Is step-j thinking an arbitrary modelling restriction or a fact of human nature?

Abstract

In `Boundedly Rational Rule Learning in a Guessing Game,' Games and Economic Behavior, 16 (1996), we combined Nagel's (1995) model of boundedly rational players with a `law of effect' learning model, and the synthesis outperformed alternative theories when confronting Nagel's data. In that model, there were four boundedly rational behavioral rules (step-j, j=0, 1, 2, 3), each corresponding to an integer level of depth of reasoning. It is legitimate to ask for a justification of the restriction to these `integer' rules. Why is it not reasonable to suppose that some player believes that 50% of the population is step-0, and 50% is step-1, and so himself adopts something like a step-1.5 rule? This paper constructs a tractable model with potentially infinitely many non-integer rules and conducts comparison tests. The main conclusion is that allowing for non-integer rules does not help to explain the data. Therefore, by Occam's Razor, the integer rule model is preferred. These results suggest that step-j thinking is a fact of human nature rather that an arbitrary modelling restriction.