1. Cognitive Load and Strategic Sophistication Sarah Allred Sean Duffy John Smith Psychology Psychology Economics Rutgers University-Camden

2. Beauty Contest-Laboratory Outcomes 2

3. 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

4. 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

5. 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

6. How to think about the manipulation? Discovered crayon in Homer Simpsons brain Was causing cognitive shortcomings 6 Homer without crayon in brain Homer with crayon in brain

7. How to Manipulate Cognitive Resources? Cognitive Load Task which occupies cognitive resources Unable to devote to deliberation Observe behavior 7

8. 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

9. Experiment Details 164 Subjects Rutgers-New Brunswick Sessions of 16 or 20 Earned average $17.89 z-Tree Fischbacher (2007) 9

10. Cognitive Load Treatments B efore 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 0s and 1s First digit always 1 Low Load 3 digit number of 0s and 1s First digit always 1 10

11. Discussion of Cognitive Load Alternate load High Low Mandatory rest period 20 seconds between the rounds Why 0s and 1s? Did not want the number to interact with decision 11

12. 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

13. 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

14. 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

15. 1-10 Game Response Bounded above by 10 And below by 1 Run tobit regressions with these bounds 15

16. 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/FemaleNoYes Observations164 112 -2 Log Likelihood 603.08597.84 383.06 High load subjects are more strategic No evidence that self-reported GPA related to choice

17. 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

18. 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

19. 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/FemaleNoYes Observations164 112 -2 Log Likelihood 742.82739.78 489.32 Relationship between self-reported GPA and strategic sophistication High load subjects are less strategic

20. 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

21. New Strategic Sophistication Papers Strategic sophistication is the result of 1. Subjects own ability to make computations 2. Subjects perception of the strategic sophistication of their opponent Agranov, Potamites, Schotter, and Tergiman (2012) Alaoui and Penta (2012) 21

22. 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

23. 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 others action Correct beliefs earn 4 additional points 23

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25. Characterize Games Number of own dominated strategies Of Initial Game Ranges from 0 to 2 Number of opponents dominated strategies Of Initial Game Ranges from 0 to 2 25

26. 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

27. 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

28. 3x3 games-L1 Classification 28 LI Classification High Load 0.136 (p=0.012) Own DS0.174 (p<0.001) Opponents DS-0.038 (p=0.21) High Load*Own DS-0.108 (p=0.007) High Load*Opponents DS-0.0842 (0.064) GPA0.128 (<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

29. 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 others dominated strategies 29

30. 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

31. 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