Hostname: page-component-54dcc4c588-2bdfx Total loading time: 0 Render date: 2025-09-30T22:14:00.819Z Has data issue: false hasContentIssue false
  • English
  • Français

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

Published online by Cambridge University Press:  16 October 2009

Wlodek Rabinowicz
Wlodek Rabinowicz
Affiliation:
Lund University
Get access Rights & Permissions [Opens in a new window]

Extract

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).)

Information

Type
Essays
Information
Economics & Philosophy , Volume 14 , Issue 1 , April 1998 , pp. 95 - 126
Copyright
Copyright © Cambridge University Press 1998

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Article purchase

Temporarily unavailable

References

REFERENCES

Aumann, Robert J. 1995. ‘Backward induction and common knowledge of rationality’. Games and Economic behavior, 8:6–19CrossRefGoogle Scholar
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 JerusalemGoogle Scholar
Bicchieri, Cristina. 1989. ‘Backward induction without common knowledge’. Proceedings of the Philosophy of Science Association, Vol. 2:329–43Google Scholar
Binmore, Ken. 1987. ‘Modelling rational players: Part 1’. Economics and Philosophy, 3:179–213CrossRefGoogle Scholar
Halpern, Joseph Y. 1997. ‘Hypothetical knowledge and counterfactual reasoning’. DraftGoogle Scholar
Hern, Richard. 1996. ‘Modelling rational changes when tastes are changing’. DraftGoogle Scholar
Jeffrey, Richard C. 1983. Logic of Decision. University of Chicago PressGoogle Scholar
Pettit, Philip and Sugden, Robert. 1989. ‘The backward induction paradox’. The Journal of Philosophy, 86:169–82CrossRefGoogle Scholar
Rabinowicz, Wlodek. 1985. ‘Ratificationism without ratification: Jeffrey meets Savage’. Theory and Decision, 19:171–200CrossRefGoogle Scholar
Rabinowicz, Wlodek. 1988. ‘Ratifiability and stability’. In Decision, Probability, and Utility, pp. 406–25. Gärdenfors, Peter and Sahlin, Nils-Eric (eds.). Cambridge University PressCrossRefGoogle Scholar
Rabinowicz, Wlodek. 1989. ‘Stable and retrievable options’. Philosophy of Science, 56:624–41CrossRefGoogle Scholar
Rabinowicz, Wlodek. 1995. ‘To have one's cake and eat it, too: sequential choice and expected-utility violations’. The Journal of Philosophy, 92:586–620CrossRefGoogle Scholar
Reny, Philip J. 1988. ‘Rationality, common knowledge and the theory of games’. Ph.D.dissertation. Princeton UniversityGoogle Scholar
Reny, Philip J. 1989. ‘Common knowledge and games with perfect information’. Proceedings of the Philosophy of Science Association, Vol. 2:363–9Google Scholar
Samet, Dov. 1996. ‘Hypothetical knowledge and games with perfect information’. Games and Economic behavior, 17:230–51CrossRefGoogle Scholar
Sobel, J. Howard. 1993. ‘Backward induction arguments in finitely iterated prisoners' dilemmas: a paradox regained’. Philosophy of Science, 60:114–33CrossRefGoogle Scholar
Selten, Reinhard. 1975. ‘Reexamination of the perfectness concept of equilibrium in extensive games’. International Journal of Game Theory, 4:25–55CrossRefGoogle Scholar
Stalnaker, Robert. 1994. ‘On the evaluation of solution concepts’. Theory and Decision, 37:49–73CrossRefGoogle Scholar
Stalnaker, Robert. 1996. ‘Knowledge, belief and counterfactual reasoning in games’. Economics and Philosophy, 12:133–63CrossRefGoogle Scholar
Weirich, Paul. 1995. Equilibrium and Rationality. Cambridge University Press, ForthcomingGoogle Scholar