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Backward Induction is not Robust: The Parity Problem and the Uncertainty Problem

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  • Kilgour, D.M.
  • Brams, S.J.

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://econ.as.nyu.edu/docs/IO/9383/RR96-21.PDF
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Bibliographic Info

Paper provided by C.V. Starr Center for Applied Economics, New York University in its series Working Papers with number 96-21.

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Length: 28 pages
Date of creation: 1996
Date of revision:
Handle: RePEc:cvs:starer:96-21

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Postal: C.V. Starr Center, Department of Economics, New York University, 19 W. 4th Street, 6th Floor, New York, NY 10012
Phone: (212) 998-8936
Fax: (212) 995-3932
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Web page: http://econ.as.nyu.edu/object/econ.cvstarr.html
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Postal: C.V. Starr Center, Department of Economics, New York University, 19 W. 4th Street, 6th Floor, New York, NY 10012
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Keywords: UNCERTAINTY; GAME THEORY; GAMES;

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References

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  1. Kreps, David M. & Wilson, Robert, 1982. "Reputation and imperfect information," Journal of Economic Theory, Elsevier, vol. 27(2), pages 253-279, August.
  2. Ariel Rubinstein, 2010. "Perfect Equilibrium in a Bargaining Model," Levine's Working Paper Archive 252, David K. Levine.
  3. Kreps,David M. & Wallis,Kenneth F. (ed.), 1997. "Advances in Economics and Econometrics: Theory and Applications," Cambridge Books, Cambridge University Press, number 9780521589826, October.
  4. Paul Milgrom & John Roberts, 1997. "Predation, reputation , and entry deterrence," Levine's Working Paper Archive 1460, David K. Levine.
  5. Dov Samet, 1994. "Hypothetical Knowledge and Games with Perfect Information," Game Theory and Information 9408001, EconWPA, revised 17 Aug 1994.
  6. Kreps,David M. & Wallis,Kenneth F. (ed.), 1997. "Advances in Economics and Econometrics: Theory and Applications," Cambridge Books, Cambridge University Press, number 9780521589819, October.
  7. Kreps,David M. & Wallis,Kenneth F. (ed.), 1997. "Advances in Economics and Econometrics: Theory and Applications," Cambridge Books, Cambridge University Press, number 9780521589833, October.
  8. Drew Fudenberg & Jean Tirole, 1991. "Game Theory," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262061414.
  9. Aumann, Robert J., 1995. "Backward induction and common knowledge of rationality," Games and Economic Behavior, Elsevier, vol. 8(1), pages 6-19.
  10. Binmore, Ken, 1996. "A Note on Backward Induction," Games and Economic Behavior, Elsevier, vol. 17(1), pages 135-137, November.
  11. 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.
  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., 1996. "Reply to Binmore," Games and Economic Behavior, Elsevier, vol. 17(1), pages 138-146, November.
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Citations

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Cited by:
  1. Dufour, J.M., 2000. "Econometrie, theorie des tests et philosophie des sciences," Cahiers de recherche 2000-14, Centre interuniversitaire de recherche en économie quantitative, CIREQ.
  2. Bossert, W. & Brams, S.J. & Kilgour, D.M., 2000. "Cooperative VS. Non-cooperative Truels: Little Agreement, but Does that Matter?," Cahiers de recherche 2000-15, Centre interuniversitaire de recherche en économie quantitative, CIREQ.

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