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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)

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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Bibliographic Info

Paper provided by Tilburg University, Center for Economic Research in its series Discussion Paper with number 1996-16.

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

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Web page: http://center.uvt.nl

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References

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  1. Mailath, G.J. & Samuelson, L. & Swinkels, J., 1990. "Extensive Form Reasoning In Normal Form Games," Papers 1-90-1, Pennsylvania State - Department of Economics.
  2. Martin J. Osborne & Ariel Rubinstein, 1994. "A Course in Game Theory," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262650401.
  3. Battigalli, Pierpaolo, 1996. "Strategic Rationality Orderings and the Best Rationalization Principle," Games and Economic Behavior, Elsevier, vol. 13(2), pages 178-200, April.
  4. Drew Fudenberg & Eddie Dekel, 1987. "Rational Behavior with Payoff Uncertainty," Working papers 471, Massachusetts Institute of Technology (MIT), Department of Economics.
  5. David Kreps & Robert Wilson, 1998. "Sequential Equilibria," Levine's Working Paper Archive 237, David K. Levine.
  6. Samuelson, L., 1990. "Dominated Strategies And Common Knowledge," Working papers 90-14, Wisconsin Madison - Social Systems.
  7. D. B. Bernheim, 2010. "Rationalizable Strategic Behavior," Levine's Working Paper Archive 661465000000000381, David K. Levine.
  8. T. Börgers, 2010. "Weak Dominance and Approximate Common Knowledge," Levine's Working Paper Archive 378, David K. Levine.
  9. Rubinstein, Ariel, 1991. "Comments on the Interpretation of Game Theory," Econometrica, Econometric Society, vol. 59(4), pages 909-24, July.
  10. 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.
  11. Pearce, David G, 1984. "Rationalizable Strategic Behavior and the Problem of Perfection," Econometrica, Econometric Society, vol. 52(4), pages 1029-50, July.
  12. 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.
  13. Samuelson, Larry, 1992. "Dominated strategies and common knowledge," Games and Economic Behavior, Elsevier, vol. 4(2), pages 284-313, April.
  14. Hendon, Ebbe, et al, 1994. "Expected Utility with Lower Probabilities," Journal of Risk and Uncertainty, Springer, vol. 8(2), pages 197-216, March.
  15. Basu, Kaushik, 1990. "On the Non-existence of a Rationality Definition for Extensive Games," International Journal of Game Theory, Springer, vol. 19(1), pages 33-44.
  16. E. Kohlberg & J.-F. Mertens, 1998. "On the Strategic Stability of Equilibria," Levine's Working Paper Archive 445, David K. Levine.
  17. Aumann, Robert & Brandenburger, Adam, 1995. "Epistemic Conditions for Nash Equilibrium," Econometrica, Econometric Society, vol. 63(5), pages 1161-80, September.
  18. Aumann, Robert J., 1995. "Backward induction and common knowledge of rationality," Games and Economic Behavior, Elsevier, vol. 8(1), pages 6-19.
  19. Borgers, Tilman & Samuelson, Larry, 1992. ""Cautious" Utility Maximization and Iterated Weak Dominance," International Journal of Game Theory, Springer, vol. 21(1), pages 13-25.
  20. Blume, Lawrence & Brandenburger, Adam & Dekel, Eddie, 1991. "Lexicographic Probabilities and Choice under Uncertainty," Econometrica, Econometric Society, vol. 59(1), pages 61-79, January.
  21. Battigalli, Pierpaolo, 1997. "On Rationalizability in Extensive Games," Journal of Economic Theory, Elsevier, vol. 74(1), pages 40-61, May.
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Citations

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Cited by:
  1. Battigalli, Pierpaolo & Siniscalchi, Marciano, 1997. "An Epistemic Characterization of Extensive Form Rationalizability," Working Papers 1009, California Institute of Technology, Division of the Humanities and Social Sciences.
  2. Vannetelbosch, Vincent J., 1996. "On Rationalizability in Two-Person Alternating-Offer Bargaining," Discussion Papers (IRES - Institut de Recherches Economiques et Sociales) 1996023, Université catholique de Louvain, Institut de Recherches Economiques et Sociales (IRES).
  3. Vincent Vannetelbosch, 1999. "Alternating-Offer Bargaining and Common Knowledge of Rationality," Theory and Decision, Springer, vol. 47(2), pages 111-138, October.

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