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The Logic of Backward Induction

  • Itai Arieli
  • Robert J. Aumann

The logic of backward induction (BI) in perfect information (PI) games has been intensely scrutinized for the past quarter century. A major development came in 2002, when P. Battigalli and M. Sinischalchi (BS) showed that an outcome of a PI game is consistent with common strong belief of utility maximization if and only if it is the BI outcome. Both BS's formulation, and their proof, are complex and deep. We show that the result continues to hold when utility maximization is replaced by a rationality condition that is even more compelling; more important, the formulation and proof become far more transparent, accessible, and self-contained.

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Paper provided by The Federmann Center for the Study of Rationality, the Hebrew University, Jerusalem in its series Discussion Paper Series with number dp652.

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Length: 25 pages
Date of creation: Nov 2013
Date of revision:
Handle: RePEc:huj:dispap:dp652
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  1. Pearce, David G, 1984. "Rationalizable Strategic Behavior and the Problem of Perfection," Econometrica, Econometric Society, vol. 52(4), pages 1029-50, July.
  2. KOHLBERG, Elon & MERTENS, Jean-François, . "On the strategic stability of equilibria," CORE Discussion Papers RP -716, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  3. Micali, Silvio & Chen, Jing, 2013. "The order independence of iterated dominance in extensive games," Theoretical Economics, Econometric Society, vol. 8(1), January.
  4. Battigalli, Pierpaolo, 1997. "On Rationalizability in Extensive Games," Journal of Economic Theory, Elsevier, vol. 74(1), pages 40-61, May.
  5. Reny, Philip J, 1992. "Backward Induction, Normal Form Perfection and Explicable Equilibria," Econometrica, Econometric Society, vol. 60(3), pages 627-49, May.
  6. P. Reny, 2010. "Common Belief and the Theory of Games with Perfect Information," Levine's Working Paper Archive 386, David K. Levine.
  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. Battigalli, Pierpaolo, 1996. "Strategic Rationality Orderings and the Best Rationalization Principle," Games and Economic Behavior, Elsevier, vol. 13(2), pages 178-200, April.
  9. Battigalli, Pierpaolo & Siniscalchi, Marciano, 2002. "Strong Belief and Forward Induction Reasoning," Journal of Economic Theory, Elsevier, vol. 106(2), pages 356-391, October.
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