Estimating depth of reasoning in a repeated guessing game with no feedback
 Mariano Runco
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This paper estimates depth of reasoning in an Iterative Best Response model using data from Weber (2003) tenperiod repeated guessing game with no feedback. Different mixture models are estimated and the type (Level0, Level1, 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 (Level0 and Level1) have a higher probability of transitioning to a higher level than Level2 or Level3. 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.
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 Title
 Estimating depth of reasoning in a repeated guessing game with no feedback
 Journal

Experimental Economics
Volume 16, Issue 3 , pp 402413
 Cover Date
 20130901
 DOI
 10.1007/s1068301293446
 Print ISSN
 13864157
 Online ISSN
 15736938
 Publisher
 Springer US
 Additional Links
 Topics
 Keywords

 Games
 Beautycontest experiment
 Learning
 Finite mixture model
 EM algorithm
 Transition matrix
 C50
 D72
 D83
 Industry Sectors
 Authors

 Mariano Runco ^{(1)}
 Author Affiliations

 1. Department of Economics, Auburn University at Montgomery, 7071 Senators Drive, Montgomery, AL, 36117, USA