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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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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
Phone: +46 8 16 20 00
Fax: +46 8 16 14 25
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  1. 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.
  2. Mailath, G.J. & Samuelson, L. & Swinkels, J., 1991. "extensive Form Reasoning in Normal Form Games," Papers 9130, Tilburg - Center for Economic Research.
  3. Blume, Lawrence & Brandenburger, Adam & Dekel, Eddie, 1991. "Lexicographic Probabilities and Choice under Uncertainty," Econometrica, Econometric Society, vol. 59(1), pages 61-79, January.
  4. Asheim, Geir B., 2002. "On the epistemic foundation for backward induction," Mathematical Social Sciences, Elsevier, vol. 44(2), pages 121-144, November.
  5. Rubinstein, Ariel, 1991. "Comments on the Interpretation of Game Theory," Econometrica, Econometric Society, vol. 59(4), pages 909-24, July.
  6. David M Kreps & Robert Wilson, 2003. "Sequential Equilibria," Levine's Working Paper Archive 618897000000000813, David K. Levine.
  7. Pearce, David G, 1984. "Rationalizable Strategic Behavior and the Problem of Perfection," Econometrica, Econometric Society, vol. 52(4), pages 1029-50, July.
  8. Drew Fudenberg & Eddie Dekel, 1987. "Rational Behavior with Payoff Uncertainty," Working papers 471, Massachusetts Institute of Technology (MIT), Department of Economics.
  9. Bernheim, B Douglas, 1984. "Rationalizable Strategic Behavior," Econometrica, Econometric Society, vol. 52(4), pages 1007-28, July.
  10. Borgers, Tilman & Samuelson, Larry, 1992. ""Cautious" Utility Maximization and Iterated Weak Dominance," International Journal of Game Theory, Springer, vol. 21(1), pages 13-25.
  11. Reny, Philip J, 1992. "Backward Induction, Normal Form Perfection and Explicable Equilibria," Econometrica, Econometric Society, vol. 60(3), pages 627-49, May.
  12. P. Battigalli & M. Siniscalchi, 1999. "Interactive Beliefs and Forward Induction," Princeton Economic Theory Papers 99f3, Economics Department, Princeton University.
  13. Samuelson, L., 1989. "Dominated Strategies And Common Knowledge," Papers 5-89-6, Pennsylvania State - Department of Economics.
  14. Battigalli, Pierpaolo, 1996. "Strategic Rationality Orderings and the Best Rationalization Principle," Games and Economic Behavior, Elsevier, vol. 13(2), pages 178-200, April.
  15. Asheim, Geir B. & Dufwenberg, Martin, 2000. "Amissibility and Common Belief," Research Papers in Economics 2000:6, Stockholm University, Department of Economics.
  16. P. Reny, 2010. "Common Belief and the Theory of Games with Perfect Information," Levine's Working Paper Archive 386, David K. Levine.
  17. Aumann, Robert J., 1995. "Backward induction and common knowledge of rationality," Games and Economic Behavior, Elsevier, vol. 8(1), pages 6-19.
  18. Samuelson, Larry, 1992. "Dominated strategies and common knowledge," Games and Economic Behavior, Elsevier, vol. 4(2), pages 284-313, April.
  19. 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.
  20. 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.
  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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