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Deductive reasoning in Extensive Games

  • Asheim, Geir B

    ()

    (Department of Economics, University of Oslo)

We justify the application to extensive games of the concept of ‘fully permissible sets’, which corresponds to choice sets when there is common certain belief of the event that each player prefer one strategy to another if and only if the former weakly dominates the latter on the set of all opponent strategies or on the union of the choice sets that are deemed possible for the opponent. he e tensive games considered illustrate how our concept yields support to forward induction, without necessarily promoting backward induction.

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File URL: http://www2.ne.su.se/paper/wp00_07.pdf
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Paper provided by Stockholm University, Department of Economics in its series Research Papers in Economics with number 2000:7.

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Length: 20 pages
Date of creation: 29 Feb 2000
Date of revision:
Handle: RePEc:hhs:sunrpe:2000_0007
Contact details of provider: Postal: Department of Economics, Stockholm, S-106 91 Stockholm, Sweden
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Fax: +46 8 16 14 25
Web page: http://www.ne.su.se/
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  1. Asheim, Geir B. & Dufwenberg, Martin, 2003. "Admissibility and common belief," Games and Economic Behavior, Elsevier, vol. 42(2), pages 208-234, February.
  2. Mailath, G.J. & Samuelson, L. & Swinkels, J., 1990. "Extensive Form Reasoning In Normal Form Games," Papers 1-90-1, Pennsylvania State - Department of Economics.
  3. Rubinstein, Ariel, 1991. "Comments on the Interpretation of Game Theory," Econometrica, Econometric Society, vol. 59(4), pages 909-24, July.
  4. Battigalli, Pierpaolo, 1997. "On Rationalizability in Extensive Games," Journal of Economic Theory, Elsevier, vol. 74(1), pages 40-61, May.
  5. Borgers, Tilman & Samuelson, Larry, 1992. ""Cautious" Utility Maximization and Iterated Weak Dominance," International Journal of Game Theory, Springer, vol. 21(1), pages 13-25.
  6. Samuelson, L., 1989. "Dominated Strategies And Common Knowledge," Papers 1-89-3, Pennsylvania State - Department of Economics.
  7. Pearce, David G, 1984. "Rationalizable Strategic Behavior and the Problem of Perfection," Econometrica, Econometric Society, vol. 52(4), pages 1029-50, July.
  8. 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.
  9. Kreps, David M & Wilson, Robert, 1982. "Sequential Equilibria," Econometrica, Econometric Society, vol. 50(4), pages 863-94, July.
  10. Battigalli, Pierpaolo, 1996. "Strategic Rationality Orderings and the Best Rationalization Principle," Games and Economic Behavior, Elsevier, vol. 13(2), pages 178-200, April.
  11. Samuelson, Larry, 1992. "Dominated strategies and common knowledge," Games and Economic Behavior, Elsevier, vol. 4(2), pages 284-313, April.
  12. Aumann, Robert J., 1995. "Backward induction and common knowledge of rationality," Games and Economic Behavior, Elsevier, vol. 8(1), pages 6-19.
  13. van Damme, E.E.C., 1989. "Stable equilibria and forward induction," Other publications TiSEM bd598a8f-f017-4cab-a9ed-8, Tilburg University, School of Economics and Management.
  14. Lawrence Blume & Adam Brandenburger & Eddie Dekel, 2014. "Lexicographic Probabilities and Choice Under Uncertainty," World Scientific Book Chapters, in: The Language of Game Theory Putting Epistemics into the Mathematics of Games, chapter 6, pages 137-160 World Scientific Publishing Co. Pte. Ltd..
  15. Rosenthal, Robert W., 1981. "Games of perfect information, predatory pricing and the chain-store paradox," Journal of Economic Theory, Elsevier, vol. 25(1), pages 92-100, August.
  16. Dekel, Eddie & Fudenberg, Drew, 1990. "Rational behavior with payoff uncertainty," Journal of Economic Theory, Elsevier, vol. 52(2), pages 243-267, December.
  17. Bernheim, B Douglas, 1984. "Rationalizable Strategic Behavior," Econometrica, Econometric Society, vol. 52(4), pages 1007-28, July.
  18. Battigalli, P. & Siniscalchi, M., 1999. "Interactive Beliefs and Forward Induction," Economics Working Papers eco99/15, European University Institute.
  19. Asheim,G.B., 1999. "On the epistemic foundation for backward induction," Memorandum 30/1999, Oslo University, Department of Economics.
  20. 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.
  21. Reny, Philip J, 1992. "Backward Induction, Normal Form Perfection and Explicable Equilibria," Econometrica, Econometric Society, vol. 60(3), pages 627-49, May.
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