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 teststhe validity of STS Category by looking at the relationships between Response Time, Guess Accuracy and Eye Movement

3. Experiment Conducted in Tilburg University CentER lab. With 4 Eye Tracker • 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

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.

5. Number of Subjects Classified into Each Category 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. AVE22.1 H0: Distribution of the Response Time is thesame between Land H. H1: Distribution of the Response Time is not the same between Land H. W = 8940, p-value = 2.369e-16 AVE37.2

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. AVE0.63 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 AVE0.5

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. AVE0.183 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 AVE0.295

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!