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The Robustness of Equilibria to Incomplete Information

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Author Info
Atsushi Kajii
Stephen Morris

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Abstract

A number of papers have shown that a strict Nash equilibrium action profile of a game may never be played if there is a small amount of incomplete information. The authors present a general approach to analyzing the robustness of equilibria to a small amount of incomplete information. A Nash equilibrium of a complete information game is said to be robust to incomplete information if every incomplete information game with payoffs almost always given by the complete information game has an equilibrium which generates behavior close to the Nash equilibrium. The authors show that many games with strict equilibria have no robust equilibrium and examine why they get such different results from existing refinements. If a game has a unique correlated equilibrium, it is robust. A natural many-player many-action generalization of risk dominance is a sufficient condition for robustness.

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Publisher Info
Article provided by Econometric Society in its journal Econometrica.

Volume (Year): 65 (1997)
Issue (Month): 6 (November)
Pages: 1283-1310
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Handle: RePEc:ecm:emetrp:v:65:y:1997:i:6:p:1283-1310

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References listed on IDEAS
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.:
  1. Aumann, Robert J, 1987. "Correlated Equilibrium as an Expression of Bayesian Rationality," Econometrica, Econometric Society, vol. 55(1), pages 1-18, January. [Downloadable!] (restricted)
  2. Kajii, Atsushi & Morris, Stephen, 1998. "Payoff Continuity in Incomplete Information Games," Journal of Economic Theory, Elsevier, vol. 82(1), pages 267-276, September. [Downloadable!] (restricted)
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  3. John C. Harsanyi & Reinhard Selten, 1988. "A General Theory of Equilibrium Selection in Games," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262582384, January.
  4. Rubinstein, Ariel, 1989. "The Electronic Mail Game: Strategic Behavior under "Almost Common Knowledge."," American Economic Review, American Economic Association, vol. 79(3), pages 385-91, June. [Downloadable!] (restricted)
  5. Cotter, Kevin D., 1991. "Correlated equilibrium in games with type-dependent strategies," Journal of Economic Theory, Elsevier, vol. 54(1), pages 48-68, June. [Downloadable!] (restricted)
  6. Dekel, Eddie & Fudenberg, Drew, 1990. "Rational behavior with payoff uncertainty," Journal of Economic Theory, Elsevier, vol. 52(2), pages 243-267, December. [Downloadable!] (restricted)
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  7. Kajii, Atsushi & Morris, Stephen, 1997. "Commonp-Belief: The General Case," Games and Economic Behavior, Elsevier, vol. 18(1), pages 73-82, January. [Downloadable!] (restricted)
  8. Carlsson, Hans & van Damme, Eric, 1993. "Global Games and Equilibrium Selection," Econometrica, Econometric Society, vol. 61(5), pages 989-1018, September. [Downloadable!] (restricted)
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  9. Drew Fudenberg & David Kreps & David K. Levine, 1988. "On the Robustness of Equilibrium Refinements," Levine's Working Paper Archive 227, David K. Levine. [Downloadable!]
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  10. Forges, Francoise, 1990. "Correlated Equilibrium in Two-Person Zero-Sum Games," Econometrica, Econometric Society, vol. 58(2), pages 515, March.
  11. Monderer, Dov & Samet, Dov, 1989. "Approximating common knowledge with common beliefs," Games and Economic Behavior, Elsevier, vol. 1(2), pages 170-190, June. [Downloadable!] (restricted)
  12. Abraham Neyman, 1997. "Correlated Equilibrium and Potential Games," International Journal of Game Theory, Springer, vol. 26(2), pages 223-227.
  13. Kohlberg, Elon & Mertens, Jean-Francois, 1986. "On the Strategic Stability of Equilibria," Econometrica, Econometric Society, vol. 54(5), pages 1003-37, September. [Downloadable!] (restricted)
  14. Morris, Stephen & Rob, Rafael & Shin, Hyun Song, 1995. "Dominance and Belief Potential," Econometrica, Econometric Society, vol. 63(1), pages 145-57, January. [Downloadable!] (restricted)
  15. Borgers Tilman, 1994. "Weak Dominance and Approximate Common Knowledge," Journal of Economic Theory, Elsevier, vol. 64(1), pages 265-276, October. [Downloadable!] (restricted)
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