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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 heterogeneous 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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Bibliographic Info

Article provided by Elsevier in its journal Journal of Economic Theory.

Volume (Year): 145 (2010)
Issue (Month): 2 (March)
Pages: 752-784

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Handle: RePEc:eee:jetheo:v:145:y:2010:i:2:p:752-784

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Web page: http://www.elsevier.com/locate/inca/622869

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Keywords: Incomplete information Robustness Common prior assumption Higher order belief;

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References

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  1. Stephen Morris & Takashi Ui, 2003. "Generalized Potentials and Robust Sets of Equilibria," Levine's Working Paper Archive 506439000000000325, David K. Levine.
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  18. Barton L. Lipman, 2005. "Finite Order Implications of Common Priors in Infinite Models," Boston University - Department of Economics - Working Papers Series WP2005-009, Boston University - Department of Economics.
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Cited by:
  1. Oyama, Daisuke & Tercieux, Olivier, 2005. "On the Strategic Impact of an Event under Non-Common Priors," MPRA Paper 4559, University Library of Munich, Germany.
  2. 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.

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