Backward Induction without Full Trust in Rationality Magnus Jiborn Wlodek Rabinowicz Department of Philosophy Lund University Kungshuset, Lundagård, 222 22 Lund Sweden magnus.jiborn@fil.lu.se , wlodek.rabinowicz@fil.lu.se Abstract: In this paper, we propose a backward induction argument that does not rest on the assumption of common knowledge of rationality. Nor is certainty of rationality assumed. Instead, each player is taken to assign a certain probability to the hypothesis that all players are rational. The advantage of this approach is that it avoids the problematic assumption that full trust in future rationality would prevail even if some players made moves that went against what rationality prescribes. Introduction The traditional backward induction argument rests on the assumption of common knowledge of rationality. That is, it is assumed that all players are rational, that all players know that all are rational, that all know that all know that all are rational, and so on ad infinitum. Aumann (1995) proves that in a game of perfect information, common knowledge of rationality implies backward induction. Several writers, however, have questioned the plausibility of the common knowledge assumption. In particular, it has been questioned whether players would retain their conviction about each other’s rationality throughout every possible path of the game, i.e. even at choice nodes that can be reached only by some players acting against what rationality prescribes. 1 In this paper, we present a probabilistic version of the backward induction argument, which avoids the problems associated with the assumption of common knowledge of rationality. We argue that common knowledge of rationality is not necessary for the backward induction solution in the Centipede game. Nor is it necessary to assume common full belief in rationality. It is 1 Cf. Binmore (1987), Reny (1988) and (1989), Bicchieri (1989), Pettit and Sugden (1989). But see Aumann (1998) and Rabinowicz (1998) for an argument that, in the Centipede, it is actually not necessary to assume that the initial beliefs in rationality would survive even at the nodes that could only be reached by irrational moves