1. Strategic Sophistication and Eye Movements Ai Takeuchi (Graduate School of Economics, Waseda University) Yukihiko Funaki (Waseda University) Jana Vyrastekova (Nijmegen University, Tilburg University)

2. Motivation  STS Category (Takeuchi, 2006)  Categorizes the subjects by whether or not they infer the others’ action, using their choices in 2 person asymmetric normal form games  This enables us to see the relationship between the Strategic Sophistication and subjects’ behavior in other games, which Strategic Sophistication cannot be directly measured from the subjects behavior (EX:social dilemma games or constant sum games.)  However, the validity of STS Category has not been tested  This paper tests the validity of STS Category by looking at the relationships between Response Time, Guess Accuracy and Eye Movement

3. Experiment  Choice Treatment  Ss made choices in 14 two person asymmetric normal form games, all with different payoff table  For each player role, 5 games had dominant strategy, 7 games were solvable by 2 steps of iteration, 2 games were solvable by 3 steps of iteration  No feedbacks were given during the experiment  Matrices were rotated so that all Ss made their choices as the row player.  Subjects were paid for the points they had earned in one randomly chosen round  Choice Treatment : Choice (→STS Category), Response Time and Eye Movements  Guess Treatment  Ss made guesses about the number of other players who chose each of the actions in the 6 (of the 14) games.  Ss were paid for the accuracy of their guesses using modified quadratic rule.  Guess Treatment: Accuracy of the Guesses, Variance of the Guesses Conducted in Tilburg University CentER lab. With 4 Eye Tracker

4. STS Category (Takeuchi, 2006)  D-Rate: Ratio the subject took the Dominant strategy  High-STS Rate: Ratio the subject took the strategy corresponding to the Equilibrium of iteration of weakly dominated strategy. STS CategoryD-RateHigh-STS Rate U (Unclassifiable)< 0.8 L (Low) ≧ 0.8 < 0.2 M (Middle) ≧ 0.8 > 0.2, < 0.8 H (High) ≧ 0.8 > 0.8

5. Number of Subjects Classified into Each Category ULMH Number of Subjects 8257 Subjects in Eye Tracker

6. Response Time and STS Category  In Rubinstein(2004), it had been shown that those subjects who chose the action which seems to need more Strategic Sophistication used longer response times  Those subjects in Category H should take longer response times than those subjects in Category L

7. H0: Distribution of the Response Time is the same between Land H. H1: Distribution of the Response Time is not the same between Land H. W = 8940, p-value = 2.369e-16 AVE 22.1 AVE 37.2

8. Eye Tracker  The Tobii Eye Tracker  Binocular eye tracking, where the data are recorded from both eyes at the same time  Eye Tracker without any restrictions on the subjects  Fixation Filter was set with fixation radius of 30 pixel and minimum duration of 100ms ratio of numbers of fixation ＝ Number of fixations on my matrix / Number of fixations on both matrix

9. STS Category and Fixation  If the subjects are inferring the others’ decisions, then the more they infer, the more fixation they would spend on the others’ payoff matrix.  Those subjects in H should have lower ratio of numbers of fixation than those subjects in L.

10. H0: The average of the Ratio of Number of Fixation is the same between L and H. H1: The average of the Ratio of Number of Fixation is not the same between L and H. t = -12.243, df = 27.37, p-value = 1.28e-12 AVE 0.63 AVE 0.5

11. Variance of the Guesses  If the subjects in Category L are not inferring the others’ decisions, they should not be able to make precise guesses of the others’ behavior, compared to those in H.  Subjects in Category L should have lower variance in their guesses compared to those in H.

12. H0: Distribution of the variance of Guesses is the same in L and H H1: Distribution of the variance of Guesses is not the same in L and H W = 2796, p-value = 0.001240 AVE 0.183 AVE 0.295

13. Conclusion  STS Category is consistent with:  Response Time  Eye Movement  Variance of the Guesses  STS Category seems to be a valid way to classify the subjects by their Strategic Sophistication.

14. Thank you!