff, 2002. "A Smooth Model of Decision,Making Under Ambiguity," Economics Series Working Papers 113, University of Oxford, Department of Economics.
  5. Lehrer, Ehud & Teper, Roee, 2011. "Justifiable preferences," Journal of Economic Theory, Elsevier, vol. 146(2), pages 762-774, March.
  6. Azrieli, Yaron, 2009. "Categorizing others in a large game," Games and Economic Behavior, Elsevier, vol. 67(2), pages 351-362, November.
  7. Martin J Osborne & Ariel Rubinstein, 2009. "A Course in Game Theory," Levine's Bibliography 814577000000000225, UCLA Department of Economics.
  8. Simone Cerreia-Vioglio & Fabio Maccheroni & Massimo Marinacci & Luigi Montrucchio, 2011. "Ambiguity and Robust Statistics," Working Papers 382, IGIER (Innocenzo Gasparini Institute for Economic Research), Bocconi University.
  9. 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.
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Cited by:
  1. Riedel, Frank & Sass, Linda, 2013. "Ellsberg Games," Annual Conference 2013 (Duesseldorf): Competition Policy and Regulation in a Global Economic Order 80012, Verein für Socialpolitik / German Economic Association.
  2. Lars Peter Hansen & Thomas J. Sargent, . "Three types of ambiguity," Working Papers 2012-006, Becker Friedman Institute for Research In Economics.

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