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

  • Wlodek Rabinowicz (a1)
Abstract

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).)

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Robert J. Aumann 1995. ‘Backward induction and common knowledge of rationality’. Games and Economic behavior, 8:619

Philip Pettit and Robert Sugden . 1989. ‘The backward induction paradox’. The Journal of Philosophy, 86:169–82

Wlodek Rabinowicz . 1985. ‘Ratificationism without ratification: Jeffrey meets Savage’. Theory and Decision, 19:171200

Wlodek Rabinowicz . 1989. ‘Stable and retrievable options’. Philosophy of Science, 56:624–41

Wlodek Rabinowicz . 1995. ‘To have one's cake and eat it, too: sequential choice and expected-utility violations’. The Journal of Philosophy, 92:586620

Dov Samet . 1996. ‘Hypothetical knowledge and games with perfect information’. Games and Economic behavior, 17:230–51

J. Howard Sobel . 1993. ‘Backward induction arguments in finitely iterated prisoners' dilemmas: a paradox regained’. Philosophy of Science, 60:114–33

Reinhard Selten . 1975. ‘Reexamination of the perfectness concept of equilibrium in extensive games’. International Journal of Game Theory, 4:2555

Robert Stalnaker . 1994. ‘On the evaluation of solution concepts’. Theory and Decision, 37:4973

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Economics & Philosophy
  • ISSN: 0266-2671
  • EISSN: 1474-0028
  • URL: /core/journals/economics-and-philosophy
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