 Some have used these kinds of observation to argue that the backward induction argument shows that standard assumptions about rationality (with other plausible assumptions) are inconsistent or self-defeating. For (with plausible assumptions) one way to ensure that a rational player will doubt one's own rationality is to behave irrationally. In the fixed-length IPD, for example, Player One may be able to deduce that, if she were to follow an appropriate “irrational” strategy, Player Two would rationally react so that they can achieve mutual cooperation in almost all rounds. So our assumptions seem to imply both that Player One should continually defect and that she would do better if she didn't. (See Skyrms 1990, pp. 125–139 and Bicchieri 1989.)