RATIONALITY, NASH EQUILIBRIUM AND BACKWARDS INDUCTION IN PERFECT-INFORMATION GAMES

We say that a player is certain of an event A if she assigns probabili ty 1 to A. There is common certainty (CC) of A if the event A occurred , each player is certain of A, each player is certain that every other player is certain of A. and so forth. It is shown that in a generic p erfect-information game the set of outcomes that are consistent with c ommon certainty of rationality (CCR) at the beginning of the game coin cides with the set of outcomes that survive one deletion of weakly dom inated strategies and then iterative deletion of strongly dominated st rategies. Thus. the backward induction outcome is not the only outcome that is consistent with CCR. In particular. cooperation in Rosenthal' s (1981) centipede game. and fighting in Selten's (1978) chainstore ga me are consistent with CCR at the beginning of the game. Next. it is s hown that. if in addition to CCR. there is CC that each player assigns a positive probability to the true strategies and beliefs of the othe r players, and if there is CC of the support of the beliefs of each pl ayer, then the outcome of the game is a Nash equilibrium outcome.