The absent-minded centipede

In this note we apply the notion of absent-mindedness (see Piccione and Rubinstein, 1994), which is a form of imperfect recall, to the Rosenthal (1981) centipede game. We show that for standard versions of the centipede game a subgame perfect equilibrium exists in which play is continued almost to the end if one player is known to be absent-minded. In fact, it is sufficient that one player is known to be absent-minded with sufficiently high probability.