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Trembles in Extensive Games with Ambiguity Averse Players

  • Gaurab Aryal
  • Ronald Stauber


We introduce and analyze three definitions of equilibrium for finite extensive games with imperfect information and ambiguity averse players. In a setting where players' preferences are represented by maxmin expected utility as characterized in Gilboa and Schmeidler (1989), our definitions capture the intuition that players may consider the possibility of slight mistakes, analogous to the intuition leading to trembling-hand perfect equilibrium as introduced in Selten (1975). We prove existence for two of our equilibrium notions, and relate our definitions to standard equilibrium concepts with expected utility maximizing players. Our analysis shows that ambiguity aversion can lead to distinct behavioral implications, even if ambiguous beliefs only arise from the possibility of slight mistakes in the implementation of unambiguous strategies.

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Paper provided by Australian National University, College of Business and Economics, School of Economics in its series ANU Working Papers in Economics and Econometrics with number 2013-606.

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Length: 28 Pages
Date of creation: Mar 2013
Date of revision:
Handle: RePEc:acb:cbeeco:2013-606
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  1. Eichberger, Jurgen & Kelsey, David, 2000. "Non-Additive Beliefs and Strategic Equilibria," Games and Economic Behavior, Elsevier, vol. 30(2), pages 183-215, February.
  2. Siniscalchi, Marciano, 2011. "Dynamic choice under ambiguity," Theoretical Economics, Econometric Society, vol. 6(3), September.
  3. Gilboa, Itzhak & Schmeidler, David, 1989. "Maxmin expected utility with non-unique prior," Journal of Mathematical Economics, Elsevier, vol. 18(2), pages 141-153, April.
  4. Hendon, Ebbe & Jacobsen, Hans Jorgen & Sloth, Birgitte, 1996. "The One-Shot-Deviation Principle for Sequential Rationality," Games and Economic Behavior, Elsevier, vol. 12(2), pages 274-282, February.
  5. Gilboa Itzhak & Schmeidler David, 1993. "Updating Ambiguous Beliefs," Journal of Economic Theory, Elsevier, vol. 59(1), pages 33-49, February.
  6. Atsushi Kajii & Takashi Ui, 2004. "Incomplete Information Games with Multiple Priors," KIER Working Papers 583, Kyoto University, Institute of Economic Research.
  7. Martin J Osborne & Ariel Rubinstein, 2009. "A Course in Game Theory," Levine's Bibliography 814577000000000225, UCLA Department of Economics.
  8. Lo, Kin Chung, 1996. "Equilibrium in Beliefs under Uncertainty," Journal of Economic Theory, Elsevier, vol. 71(2), pages 443-484, November.
  9. Subir Bose & Arup Daripa, 2007. "A Dynamic Mechanism and Surplus Extraction Under Ambiguity," Birkbeck Working Papers in Economics and Finance 0716, Birkbeck, Department of Economics, Mathematics & Statistics.
  10. Stauber, Ronald, 2011. "Knightian games and robustness to ambiguity," Journal of Economic Theory, Elsevier, vol. 146(1), pages 248-274, January.
  11. Nishimura, Kiyohiko G. & Ozaki, Hiroyuki, 2004. "Search and Knightian uncertainty," Journal of Economic Theory, Elsevier, vol. 119(2), pages 299-333, December.
  12. Larry G. Epstein & Martin Schneider, 2001. "Recursive Multiple-Priors," RCER Working Papers 485, University of Rochester - Center for Economic Research (RCER).
  13. Thibault Gajdos & Takashi Hayashi & Jean-Marc Tallon & Jean-Christophe Vergnaud, 2008. "Attitude toward imprecise information," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-00451982, HAL.
  14. Andreas Pape & Subir Bose & Emre Ozdenoren, 2004. "Optimal auctions with ambiguity," Econometric Society 2004 North American Summer Meetings 609, Econometric Society.
  15. Azrieli, Yaron & Teper, Roee, 2009. "Uncertainty aversion and equilibrium existence in games with incomplete information," MPRA Paper 17617, University Library of Munich, Germany.
  16. Roman Kozhan & Michael Zarichnyi, 2008. "Nash equilibria for games in capacities," Economic Theory, Springer, vol. 35(2), pages 321-331, May.
  17. Aryal, Gaurab & Stauber, Ronald, 2014. "A note on Kuhn’s Theorem with ambiguity averse players," Economics Letters, Elsevier, vol. 125(1), pages 110-114.
  18. Igor Mouraviev & Frank Riedel & Linda Sass, 2014. "Kuhn's Theorem for Extensive Form Ellsberg Games," Center for Mathematical Economics Working Papers 510, Center for Mathematical Economics, Bielefeld University.
  19. Frank Riedel & Linda Sass, 2011. "The Strategic Use of Ambiguity," Center for Mathematical Economics Working Papers 452, Center for Mathematical Economics, Bielefeld University.
  20. Eichberger, Jürgen & Kelsey, David, 2008. "Are the Treasures of Game Theory Ambiguous?," Sonderforschungsbereich 504 Publications 08-08, Sonderforschungsbereich 504, Universität Mannheim;Sonderforschungsbereich 504, University of Mannheim.
  21. Lo, Kin Chung, 1999. "Extensive Form Games with Uncertainty Averse Players," Games and Economic Behavior, Elsevier, vol. 28(2), pages 256-270, August.
  22. Thomas Jungbauer & Klaus Ritzberger, 2011. "Strategic games beyond expected utility," Economic Theory, Springer, vol. 48(2), pages 377-398, October.
  23. Dionysius Glycopantis & Allan Muir, 2008. "Nash equilibria with Knightian uncertainty; the case of capacities," Economic Theory, Springer, vol. 37(1), pages 147-159, October.
  24. Bade, Sophie, 2011. "Ambiguous act equilibria," Games and Economic Behavior, Elsevier, vol. 71(2), pages 246-260, March.
  25. Ronald Stauber, 2014. "A framework for robustness to ambiguity of higher-order beliefs," International Journal of Game Theory, Springer, vol. 43(3), pages 525-550, August.
  26. Klibanoff, Peter & Hanany, Eran, 2007. "Updating preferences with multiple priors," Theoretical Economics, Econometric Society, vol. 2(3), September.
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