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Admissibility and common knowledge

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Author Info
Asheim, G.B.
Dufwenberg, M. (Tilburg University, Center for Economic Research)

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Abstract

The implications of assuming that it is commonly known that players consider only admissible best responses are investigated. Within a states-of-the-world model where a state, for each player, determines a strategy set rather than a strategy the concept of fully permissible sets is defined. General existence is established, and a finite algorithm (eliminating strategy sets instead of strategies) is provided. The concept refines rationalizability as well as the Dekel-Fudenberg procedure, and captures a notion of forward induction. When players consider all best responses, the same framework can be used to define the concept of rationalizable sets, which characterizes rationalizability.

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Paper provided by Tilburg University, Center for Economic Research in its series Discussion Paper with number 16.

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Date of creation: 1996
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Handle: RePEc:dgr:kubcen:199616

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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. Battigalli, Pierpaolo, 1996. "Strategic Rationality Orderings and the Best Rationalization Principle," Games and Economic Behavior, Elsevier, vol. 13(2), pages 178-200, April. [Downloadable!] (restricted)
  2. Tan, Tommy Chin-Chiu & da Costa Werlang, Sergio Ribeiro, 1988. "The Bayesian foundations of solution concepts of games," Journal of Economic Theory, Elsevier, vol. 45(2), pages 370-391, August. [Downloadable!] (restricted)
  3. Samuelson, Larry, 1992. "Dominated strategies and common knowledge," Games and Economic Behavior, Elsevier, vol. 4(2), pages 284-313, April. [Downloadable!] (restricted)
  4. Hendon, Ebbe, et al, 1994. "Expected Utility with Lower Probabilities," Journal of Risk and Uncertainty, Springer, vol. 8(2), pages 197-216, March.
  5. 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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  6. Rubinstein, Ariel, 1991. "Comments on the Interpretation of Game Theory," Econometrica, Econometric Society, vol. 59(4), pages 909-24, July. [Downloadable!] (restricted)
  7. Reny Philip J., 1993. "Common Belief and the Theory of Games with Perfect Information," Journal of Economic Theory, Elsevier, vol. 59(2), pages 257-274, April. [Downloadable!] (restricted)
  8. Bernheim, B Douglas, 1984. "Rationalizable Strategic Behavior," Econometrica, Econometric Society, vol. 52(4), pages 1007-28, July. [Downloadable!] (restricted)
  9. Mailath, George J & Samuelson, Larry & Swinkels, Jeroen M, 1993. "Extensive Form Reasoning in Normal Form Games," Econometrica, Econometric Society, vol. 61(2), pages 273-302, March. [Downloadable!] (restricted)
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  10. Samuelson, L., 1991. "Dominated Strategies and Common Knowledge," Papers 9110, Tilburg - Center for Economic Research.
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  11. Pearce, David G, 1984. "Rationalizable Strategic Behavior and the Problem of Perfection," Econometrica, Econometric Society, vol. 52(4), pages 1029-50, July. [Downloadable!] (restricted)
  12. Aumann, Robert & Brandenburger, Adam, 1995. "Epistemic Conditions for Nash Equilibrium," Econometrica, Econometric Society, vol. 63(5), pages 1161-80, September. [Downloadable!] (restricted)
  13. Borgers, Tilman & Samuelson, Larry, 1992. ""Cautious" Utility Maximization and Iterated Weak Dominance," International Journal of Game Theory, Springer, vol. 21(1), pages 13-25.
  14. Blume, Lawrence & Brandenburger, Adam & Dekel, Eddie, 1991. "Lexicographic Probabilities and Choice under Uncertainty," Econometrica, Econometric Society, vol. 59(1), pages 61-79, January. [Downloadable!] (restricted)
  15. Kohlberg, Elon & Mertens, Jean-Francois, 1986. "On the Strategic Stability of Equilibria," Econometrica, Econometric Society, vol. 54(5), pages 1003-37, September. [Downloadable!] (restricted)
  16. Battigalli, Pierpaolo, 1997. "On Rationalizability in Extensive Games," Journal of Economic Theory, Elsevier, vol. 74(1), pages 40-61, May. [Downloadable!] (restricted)
  17. Borgers Tilman, 1994. "Weak Dominance and Approximate Common Knowledge," Journal of Economic Theory, Elsevier, vol. 64(1), pages 265-276, October. [Downloadable!] (restricted)
  18. Kreps, David M & Wilson, Robert, 1982. "Sequential Equilibria," Econometrica, Econometric Society, vol. 50(4), pages 863-94, July. [Downloadable!] (restricted)
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(explanations, 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. Pierpaolo Battigalli & Marciano Siniscalchi, . "An Epistemic Characterisation of Extensive Form Rationalisability," Working Papers 1999.25, Fondazione Eni Enrico Mattei. [Downloadable!]
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  2. Herings, P.J.J. & Vannetelbosch, V.J., 1997. "Refinements of rationalizability for normal-form games," Discussion Paper 3, Tilburg University, Center for Economic Research. [Downloadable!]
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  3. Vannetelbosch, Vincent J., 1996. "On Rationalizability in Two-Person Alternating-Offer Bargaining," Université catholique de Louvain, Institut de Recherches Economiques et Sociales (IRES) Discussion Paper 1996023, Université catholique de Louvain, Institut de Recherches Economiques et Sociales (IRES). [Downloadable!]
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