Cognitive Load and

Strategic Sophistication

Sarah Allred Sean Duffy John SmithPsychology Psychology Economics

Rutgers University-Camden

Beauty Contest-Laboratory Outcomes

0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95100

2

Models of Strategic Sophistication Level-k/Cognitive Hierarchy Models

Stahl and Wilson, 1994, 1995; Nagel, 1995; Costa-Gomes et al., 2001; Camerer et al., 2004

Different levels of strategic sophistication

Very successful in interpreting heterogeneous experimental data

3

Strategic Sophistication (continued) Does the observed strategic sophistication

relate to a fundamental characteristic of the subject?

Examine relationship between measures of cognitive ability and strategic behavior

Ballinger et al. (2011), Bayer and Renou (2011), Brañas-Garza et al. (2012), Brañas-Garza et al. (2011), Burnham et al. (2009), Carpenter et al. (2013), Chen et al. (2009), Chen et al. (2011), Devetag and Warglien (2003), Georganas et al. (2010), Gill and Prowse (2012), Jones (2011), Jones (2008), Palacios-Huerta (2003), Putterman et al. (2011) and Rydval (2011)

4

Experimental Rather than measure cognitive ability

We manipulate it

Advantage to manipulating cognitive ability Cognitive ability related to lots of other things Maybe X determines strategic sophistication

And X merely related to cognitive ability

Complementary means of investigating effects of Cognitive ability on strategic behavior

5

How to think about the manipulation? Discovered crayon in Homer Simpson’s brain

Was causing cognitive shortcomings

6

Homer without crayon in brainHomer with crayon in brain

How to Manipulate Cognitive Resources? Cognitive Load

Task which occupies cognitive resources Unable to devote to deliberation Observe behavior

7

Cognitive Load in Games Cognitive load and games

Roch et al. (2000) Cappelletti et al. (2008) Duffy and Smith (2012)

Not designed to measure strategic sophistication

Carpenter, Graham, Wolf (2013)

8

Experiment Details 164 Subjects

Rutgers-New Brunswick

Sessions of 16 or 20

Earned average $17.89

z-Tree Fischbacher (2007)

9

Cognitive Load Treatments Before play in each period Subjects given number

to commit to memory Up to 15 seconds

After play in game asked for the number

High Load 9 digit number of 0’s and 1’s First digit always 1

Low Load 3 digit number of 0’s and 1’s First digit always 1

10

Discussion of Cognitive Load Alternate load

High Low

Mandatory rest period 20 seconds between the rounds

Why 0’s and 1’s? Did not want the number to interact with decision

11

Timeline across periods Ten 3x3 games

Pay 3 randomly selected if 10 memorization correct Pay 2 if 9 correct Pay 1 if 8 correct Pay 0 if less than 8

Version of 11-20 Game Version of Beauty Contest

Only paid if memorization correct for both

Randomly matched every period

No feedback

12

Manipulation Checks Load Time

High Load: 10.3 seconds Low Load: 2.4 seconds

p<0.001

Correct Memorization Task Low Load: 98.8% High Load: 97.1%

p=0.004

13

Our version of 11-20 Game Adapted from Arad and

Rubenstein (2012) Subjects are paired Each selects an integer

between 1 and 10 Receive request

10 points = $3.50 Earn a bonus of 10 if

select exactly one lower than opponent

Allows straightforward measure of strategic thinking

Instructions were given before load

Equilibrium 10 w prob. 0.1 9 w prob. 0.2 8 w prob. 0.3 7 w prob. 0.4

14

1-10 Game Response

Bounded above by 10 And below by 1

Run tobit regressions with these bounds

15

1-10 Game Response

16

1-10 Game responses

High Load -0.613(p=0.032)

-0.631(p=0.027)

-0.526 (p=0.087)

Self-reported GPA - - 0.210(p=0.59)

Econ/Game Theory/Female No Yes Yes

Observations 164 164 112

-2 Log Likelihood 603.08 597.84 383.06

High load subjects are more strategic

No evidence that self-reported GPA related to choice

1-10 Game Response

High load more sophisticated! (Not less!!!!!)

High Load subjects expect to face more cognitively able opponent

Low Load subjects expect to face less cognitively able opponent

High Load highlights own limitations

17

Our version of Beauty Contest Every subject selects a half integer

between 0 and 10

Winner guesses closest to 2/3 of average Wins $30

Bounded between 0 and 10

Run tobit regressions with these bounds

18

Beauty Contest Game Response

19

Beauty contest action

High Load 0.667(p=0.085)

0.647(p=0.10)

0.941 (p=0.030)

Self-reported GPA - - -2.079(p<0.001)

Econ/Game Theory/Female No Yes Yes

Observations 164 164 112

-2 Log Likelihood 742.82 739.78 489.32

Relationship between self-reported GPA and strategic sophistication

High load subjects are less strategic

1-10 and Beauty Contest Wrap-up 1-10 game

High load more strategic

Uncomplicated game Play 1 less

than the other guy Self-reported GPA

not related choice

Beauty contest High load

less strategic

Complicated game Guess 2/3

of the average of the session

Self-reported GPA related to choice

20

New Strategic Sophistication Papers Strategic sophistication is the result of

1. Subject’s own ability to make computations

2. Subject’s perception of the strategic sophistication of their opponent

Agranov, Potamites, Schotter, and Tergiman (2012) Alaoui and Penta (2012)

21

1-10 and Beauty Contest Wrap-up Two effects of reduced cognitive resources

1. Reduced ability to make computations

2. Disadvantaged in distribution of cognitive resources of subjects

2 dominates 1 in 1-10 game Relatively uncomplicated

1 dominates 2 in beauty contest game Relatively complicated

22

3x3 Games Always shown as row

player

All payoffs between 1 and 11 points 10 points = $3.50

Unique NE

To specify action And point beliefs of

other’s action

Correct beliefs earn 4 additional points

23

24

Characterize Games Number of own

dominated strategies Of Initial Game

Ranges from 0 to 2

Number of opponent’s dominated strategies Of Initial Game

Ranges from 0 to 2

25

Characterize Strategic Behavior Is the subject selecting the best action

Given that the opponent is selecting each action with prob 0.33?

L1 is not particularly sophisticated

L1 classification behavior 1 if behavior consistent with L1 0 otherwise

26

Repeated measures regressions Regressions

Unstructured covariance matrix within subjects And across observations

Each regression has 1640 observations (164 subjects playing 10 games)

Provide coefficient estimates and p-values

27

3x3 games-L1 Classification

28

LI Classification

High Load 0.136 (p=0.012)

Own DS 0.174(p<0.001)

Opponent’s DS -0.038(p=0.21)

High Load*Own DS -0.108(p=0.007)

High Load*Opponent’s DS -0.0842(0.064)

GPA 0.128(<0.003)

-2 Log Likelihood 1253.3

High load subjects more likely to be classified as L1

High load subjects less sensitive to own dominated strategies

High load subjects more sensitive to opponents dominated strategies

High GPA subjects more likely to be classified as L1

3x3 games-Wrap-up High load subjects

More likely to be L1 Less sensitive to number of own dominated

strategies More sensitive to number of other’s dominated

strategies

29

Conclusion Cognitive load helpful in examining relationship

between cognitive ability and strategic behavior

Pay attention to both Cognitive ability and Perception of cognitive ability of others

30

Future Work Observe timing of the

Action and belief decisions

9 binary digits too easy to remember?

Tell subjects Nash Equilibrium Cognitive resources devoted to behavior of other

Do not solicit beliefs Perhaps prompts subjects to be more strategic

31