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Deductive reasoning in extensive games

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  • Asheim,G.B.
  • Dufwenberg,M.

    (University of Oslo, Department of Economics)

Abstract

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://www.sv.uio.no/econ/english/research/memorandum/pdf-files/2000/Memo-08-2000.pdf
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Bibliographic Info

Paper provided by Oslo University, Department of Economics in its series Memorandum with number 08/2000.

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Date of creation: 2000
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Handle: RePEc:hhs:osloec:2000_008

Contact details of provider:
Postal: Department of Economics, University of Oslo, P.O Box 1095 Blindern, N-0317 Oslo, Norway
Phone: 22 85 51 27
Fax: 22 85 50 35
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Web page: http://www.oekonomi.uio.no/indexe.html
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References

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  1. Samuelson, L., 1989. "Dominated Strategies And Common Knowledge," Papers 5-89-6, Pennsylvania State - Department of Economics.
  2. Asheim, Geir B., 2002. "On the epistemic foundation for backward induction," Mathematical Social Sciences, Elsevier, vol. 44(2), pages 121-144, November.
  3. Battigalli, P. & Siniscalchi, M., 1999. "Interactive Beliefs and Forward Induction," Economics Working Papers eco99/15, European University Institute.
  4. Mailath, G. & Samuelson, L. & Swinkels, J., 1991. "Extensive form reasoning in normal form games," Discussion Paper 1991-30, Tilburg University, Center for Economic Research.
  5. D. B. Bernheim, 2010. "Rationalizable Strategic Behavior," Levine's Working Paper Archive 661465000000000381, David K. Levine.
  6. P. Reny, 2010. "Common Belief and the Theory of Games with Perfect Information," Levine's Working Paper Archive 386, David K. Levine.
  7. Blume, Lawrence & Brandenburger, Adam & Dekel, Eddie, 1991. "Lexicographic Probabilities and Choice under Uncertainty," Econometrica, Econometric Society, vol. 59(1), pages 61-79, January.
  8. David M Kreps & Robert Wilson, 2003. "Sequential Equilibria," Levine's Working Paper Archive 618897000000000813, David K. Levine.
  9. Aumann, Robert J., 1995. "Backward induction and common knowledge of rationality," Games and Economic Behavior, Elsevier, vol. 8(1), pages 6-19.
  10. Asheim, Geir B. & Dufwenberg, Martin, 2000. "Amissibility and Common Belief," Research Papers in Economics 2000:6, Stockholm University, Department of Economics.
  11. Drew Fudenberg & Eddie Dekel, 1987. "Rational Behavior with Payoff Uncertainty," Working papers 471, Massachusetts Institute of Technology (MIT), Department of Economics.
  12. 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.
  13. Rubinstein, Ariel, 1991. "Comments on the Interpretation of Game Theory," Econometrica, Econometric Society, vol. 59(4), pages 909-24, July.
  14. Samuelson, Larry, 1992. "Dominated strategies and common knowledge," Games and Economic Behavior, Elsevier, vol. 4(2), pages 284-313, April.
  15. Borgers, Tilman & Samuelson, Larry, 1992. ""Cautious" Utility Maximization and Iterated Weak Dominance," International Journal of Game Theory, Springer, vol. 21(1), pages 13-25.
  16. Pearce, David G, 1984. "Rationalizable Strategic Behavior and the Problem of Perfection," Econometrica, Econometric Society, vol. 52(4), pages 1029-50, July.
  17. Battigalli, Pierpaolo, 1996. "Strategic Rationality Orderings and the Best Rationalization Principle," Games and Economic Behavior, Elsevier, vol. 13(2), pages 178-200, April.
  18. Damme, E.E.C. van, 1989. "Stable equilibria and forward induction," Open Access publications from Tilburg University urn:nbn:nl:ui:12-154422, Tilburg University.
  19. 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.
  20. Reny, Philip J, 1992. "Backward Induction, Normal Form Perfection and Explicable Equilibria," Econometrica, Econometric Society, vol. 60(3), pages 627-49, May.
  21. van Damme,Eric, 1987. "Stable equilibria and forward induction," Discussion Paper Serie A 128, University of Bonn, Germany.
  22. 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. Steven D. Levitt & John A. List & Sally E. Sadoff, 2011. "Checkmate: Exploring Backward Induction among Chess Players," American Economic Review, American Economic Association, vol. 101(2), pages 975-90, April.
  2. Asheim, Geir B. & Dufwenberg, Martin, 2003. "Admissibility and common belief," Games and Economic Behavior, Elsevier, vol. 42(2), pages 208-234, February.
  3. Sabrina Teyssier, 2007. "Optimal Group Incentives with Social Preferences and Self-Selection," Post-Print halshs-00144901, HAL.
  4. Ignacio Palacios-Huerta & Oscar Volij, . "Field Centipedes," Economic theory and game theory 020, Oscar Volij.
  5. Janssen, Maarten C.W., 2006. "Auctions as coordination devices," European Economic Review, Elsevier, vol. 50(3), pages 517-532, April.

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