Score contribution per author:
α: calibrated so average coauthorship-adjusted count equals average raw count
As demonstrated by the email game of Rubinstein (1989), the predictions of the standard equilibrium models of game theory are sensitive to assumptions about the fine details of the higher order beliefs. This paper shows that models of bounded depth of reasoning based on level-k thinking or cognitive hierarchy make predictions that are independent of the tail assumptions on the higher order beliefs. The framework developed here provides a language that makes it possible to identify general conditions on depth of reasoning, instead of committing to a particular model such as level-k thinking or cognitive hierarchy.