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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
Phone: +46 8 16 20 00
Fax: +46 8 16 14 25
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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. David Kreps & Robert Wilson, 1998. "Sequential Equilibria," Levine's Working Paper Archive 237, David K. Levine.
  2. Blume, Lawrence & Brandenburger, Adam & Dekel, Eddie, 1991. "Lexicographic Probabilities and Choice under Uncertainty," Econometrica, Econometric Society, vol. 59(1), pages 61-79, January.
  3. E. Dekel & D. Fudenberg, 2010. "Rational Behavior with Payoff Uncertainty," Levine's Working Paper Archive 379, David K. Levine.
  4. 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.
  5. Rubinstein, Ariel, 1991. "Comments on the Interpretation of Game Theory," Econometrica, Econometric Society, vol. 59(4), pages 909-24, July.
  6. D. B. Bernheim, 2010. "Rationalizable Strategic Behavior," Levine's Working Paper Archive 661465000000000381, David K. Levine.
  7. Asheim, Geir B., 2002. "On the epistemic foundation for backward induction," Mathematical Social Sciences, Elsevier, vol. 44(2), pages 121-144, November.
  8. 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.
  9. Samuelson, Larry, 1992. "Dominated strategies and common knowledge," Games and Economic Behavior, Elsevier, vol. 4(2), pages 284-313, April.
  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. Mailath, G.J. & Samuelson, L. & Swinkels, J., 1990. "Extensive Form Reasoning In Normal Form Games," Working papers 90-13, Wisconsin Madison - Social Systems.
  12. Samuelson, L., 1990. "Dominated Strategies And Common Knowledge," Working papers 90-14, Wisconsin Madison - Social Systems.
  13. P. Reny, 2010. "Common Belief and the Theory of Games with Perfect Information," Levine's Working Paper Archive 386, David K. Levine.
  14. Asheim,G.B. & Dufwenberg,M., 2000. "Admissibility and common belief," Memorandum 07/2000, Oslo University, Department of Economics.
  15. van Damme, Eric, 1989. "Stable equilibria and forward induction," Journal of Economic Theory, Elsevier, vol. 48(2), pages 476-496, August.
  16. Battigalli, P. & Siniscalchi, M., 1999. "Interactive Beliefs and Forward Induction," Economics Working Papers eco99/15, European University Institute.
  17. Reny, Philip J, 1992. "Backward Induction, Normal Form Perfection and Explicable Equilibria," Econometrica, Econometric Society, vol. 60(3), pages 627-49, May.
  18. Battigalli, Pierpaolo, 1996. "Strategic Rationality Orderings and the Best Rationalization Principle," Games and Economic Behavior, Elsevier, vol. 13(2), pages 178-200, 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. Aumann, Robert J., 1995. "Backward induction and common knowledge of rationality," Games and Economic Behavior, Elsevier, vol. 8(1), pages 6-19.
  21. Battigalli, Pierpaolo, 1997. "On Rationalizability in Extensive Games," Journal of Economic Theory, Elsevier, vol. 74(1), pages 40-61, May.
  22. Pearce, David G, 1984. "Rationalizable Strategic Behavior and the Problem of Perfection," Econometrica, Econometric Society, vol. 52(4), pages 1029-50, July.
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Citations

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Cited by:
  1. Asheim,G.B. & Dufwenberg,M., 2000. "Admissibility and common belief," Memorandum 07/2000, Oslo University, Department of Economics.
  2. Steven D. Levitt & John A. List & Sally E. Sadoff, 2009. "Checkmate: Exploring Backward Induction Among Chess Players," NBER Working Papers 15610, National Bureau of Economic Research, Inc.
  3. Martin Dufwenberg & Gunnar Köhlin & Peter Martinsson & Haileselassie Medhin, 2014. "Thanks but No Thanks: A New Policy to Reduce Land Conflict," CESifo Working Paper Series 4864, CESifo Group Munich.
  4. Ignacio Palacios-Huerta & Oscar Volij, 2009. "Field Centipedes," American Economic Review, American Economic Association, vol. 99(4), pages 1619-35, September.
  5. Sabrina Teyssier, 2007. "Optimal Group Incentives with Social Preferences and Self-Selection," Working Papers 0710, Groupe d'Analyse et de Théorie Economique (GATE), Centre national de la recherche scientifique (CNRS), Université Lyon 2, Ecole Normale Supérieure.
  6. Janssen, Maarten C.W., 2006. "Auctions as coordination devices," European Economic Review, Elsevier, vol. 50(3), pages 517-532, April.

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