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

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  • Licun Xue

    ()
    (Department of Economics, University of Aarhus, Denmark)

Abstract

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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Bibliographic Info

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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Length: 21
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Handle: RePEc:aah:aarhec:2000-4

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Keywords: Rationality; beliefs; extensive games; rationalizability;

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References

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  1. P. Reny, 2010. "Common Belief and the Theory of Games with Perfect Information," Levine's Working Paper Archive 386, David K. Levine.
  2. Samuelson, L., 1989. "Dominated Strategies And Common Knowledge," Papers 5-89-6, Pennsylvania State - Department of Economics.
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  4. Pierpaolo Battigali & Giacomo Bonanno, . "Recent Results On Belief, Knowledge And The Epistemic Foundations Of Game Theory," Department of Economics 98-14, California Davis - Department of Economics.
  5. 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.
  6. Kreps,David M. & Wallis,Kenneth F. (ed.), 1997. "Advances in Economics and Econometrics: Theory and Applications," Cambridge Books, Cambridge University Press, number 9780521589833, October.
  7. Pierpaolo Battigalli, . "Hierarchies of Conditional Beliefs and Interactive Epistemology in Dynamic Games," Working Papers 111, IGIER (Innocenzo Gasparini Institute for Economic Research), Bocconi University.
  8. van Damme,Eric, 1987. "Stable equilibria and forward induction," Discussion Paper Serie A 128, University of Bonn, Germany.
  9. Aumann, Robert J., 1998. "On the Centipede Game," Games and Economic Behavior, Elsevier, vol. 23(1), pages 97-105, April.
  10. 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.
  11. Drew Fudenberg & Eddie Dekel, 1987. "Rational Behavior with Payoff Uncertainty," Working papers 471, Massachusetts Institute of Technology (MIT), Department of Economics.
  12. Kreps,David M. & Wallis,Kenneth F. (ed.), 1997. "Advances in Economics and Econometrics: Theory and Applications," Cambridge Books, Cambridge University Press, number 9780521589819, October.
  13. 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.
  14. Kreps,David M. & Wallis,Kenneth F. (ed.), 1997. "Advances in Economics and Econometrics: Theory and Applications," Cambridge Books, Cambridge University Press, number 9780521589826, October.
  15. Battigalli, Pierpaolo, 1997. "On Rationalizability in Extensive Games," Journal of Economic Theory, Elsevier, vol. 74(1), pages 40-61, May.
  16. Samuelson, Larry, 1992. "Dominated strategies and common knowledge," Games and Economic Behavior, Elsevier, vol. 4(2), pages 284-313, April.
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  18. Pearce, David G, 1984. "Rationalizable Strategic Behavior and the Problem of Perfection," Econometrica, Econometric Society, vol. 52(4), pages 1029-50, July.
  19. Shimoji, Makoto & Watson, Joel, 1998. "Conditional Dominance, Rationalizability, and Game Forms," Journal of Economic Theory, Elsevier, vol. 83(2), pages 161-195, December.
  20. Gul, Faruk, 1996. "Rationality and Coherent Theories of Strategic Behavior," Journal of Economic Theory, Elsevier, vol. 70(1), pages 1-31, July.
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Citations

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Cited by:
  1. Effrosyni Diamantoudi, . "Equilibrium Binding Agreements under Diverse Bahavioral Assumptions," Economics Working Papers 2001-9, School of Economics and Management, University of Aarhus.
  2. Boriss Siliverstovs, 2005. "The Bi-parameter Smooth Transition Autoregressive model," Economics Bulletin, AccessEcon, vol. 3(23), pages 1-11.
  3. Nikolaj Malchow-Moeller & Bo Jellesmark Thorsen, . "Investment under Uncertainty - the Case of Repeated Investment Options," Economics Working Papers 2000-15, School of Economics and Management, University of Aarhus.
  4. Bo Sandemann Rasmussen, . "Government Debt and Capital Accumulation in the Blanchard-Cass-Yaari OLG Model," Economics Working Papers 2000-14, School of Economics and Management, University of Aarhus.
  5. Nikolaj Malchow-Moeller & Bo Jellesmark Thorsen, . "A Dynamic Agricultural Household Model with Uncertain Income and Irreversible and Indivisible Investments under Credit Constraints," Economics Working Papers 2000-7, School of Economics and Management, University of Aarhus.

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