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The Robustness of Equilibria to Incomplete Information

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  • Atsushi Kajii
  • Stephen Morris

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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Paper provided by Penn Economics Department in its series Penn CARESS Working Papers with number ed504c985fc375cbe719b3f60d7ff5c6.

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Handle: RePEc:cla:penntw:ed504c985fc375cbe719b3f60d7ff5c6

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  1. Aumann, Robert J, 1987. "Correlated Equilibrium as an Expression of Bayesian Rationality," Econometrica, Econometric Society, vol. 55(1), pages 1-18, January.
  2. Drew Fudenberg & David M. Kreps & David K. Levine, 1986. "On the Robustness of Equilibrium Refinements," UCLA Economics Working Papers 398, UCLA Department of Economics.
  3. Kajii, Atsushi & Morris, Stephen, 1998. "Payoff Continuity in Incomplete Information Games," Journal of Economic Theory, Elsevier, vol. 82(1), pages 267-276, September.
  4. 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.
  5. Drew Fudenberg & Eddie Dekel, 1987. "Rational Behavior with Payoff Uncertainty," Working papers 471, Massachusetts Institute of Technology (MIT), Department of Economics.
  6. S. Morris & R. Rob & H. Shin, 2010. "p-dominance and Belief Potential," Levine's Working Paper Archive 505, David K. Levine.
  7. T. Börgers, 2010. "Weak Dominance and Approximate Common Knowledge," Levine's Working Paper Archive 378, David K. Levine.
  8. 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.
  9. Cotter, Kevin D., 1991. "Correlated equilibrium in games with type-dependent strategies," Journal of Economic Theory, Elsevier, vol. 54(1), pages 48-68, June.
  10. Carlsson, Hans & van Damme, Eric, 1993. "Global Games and Equilibrium Selection," Econometrica, Econometric Society, vol. 61(5), pages 989-1018, September.
  11. Van Damme, E., 1991. "Equilibrium Selection in 2 x 2 Games," Papers 9108, Tilburg - Center for Economic Research.
  12. Carlsson, H. & Van Dame, E., 1991. "Equilibrium Selection in Stag Hunt Games," Papers 9170, Tilburg - Center for Economic Research.
  13. Kajii, Atsushi & Morris, Stephen, 1997. "Commonp-Belief: The General Case," Games and Economic Behavior, Elsevier, vol. 18(1), pages 73-82, January.
  14. Forges, Francoise, 1990. "Correlated Equilibrium in Two-Person Zero-Sum Games," Econometrica, Econometric Society, vol. 58(2), pages 515, March.
  15. E. Kohlberg & J.-F. Mertens, 1998. "On the Strategic Stability of Equilibria," Levine's Working Paper Archive 445, David K. Levine.
  16. Monderer, Dov & Samet, Dov, 1989. "Approximating common knowledge with common beliefs," Games and Economic Behavior, Elsevier, vol. 1(2), pages 170-190, June.
  17. Abraham Neyman, 1997. "Correlated Equilibrium and Potential Games," International Journal of Game Theory, Springer, vol. 26(2), pages 223-227.
  18. Kohlberg, E., 1986. "On the Strategic Stability of Equilibria. Econometrica," Open Access publications from Université catholique de Louvain info:hdl:2078.1/54777, Université catholique de Louvain.
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