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Backward Induction Is Not Robust: The Parity Problem and the Uncertainty Problem

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Author Info

  • Steven Brams
  • D. Kilgour

Abstract

A cornerstone of game theory is backward induction, whereby players reason backward from the end of a game in extensive form to the beginning in order to determine what choices are rational at each stage of play. Truels, or three-person duels, are used to illustrate how the outcome can depend on (1) the evenness/oddness of the number of rounds (the parity problem) and (2) uncertainty about the endpoint of the game (the uncertainty problem).

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File URL: http://hdl.handle.net/10.1023/A:1005038921033
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Bibliographic Info

Article provided by Springer in its journal Theory and Decision.

Volume (Year): 45 (1998)
Issue (Month): 3 (December)
Pages: 263-289

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Handle: RePEc:kap:theord:v:45:y:1998:i:3:p:263-289

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Web page: http://www.springerlink.com/link.asp?id=100341

Related research

Keywords: Backward induction; Bounded rationality; Continuation probability; Infinite horizon; Parity; Uncertainty;

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References

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  1. Ariel Rubinstein, 2010. "Perfect Equilibrium in a Bargaining Model," Levine's Working Paper Archive 252, David K. Levine.
  2. Binmore, Ken, 1996. "A Note on Backward Induction," Games and Economic Behavior, Elsevier, vol. 17(1), pages 135-137, November.
  3. Kreps,David M. & Wallis,Kenneth F. (ed.), 1997. "Advances in Economics and Econometrics: Theory and Applications," Cambridge Books, Cambridge University Press, number 9780521589833.
  4. Aumann, Robert J., 1996. "Reply to Binmore," Games and Economic Behavior, Elsevier, vol. 17(1), pages 138-146, November.
  5. Drew Fudenberg & Jean Tirole, 1991. "Game Theory," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262061414.
  6. repec:cup:cbooks:9780521580137 is not listed on IDEAS
  7. Paul Milgrom & John Roberts, 1997. "Predation, reputation , and entry deterrence," Levine's Working Paper Archive 1460, David K. Levine.
  8. Samet, Dov, 1996. "Hypothetical Knowledge and Games with Perfect Information," Games and Economic Behavior, Elsevier, vol. 17(2), pages 230-251, December.
  9. Kreps, David M. & Wilson, Robert, 1982. "Reputation and imperfect information," Journal of Economic Theory, Elsevier, vol. 27(2), pages 253-279, August.
  10. Kreps,David M. & Wallis,Kenneth F. (ed.), 1997. "Advances in Economics and Econometrics: Theory and Applications," Cambridge Books, Cambridge University Press, number 9780521589819.
  11. Kreps,David M. & Wallis,Kenneth F. (ed.), 1997. "Advances in Economics and Econometrics: Theory and Applications," Cambridge Books, Cambridge University Press, number 9780521589826.
  12. Stephen Willson, 1998. "Long-Term Behavior in the Theory of Moves," Theory and Decision, Springer, vol. 45(3), pages 201-240, December.
  13. Aumann, Robert J., 1995. "Backward induction and common knowledge of rationality," Games and Economic Behavior, Elsevier, vol. 8(1), pages 6-19.
  14. Stuart, Harborne Jr., 1997. "Common Belief of Rationality in the Finitely Repeated Prisoners' Dilemma," Games and Economic Behavior, Elsevier, vol. 19(1), pages 133-143, April.
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Cited by:
  1. Jean-Marie Dufour, 2000. "Économétrie, théorie des tests et philosophie des sciences," CIRANO Working Papers 2000s-47, CIRANO.
  2. Bossert, Walter & Brams, Steven J. & Kilgour, D. Marc, 2002. "Cooperative vs non-cooperative truels: little agreement, but does that matter?," Games and Economic Behavior, Elsevier, vol. 40(2), pages 185-202, August.

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