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Deductive reasoning in Extensive Games

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  • Asheim, Geir B

    ()
    (Department of Economics, University of Oslo)

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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Bibliographic Info

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

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Postal: Department of Economics, Stockholm, S-106 91 Stockholm, Sweden
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Web page: http://www.ne.su.se/
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Keywords: Extensive Game; Deductive reasoning; backward induction;

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References

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  1. Asheim,G.B., 1999. "On the epistemic foundation for backward induction," Memorandum 30/1999, Oslo University, Department of Economics.
  2. 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.
  3. David M Kreps & Robert Wilson, 2003. "Sequential Equilibria," Levine's Working Paper Archive 618897000000000813, David K. Levine.
  4. Samuelson, L., 1990. "Dominated Strategies And Common Knowledge," Working papers 90-14, Wisconsin Madison - Social Systems.
  5. Battigalli, Pierpaolo, 1996. "Strategic Rationality Orderings and the Best Rationalization Principle," Games and Economic Behavior, Elsevier, vol. 13(2), pages 178-200, April.
  6. Borgers, Tilman & Samuelson, Larry, 1992. ""Cautious" Utility Maximization and Iterated Weak Dominance," International Journal of Game Theory, Springer, vol. 21(1), pages 13-25.
  7. Rubinstein, Ariel, 1991. "Comments on the Interpretation of Game Theory," Econometrica, Econometric Society, vol. 59(4), pages 909-24, July.
  8. Asheim, Geir B. & Dufwenberg, Martin, 2003. "Admissibility and common belief," Games and Economic Behavior, Elsevier, vol. 42(2), pages 208-234, February.
  9. 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.
  10. van Damme, Eric, 1989. "Stable equilibria and forward induction," Journal of Economic Theory, Elsevier, vol. 48(2), pages 476-496, August.
  11. Mailath, G.J. & Samuelson, L. & Swinkels, J., 1991. "extensive Form Reasoning in Normal Form Games," Papers 9130, Tilburg - Center for Economic Research.
  12. D. B. Bernheim, 2010. "Rationalizable Strategic Behavior," Levine's Working Paper Archive 514, David K. Levine.
  13. Dekel, Eddie & Fudenberg, Drew, 1990. "Rational behavior with payoff uncertainty," Journal of Economic Theory, Elsevier, vol. 52(2), pages 243-267, December.
  14. P. Battigalli & M. Siniscalchi, 1999. "Interactive Beliefs and Forward Induction," Princeton Economic Theory Papers 99f3, Economics Department, Princeton University.
  15. Pearce, David G, 1984. "Rationalizable Strategic Behavior and the Problem of Perfection," Econometrica, Econometric Society, vol. 52(4), pages 1029-50, July.
  16. 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.
  17. Battigalli, Pierpaolo, 1997. "On Rationalizability in Extensive Games," Journal of Economic Theory, Elsevier, vol. 74(1), pages 40-61, May.
  18. Reny, Philip J, 1992. "Backward Induction, Normal Form Perfection and Explicable Equilibria," Econometrica, Econometric Society, vol. 60(3), pages 627-49, May.
  19. Samuelson, Larry, 1992. "Dominated strategies and common knowledge," Games and Economic Behavior, Elsevier, vol. 4(2), pages 284-313, April.
  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. Aumann, Robert J., 1995. "Backward induction and common knowledge of rationality," Games and Economic Behavior, Elsevier, vol. 8(1), pages 6-19.
  22. Blume, Lawrence & Brandenburger, Adam & Dekel, Eddie, 1991. "Lexicographic Probabilities and Choice under Uncertainty," Econometrica, Econometric Society, vol. 59(1), pages 61-79, January.
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Citations

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Cited by:
  1. Steven Levitt & John List & Sally Sadoff, 2010. "Checkmate: Exploring backward induction among chess players," Artefactual Field Experiments 00081, The Field Experiments Website.
  2. Asheim, Geir B. & Dufwenberg, Martin, 2000. "Amissibility and Common Belief," Research Papers in Economics 2000:6, Stockholm University, Department of Economics.
  3. Sabrina Teyssier, 2007. "Optimal Group Incentives with Social Preferences and Self-Selection," Post-Print halshs-00144901, HAL.
  4. Janssen, Maarten C.W., 2006. "Auctions as coordination devices," European Economic Review, Elsevier, vol. 50(3), pages 517-532, April.
  5. Ignacio Palacios-Huerta & Oscar Volij, 2009. "Field Centipedes," American Economic Review, American Economic Association, vol. 99(4), pages 1619-35, September.

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