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Admissibility and common belief

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  • Asheim, Geir B.
  • Dufwenberg, Martin

Abstract

The concept of ‘fully permissible sets ’ is defined by an algorithm that eliminate strategy subset . It is characterized as 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 dominate the latter on the sets of all opponent strategie or on the union of the choice sets that are deemed possible for the opponent. the concept refines the Dekel-Fudenberg procedure and captures aspects of forward induction.

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Bibliographic Info

Article provided by Elsevier in its journal Games and Economic Behavior.

Volume (Year): 42 (2003)
Issue (Month): 2 (February)
Pages: 208-234

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Handle: RePEc:eee:gamebe:v:42:y:2003:i:2:p:208-234

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Web page: http://www.elsevier.com/locate/inca/622836

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References

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  1. Asheim,G.B., 1999. "Proper consistency," Memorandum 31/1999, Oslo University, Department of Economics.
  2. Asheim,G.B. & Dufwenberg,M., 2000. "Deductive reasoning in extensive games," Memorandum 08/2000, Oslo University, Department of Economics.
  3. Geir B. Asheim, 2002. "Proper rationalizability in lexicographic beliefs," International Journal of Game Theory, Springer, vol. 30(4), pages 453-478.
  4. Borgers Tilman, 1994. "Weak Dominance and Approximate Common Knowledge," Journal of Economic Theory, Elsevier, vol. 64(1), pages 265-276, October.
  5. Battigalli, P. & Siniscalchi, M., 1999. "Interactive Beliefs and Forward Induction," Economics Working Papers eco99/15, European University Institute.
  6. Battigalli, Pierpaolo & Siniscalchi, Marciano, 2002. "Strong Belief and Forward Induction Reasoning," Journal of Economic Theory, Elsevier, vol. 106(2), pages 356-391, October.
  7. Samuelson, L., 1991. "Dominated Strategies and Common Knowledge," Papers 9110, Tilburg - Center for Economic Research.
  8. D. B. Bernheim, 2010. "Rationalizable Strategic Behavior," Levine's Working Paper Archive 661465000000000381, David K. Levine.
  9. Ben-Porath, Elchanan, 1997. "Rationality, Nash Equilibrium and Backwards Induction in Perfect-Information Games," Review of Economic Studies, Wiley Blackwell, vol. 64(1), pages 23-46, January.
  10. Hurkens, S., 1993. "Multi-Sided Pre-Play Communication By Burning Money," Papers 9319, Tilburg - Center for Economic Research.
  11. van Damme, Eric, 1989. "Stable equilibria and forward induction," Journal of Economic Theory, Elsevier, vol. 48(2), pages 476-496, August.
  12. Werlang, Sérgio Ribeiro da Costa & Chin-Chiu Tan, Tommy, 1987. "The Bayesian Foundations of Solution Concepts of Games," Economics Working Papers (Ensaios Economicos da EPGE) 111, FGV/EPGE Escola Brasileira de Economia e Finanças, Getulio Vargas Foundation (Brazil).
  13. E. Dekel & D. Fudenberg, 2010. "Rational Behavior with Payoff Uncertainty," Levine's Working Paper Archive 379, David K. Levine.
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  15. Rajan, Uday, 1998. "Trembles in the Bayesian Foundations of Solution Concepts of Games," Journal of Economic Theory, Elsevier, vol. 82(1), pages 248-266, September.
  16. Brandenburger Adam & Dekel Eddie, 1993. "Hierarchies of Beliefs and Common Knowledge," Journal of Economic Theory, Elsevier, vol. 59(1), pages 189-198, February.
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  18. Borgers, Tilman & Samuelson, Larry, 1992. ""Cautious" Utility Maximization and Iterated Weak Dominance," International Journal of Game Theory, Springer, vol. 21(1), pages 13-25.
  19. Christian Ewerhart, 1998. "Rationality and the definition of consistent pairs," International Journal of Game Theory, Springer, vol. 27(1), pages 49-59.
  20. Blume, Lawrence & Brandenburger, Adam & Dekel, Eddie, 1991. "Lexicographic Probabilities and Choice under Uncertainty," Econometrica, Econometric Society, vol. 59(1), pages 61-79, January.
  21. Pearce, David G, 1984. "Rationalizable Strategic Behavior and the Problem of Perfection," Econometrica, Econometric Society, vol. 52(4), pages 1029-50, July.
  22. 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.
  23. Blume, Lawrence & Brandenburger, Adam & Dekel, Eddie, 1991. "Lexicographic Probabilities and Equilibrium Refinements," Econometrica, Econometric Society, vol. 59(1), pages 81-98, January.
  24. Epstein, Larry G & Wang, Tan, 1996. ""Beliefs about Beliefs" without Probabilities," Econometrica, Econometric Society, vol. 64(6), pages 1343-73, November.
  25. Samuelson, Larry, 1992. "Dominated strategies and common knowledge," Games and Economic Behavior, Elsevier, vol. 4(2), pages 284-313, April.
  26. Asheim, Geir B., 2002. "On the epistemic foundation for backward induction," Mathematical Social Sciences, Elsevier, vol. 44(2), pages 121-144, November.
  27. Battigalli, Pierpaolo, 1996. "Strategic Rationality Orderings and the Best Rationalization Principle," Games and Economic Behavior, Elsevier, vol. 13(2), pages 178-200, April.
  28. Battigalli, Pierpaolo, 1997. "On Rationalizability in Extensive Games," Journal of Economic Theory, Elsevier, vol. 74(1), pages 40-61, May.
  29. Marco Mariotti, 1997. "Decisions in games: why there should be a special exemption from Bayesian rationality," Journal of Economic Methodology, Taylor & Francis Journals, vol. 4(1), pages 43-60.
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