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A Notion of Consistent Rationalizability - Between Weak and Pearce's Extensive Form Rationalizability

  • Licun Xue

    ()

    (Department of Economics, University of Aarhus, Denmark)

Ben-Porath (1997) characterizes the strategies consistent with common certainty of rationality (CCR) and the origin of a generic game of perfect information. More generally, the notion of "weak extensive form rationalizability" (weak EFR) captures the implications initial CCR in an extensive form game. We go one step further by ascertaining at which additional information sets initial CCR can be maintained "consistently". Our consistency notion has two aspects: we examine whether there is "internal consistency" in assuming CCR at a given collection of information sets by using Battigalli and Siniscalchi's (1999) recent result while we introduce "external consistency" to account for all reachable information sets. For a class of games, including all belief- consistent games [cf. Reny (1993)], we identify a unique collection of information sets and hence a unique set of strategy profiles; moreover, we show that in this case our notion is outcome-equivalent to Pearce's (1984) EFR. But in general out notion is between weak and Pearce's EFR.

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Paper provided by School of Economics and Management, University of Aarhus in its series Economics Working Papers with number 2000-4.

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Handle: RePEc:aah:aarhec:2000-4
Contact details of provider: Web page: http://www.econ.au.dk/afn/

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  1. Leslie McFarland-Marx & Jeroen M. Swinkels, 1993. "Order Independence for Iterated Weak Dominance," Discussion Papers 1040, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  2. Giacomo Bonanno & Pierpaolo Battigalli, 2003. "Recent Results On Belief, Knowledge And The Epistemic Foundations Of Game Theory," Working Papers 9814, University of California, Davis, Department of Economics.
  3. Bernheim, B Douglas, 1984. "Rationalizable Strategic Behavior," Econometrica, Econometric Society, vol. 52(4), pages 1007-28, July.
  4. Pierpaolo Battigalli, . "Hierarchies of Conditional Beliefs and Interactive Epistemology in Dynamic Games," Working Papers 111, IGIER (Innocenzo Gasparini Institute for Economic Research), Bocconi University.
  5. E. Dekel & D. Fudenberg, 2010. "Rational Behavior with Payoff Uncertainty," Levine's Working Paper Archive 379, David K. Levine.
  6. Aumann, Robert J., 1998. "On the Centipede Game," Games and Economic Behavior, Elsevier, vol. 23(1), pages 97-105, April.
  7. repec:ner:tilbur:urn:nbn:nl:ui:12-154422 is not listed on IDEAS
  8. Samuelson, L., 1991. "Dominated Strategies and Common Knowledge," Papers 9110, Tilburg - Center for Economic Research.
  9. P. Reny, 2010. "Common Belief and the Theory of Games with Perfect Information," Levine's Working Paper Archive 386, David K. Levine.
  10. 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.
  11. repec:cup:cbooks:9780521589833 is not listed on IDEAS
  12. van Damme, Eric, 1989. "Stable equilibria and forward induction," Journal of Economic Theory, Elsevier, vol. 48(2), pages 476-496, August.
  13. 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.
  14. Samuelson, Larry, 1992. "Dominated strategies and common knowledge," Games and Economic Behavior, Elsevier, vol. 4(2), pages 284-313, April.
  15. repec:cup:cbooks:9780521589826 is not listed on IDEAS
  16. Shimoji, Makoto & Watson, Joel, 1998. "Conditional Dominance, Rationalizability, and Game Forms," Journal of Economic Theory, Elsevier, vol. 83(2), pages 161-195, December.
  17. repec:cup:cbooks:9780521589819 is not listed on IDEAS
  18. Gul, Faruk, 1996. "Rationality and Coherent Theories of Strategic Behavior," Journal of Economic Theory, Elsevier, vol. 70(1), pages 1-31, July.
  19. Battigalli, Pierpaolo, 1997. "On Rationalizability in Extensive Games," Journal of Economic Theory, Elsevier, vol. 74(1), pages 40-61, May.
  20. 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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