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

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).)