Common belief of rationality in games of perfect information

Aumann (1995) showed that for games with perfect information common knowledge of substantive rationality implies backward induction. Substantive rationality is defined in epistemic terms, that is, in terms of knowledge. We show that when substantive rationality is defined in doxastic terms, that is, in terms of belief, then common belief of substantive rationality implies backward induction. Aumann (1998) showed that material rationality implies backward induction in the centipede game. This result does not hold when rationality is defined doxastically. However, if beliefs are interpersonally consistent then common belief of material rationality in the centipede game implies common belief of backward induction.