Strategic Sophistication and Eye Movements

Ai Takeuchi(Graduate School of Economics, Waseda University)

Yukihiko Funaki (Waseda University)

Jana Vyrastekova (Nijmegen University, Tilburg University)

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

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

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 Category D-Rate High-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

Number of Subjects Classified into Each Category

U L M HNumber of Subjects 8 2 5 7

Subjects in Eye Tracker

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

Response Ti me of L

Response Ti me

Freq

uenc

y

0 50 100 150 200

010

3050

Response Ti me of H

Response Ti me

Freq

uenc

y

0 50 100 150 200

050

100

150

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

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

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.

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

Hi stogram of Rati o of Number of Fi xati on (L)

Rati o of Number of Fi xati ons

Dens

ity

0. 3 0. 4 0. 5 0. 6 0. 7 0. 8 0. 9 1. 0

01

23

45

Hi stogram of Rati o of Number of Fi xati on (H)

Rati o of Number of Fi xati ons

Dens

ity

0. 3 0. 4 0. 5 0. 6 0. 7 0. 8 0. 9 1. 0

01

23

45

AVE 0.63

AVE 0.5

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.

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

Hi stogram of Vari ance of Guess (L)

Vari ance of Guess

Freq

uenc

y

0. 0 0. 1 0. 2 0. 3 0. 4 0. 5

05

1015

2025

Hi stogram of Vari ance of Guess (H)

Vari ance of Guess

Freq

uenc

y

0. 0 0. 1 0. 2 0. 3 0. 4 0. 5

020

4060

80

AVE 0.183

AVE 0.295

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.

Thank you!