Skip to main content

Grappling With the Centipede: Defence of Backward Induction for BI-Terminating Games

  • Wlodek Rabinowicz (a1)

According to the standard objection to backward induction in games, its application depends on highly questionable assumptions about the players' expectations as regards future counterfactual game developments. It seems that, in order to make predictions needed for backward reasoning, the players must expect (i) each player to act rationally at each node that in principle could be reached in the game, and also to expect (ii) that this confidence in the future rationality of the players would be kept by each player come what may: even at the game-nodes that could only be reached by irrational play. Both expectations seem to be rather unreasonable: a player's initial disposition to rational behaviour may be weakened by a long stretch of irrational play on his part and, even more importantly, his initial confidence in the other players' future rationality may be undermined by an irrational play on their part. For different formulations of this objection see Binmore (1987), Reny (1988) and (1989), Bicchieri (1989), Pettit and Sugden (1989). (For defences of backward induction see Sobel (1993) and Aumann (1995) and (1996).)

Hide All
Aumann Robert J. 1995. ‘Backward induction and common knowledge of rationality’. Games and Economic behavior, 8:619
Aumann Robert J. 1996. ‘A note on the Centipede Game’. Discussion paper (June 1996), Center for Rationality and Interactive Decision Theory, The Hebrew University of Jerusalem
Bicchieri Cristina. 1989. ‘Backward induction without common knowledge’. Proceedings of the Philosophy of Science Association, Vol. 2:329–43
Binmore Ken. 1987. ‘Modelling rational players: Part 1’. Economics and Philosophy, 3:179213
Halpern Joseph Y. 1997. ‘Hypothetical knowledge and counterfactual reasoning’. Draft
Hern Richard. 1996. ‘Modelling rational changes when tastes are changing’. Draft
Jeffrey Richard C. 1983. Logic of Decision. University of Chicago Press
Pettit Philip and Sugden Robert. 1989. ‘The backward induction paradox’. The Journal of Philosophy, 86:169–82
Rabinowicz Wlodek. 1985. ‘Ratificationism without ratification: Jeffrey meets Savage’. Theory and Decision, 19:171200
Rabinowicz Wlodek. 1988. ‘Ratifiability and stability’. In Decision, Probability, and Utility, pp. 406–25. Gärdenfors Peter and Sahlin Nils-Eric (eds.). Cambridge University Press
Rabinowicz Wlodek. 1989. ‘Stable and retrievable options’. Philosophy of Science, 56:624–41
Rabinowicz Wlodek. 1995. ‘To have one's cake and eat it, too: sequential choice and expected-utility violations’. The Journal of Philosophy, 92:586620
Reny Philip J. 1988. ‘Rationality, common knowledge and the theory of games’. Ph.D.dissertation. Princeton University
Reny Philip J. 1989. ‘Common knowledge and games with perfect information’. Proceedings of the Philosophy of Science Association, Vol. 2:363–9
Samet Dov. 1996. ‘Hypothetical knowledge and games with perfect information’. Games and Economic behavior, 17:230–51
Sobel J. Howard. 1993. ‘Backward induction arguments in finitely iterated prisoners' dilemmas: a paradox regained’. Philosophy of Science, 60:114–33
Selten Reinhard. 1975. ‘Reexamination of the perfectness concept of equilibrium in extensive games’. International Journal of Game Theory, 4:2555
Stalnaker Robert. 1994. ‘On the evaluation of solution concepts’. Theory and Decision, 37:4973
Stalnaker Robert. 1996. ‘Knowledge, belief and counterfactual reasoning in games’. Economics and Philosophy, 12:133–63
Weirich Paul. 1995. Equilibrium and Rationality. Cambridge University Press, Forthcoming
Recommend this journal

Email your librarian or administrator to recommend adding this journal to your organisation's collection.

Economics & Philosophy
  • ISSN: 0266-2671
  • EISSN: 1474-0028
  • URL: /core/journals/economics-and-philosophy
Please enter your name
Please enter a valid email address
Who would you like to send this to? *


Full text views

Total number of HTML views: 0
Total number of PDF views: 28 *
Loading metrics...

Abstract views

Total abstract views: 200 *
Loading metrics...

* Views captured on Cambridge Core between September 2016 - 19th February 2018. This data will be updated every 24 hours.