Cognitive Load and Strategic Sophistication

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

2. Beauty Contest Guesses

3. Brains in Games • Level-k/Cognitive Hierarchy Models • Stahl and Wilson, 1994, 1995; Nagel, 1995; Costa-Gomes et al., 2001; Camerer et al., 2004 • Interpret heterogeneous experimental data • Different levels of strategic sophistication

4. Brains in Games (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), Chen et al. (2009), Chen et al. (2011), Devetag and Warglien (2003), Gill and Prowse (2012), Jones (2011), Jones (2008), Palacios-Huerta (2003), Putterman et al. (2011) and Rydval (2011) • Evidencethatmeasuredcognitiveabilitynotsignificantlyrelated • tostrategicsophistication • Georganas et al. (2010)

5. Experimental • Rather than measure cognitive ability • We manipulate it • Advantage to manipulating cognitive ability • Cognitive ability related to lots of other things • Complementary means of investigating effects of • Cognitive ability • on strategic behavior

6. How to think about the manipulation? • Discovered crayon in • Homer Simpson’s brain • Was causing cognitive shortcomings 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 • Require subjects to memorize a number • Big number • Small number • Differences in behavior?

8. Cognitive Load Literature • Well established cognitive load literature • in nonstrategic settings • Cognitive load and games • Roch et al. (2000) • Cappelletti et al. (2008) • Duffy and Smith (2012) • Not designed to measure strategic sophistication

9. Experiment Details • 108 Subjects • Rutgers • Camden and • New Brunswick • Sessions of • 16 or 20 • Earned average $17.50 • z-Tree • Fischbacher (2007)

10. 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 • Alternate treatments • !!!!! • Why 0’s and 1’s? • Did not want the number to interact with decision

11. Example of Cognitive Load • Low 101 • High 101110011 101-110-011

12. Timeline across periods • 10, 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

13. 3x3 Games • Adapted from: • Bayer and Renou (2011), Rey-Biel (2009), and Costa-Gomes and Weizsacker (2008) • 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 • 2 versions of 5 games • Play both in both roles

16. Manipulation Checks • Load Time • High Load: 10.3 seconds • Low Load: 3.0 seconds • p<0.0001 • Play Time • High Load: 18.0 seconds • Low Load: 19.3 seconds • p=0.036 • Correct Memorization Task • Low Load: 99.6% • High Load: 95.6% • p<0.0001

17. …but High Load Subjects not Stupid • Subjects performed two simple additions, • One under high load • One under low load • 105 of 108 performed both correctly • 2 wrong under high load • 1 wrong under low load

18. 3x3 Games Results • High Load subjects less likely to exhibit: • Nash Actions? • Nash Beliefs? • Nash Actions: 50.7% • Nash Beliefs: 47.3% • Logistic regressions

19. Characterize Games • Measure of Easiness • Sum of dominated strategies • Of Initial Game • Own and Other • Range from 0 to 4 • Measure of Asymmetry • Absolute value of • Difference between • number of own dominated strategies • And number of other’s dominated strategies • Range from 0 to 2

20. 3x3 Games Results-Nash Behavior High Load Fewer Nash Actions High Load Actions Negatively Affected by Asymmetry Logistic regressions Interactions not shown (ns) High Load Beliefs Positively Affected by Ease of Game

21. 3x3 Games Results-Nash Beliefs Logistic regressions High Load More Nash Beliefs High Load Beliefs Less Sensitive to Ease of Game

22. 3x3 Games Results-BR to Beliefs Logistic regressions High Load Better BR To Own Beliefs Asymmetry Negatively Affects High Load BR To Own Beliefs BR to Own Beliefs Less Sensitive to Ease of Game for High Load

23. Given Beliefs: BR and Action Given Beliefs Difference between BR and payoff from action “Payoff Loss” Tobits with lower bound of 0 High Load Lower Payoff Loss Asymmetry Negatively Affects High Load Payoff Loss

24. 3x3 Games Wrap Up • High Load • play less strategically • Less likely to play Nash • have beliefs of more strategic opponent • More likely to express Nash Beliefs • Better BR to stated beliefs • Differentially affected by • Asymmetry • Difficulty

25. Our version of 11-20 Game • Adapted from Arad and Rubenstein (2010) • 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

26. Results of 1-10 Game • High Load Average: • 7.70 • Low Load Average: • 8.48 • High load more sophisticated! • (Not less!!!!!) • Significant at 5% • in every specification • High Load subjects • expect to face smarter opponent • Low Load subjects • expect to face less smart opponent • High Load highlights own limitations

27. 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

28. Results of Beauty Contest Game • High Load Average: • 6.44 • Low Load Average: • 5.83 • Not significantly different • Backdoor? • Make decision while reading instructions?

29. Conclusion • Similar to Georganas et al. (2010) • We do not find the obvious relationship between • cognitive ability • And strategic behavior • 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. What can cognitive load do for you? • Are you interested in relationship between • cognitive ability • and something else? • Complicated games? • Communication outcomes? • Worse at processing information? • Helpful in Rational Inattention experiments?

31. Future Work • Load not alternating? • 9 binary digits too easy to remember? • Tell subjects Nash Equilibrium • Cognitive resources devoted to behavior of other • Give instructions under differential load? • Eliminate “backdoor?”