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Robust Equilibria under Non-Common Priors

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  • Oyama, Daisuke
  • Tercieux, Olivier

Abstract

This paper considers the robustness of equilibria to a small amount of incomplete information, where players are allowed to have heterogenous priors. An equilibrium of a complete information game is robust to incomplete information under non-common priors if for every incomplete information game where each player's prior assigns high probability on the event that the players know at arbitrarily high order that the payoffs are given by the complete information game, there exists a Bayesian Nash equilibrium that generates behavior close to the equilibrium in consideration. It is shown that for generic games, an equilibrium is robust under non-common priors if and only if it is the unique rationalizable action profile. Set-valued concepts are also introduced, and for generic games, a smallest robust set is shown to exist and coincide with the set of a posteriori equilibria.

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File URL: http://mpra.ub.uni-muenchen.de/14287/
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Bibliographic Info

Paper provided by University Library of Munich, Germany in its series MPRA Paper with number 14287.

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Date of creation: 31 Dec 2005
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Handle: RePEc:pra:mprapa:14287

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Keywords: incomplete information; robustness; common prior assumption; higher order belief;

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References

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  1. Jonathan Weinstein & Muhamet Yildiz, 2004. "Finite-Order Implications of Any Equilibrium," Levine's Working Paper Archive 122247000000000065, David K. Levine.
  2. Ui, Takashi, 2001. "Robust Equilibria of Potential Games," Econometrica, Econometric Society, Econometric Society, vol. 69(5), pages 1373-80, September.
  3. Lipman, Barton L., 2010. "Finite order implications of common priors in infinite models," Journal of Mathematical Economics, Elsevier, vol. 46(1), pages 56-70, January.
  4. Dekel, Eddie & Fudenberg, Drew & Morris, Stephen, 2007. "Interim correlated rationalizability," Theoretical Economics, Econometric Society, Econometric Society, vol. 2(1), pages 15-40, March.
  5. P. Battigalli & M. Siniscalchi, 2002. "Rationalization and Incomplete Information," Princeton Economic Theory Working Papers, David K. Levine 9817a118e65062903de7c3577, David K. Levine.
  6. Morris, Stephen & Rob, Rafael & Shin, Hyun Song, 1995. "Dominance and Belief Potential," Econometrica, Econometric Society, Econometric Society, vol. 63(1), pages 145-57, January.
  7. Drew Fudenberg & David M. Kreps & David K. Levine, 1986. "On the Robustness of Equilibrium Refinements," UCLA Economics Working Papers, UCLA Department of Economics 398, UCLA Department of Economics.
  8. Kohlberg, Elon & Mertens, Jean-Francois, 1986. "On the Strategic Stability of Equilibria," Econometrica, Econometric Society, Econometric Society, vol. 54(5), pages 1003-37, September.
  9. Eddie Dekel & Drew Fudenberg & David K. Levine, 2001. "Learning to Play Bayesian Games," Harvard Institute of Economic Research Working Papers, Harvard - Institute of Economic Research 1926, Harvard - Institute of Economic Research.
  10. R. Aumann, 2010. "Subjectivity and Correlation in Randomized Strategies," Levine's Working Paper Archive 389, David K. Levine.
  11. Jonathan Weinstein & Muhamet Yildiz, 2007. "A Structure Theorem for Rationalizability with Application to Robust Predictions of Refinements," Econometrica, Econometric Society, Econometric Society, vol. 75(2), pages 365-400, 03.
  12. Atsushi Kajii & Stephen Morris, . "The Robustness of Equilibria to Incomplete Information," Penn CARESS Working Papers, Penn Economics Department ed504c985fc375cbe719b3f60, Penn Economics Department.
  13. Oyama, Daisuke & Tercieux, Olivier, 2012. "On the strategic impact of an event under non-common priors," Games and Economic Behavior, Elsevier, Elsevier, vol. 74(1), pages 321-331.
  14. Aumann, Robert J, 1987. "Correlated Equilibrium as an Expression of Bayesian Rationality," Econometrica, Econometric Society, Econometric Society, vol. 55(1), pages 1-18, January.
  15. Morris, Stephen & Ui, Takashi, 2005. "Generalized potentials and robust sets of equilibria," Journal of Economic Theory, Elsevier, Elsevier, vol. 124(1), pages 45-78, September.
  16. Oyama, Daisuke & Tercieux, Olivier, 2009. "Iterated potential and robustness of equilibria," Journal of Economic Theory, Elsevier, Elsevier, vol. 144(4), pages 1726-1769, July.
  17. Brandenburger, Adam & Dekel, Eddie, 1987. "Rationalizability and Correlated Equilibria," Econometrica, Econometric Society, Econometric Society, vol. 55(6), pages 1391-1402, November.
  18. Brandenburger Adam & Dekel Eddie, 1993. "Hierarchies of Beliefs and Common Knowledge," Journal of Economic Theory, Elsevier, Elsevier, vol. 59(1), pages 189-198, February.
  19. Monderer, Dov & Samet, Dov, 1989. "Approximating common knowledge with common beliefs," Games and Economic Behavior, Elsevier, Elsevier, vol. 1(2), pages 170-190, June.
  20. Barton L. Lipman, 2003. "Finite Order Implications of Common Priors," Econometrica, Econometric Society, Econometric Society, vol. 71(4), pages 1255-1267, 07.
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Cited by:
  1. Oyama, Daisuke & Tercieux, Olivier, 2012. "On the strategic impact of an event under non-common priors," Games and Economic Behavior, Elsevier, Elsevier, vol. 74(1), pages 321-331.
  2. Ronald Stauber, 2014. "A framework for robustness to ambiguity of higher-order beliefs," International Journal of Game Theory, Springer, Springer, vol. 43(3), pages 525-550, August.

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