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Admissibility and common belief

  • Asheim, Geir B.
  • Dufwenberg, Martin

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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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
Contact details of provider: Web page: http://www.elsevier.com/locate/inca/622836

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  1. Drew Fudenberg & Eddie Dekel, 1987. "Rational Behavior with Payoff Uncertainty," Working papers 471, Massachusetts Institute of Technology (MIT), Department of Economics.
  2. Asheim, Geir B, 2000. "Deductive reasoning in Extensive Games," Research Papers in Economics 2000:7, Stockholm University, Department of Economics.
  3. Battigalli, Pierpaolo, 1996. "Strategic Rationality Orderings and the Best Rationalization Principle," Games and Economic Behavior, Elsevier, vol. 13(2), pages 178-200, April.
  4. Battigalli, Pierpaolo, 1997. "On Rationalizability in Extensive Games," Journal of Economic Theory, Elsevier, vol. 74(1), pages 40-61, May.
  5. Battigalli, Pierpaolo & Siniscalchi, Marciano, 2002. "Strong Belief and Forward Induction Reasoning," Journal of Economic Theory, Elsevier, vol. 106(2), pages 356-391, October.
  6. Samuelson, L., 1990. "Dominated Strategies And Common Knowledge," Working papers 90-14, Wisconsin Madison - Social Systems.
  7. Brandenburger Adam & Dekel Eddie, 1993. "Hierarchies of Beliefs and Common Knowledge," Journal of Economic Theory, Elsevier, vol. 59(1), pages 189-198, February.
  8. Asheim, Geir B. & Perea, Andres, 2005. "Sequential and quasi-perfect rationalizability in extensive games," Games and Economic Behavior, Elsevier, vol. 53(1), pages 15-42, October.
  9. Pearce, David G, 1984. "Rationalizable Strategic Behavior and the Problem of Perfection," Econometrica, Econometric Society, vol. 52(4), pages 1029-50, July.
  10. Blume, Lawrence & Brandenburger, Adam & Dekel, Eddie, 1991. "Lexicographic Probabilities and Equilibrium Refinements," Econometrica, Econometric Society, vol. 59(1), pages 81-98, January.
  11. T. Börgers, 2010. "Weak Dominance and Approximate Common Knowledge," Levine's Working Paper Archive 378, David K. Levine.
  12. 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.
  13. 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.
  14. Christian Ewerhart, 1998. "Rationality and the definition of consistent pairs," International Journal of Game Theory, Springer, vol. 27(1), pages 49-59.
  15. Bernheim, B Douglas, 1984. "Rationalizable Strategic Behavior," Econometrica, Econometric Society, vol. 52(4), pages 1007-28, July.
  16. Samuelson, Larry, 1992. "Dominated strategies and common knowledge," Games and Economic Behavior, Elsevier, vol. 4(2), pages 284-313, April.
  17. Basu, K. & Weibull, J., 1990. "Strategy Subsets Closed Under Rational Behavior," Papers 62, Princeton, Woodrow Wilson School - Discussion Paper.
  18. Hurkens, S., 1993. "Multi-Sided Pre-Play Communication By Burning Money," Papers 9319, Tilburg - Center for Economic Research.
  19. Blume, Lawrence & Brandenburger, Adam & Dekel, Eddie, 1991. "Lexicographic Probabilities and Choice under Uncertainty," Econometrica, Econometric Society, vol. 59(1), pages 61-79, January.
  20. Asheim,G.B., 1999. "On the epistemic foundation for backward induction," Memorandum 30/1999, Oslo University, Department of Economics.
  21. Battigalli, P. & Siniscalchi, M., 1999. "Interactive Beliefs and Forward Induction," Economics Working Papers eco99/15, European University Institute.
  22. Asheim,G.B., 1999. "Proper consistency," Memorandum 31/1999, Oslo University, Department of Economics.
  23. 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).
  24. Borgers, Tilman & Samuelson, Larry, 1992. ""Cautious" Utility Maximization and Iterated Weak Dominance," International Journal of Game Theory, Springer, vol. 21(1), pages 13-25.
  25. Epstein, Larry G & Wang, Tan, 1996. ""Beliefs about Beliefs" without Probabilities," Econometrica, Econometric Society, vol. 64(6), pages 1343-73, November.
  26. 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.
  27. Geir B. Asheim, 2002. "Proper rationalizability in lexicographic beliefs," International Journal of Game Theory, Springer, vol. 30(4), pages 453-478.
  28. 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.
  29. Epstein, Larry G., 1997. "Preference, Rationalizability and Equilibrium," Journal of Economic Theory, Elsevier, vol. 73(1), pages 1-29, March.
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