Estimating depth of reasoning in a repeated guessing game with no feedback

This paper estimates depth of reasoning in an Iterative Best Response model using data from Weber (<CitationRef CitationID="CR20">2003</CitationRef>) ten-period repeated guessing game with no feedback. Different mixture models are estimated and the type (Level-0, Level-1, etc) of each player is determined in every round using the Expectation Maximization algorithm. The matrices showing the number of individuals transitioning among levels is computed in each case. It is found that most players either remain in the same level or advance to the next two levels they were in the previous period. The lowest levels (Level-0 and Level-1) have a higher probability of transitioning to a higher level than Level-2 or Level-3. Thus, we can conclude that subjects, through repetition of the task, quickly become more sophisticated strategic thinkers as defined by higher levels. However, in some specifications the highest levels have a relatively large probability of switching to a lower level in the next period. In general, depth of reasoning increases monotonically in small steps as individuals are subjected to the same task repeatedly. Copyright Economic Science Association 2013