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Cognitive Load and Strategic Sophistication

Cognitive Load and Strategic Sophistication. Sarah Allred Sean Duffy John Smith Psychology Psychology Economics Rutgers University-Camden. Beauty Contest-Laboratory Outcomes. Models of Strategic Sophistication.

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Cognitive Load and Strategic Sophistication

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

  2. Beauty Contest-Laboratory Outcomes

  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

  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)

  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

  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

  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)

  9. Experiment Details • 164 Subjects • Rutgers-New Brunswick • Sessions of • 16 or 20 • Earned average $17.89 • 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

  11. 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

  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

  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

  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

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

  16. 1-10 Game Response 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

  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

  19. Beauty Contest Game Response High load subjects are less strategic Relationship between self-reported GPA and strategic sophistication

  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

  21. 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) • Alaouiand Penta (2012)

  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

  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 other’s action • Correct beliefs • earn 4 additional points

  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 High load subjects more likely to be classified as L1 High load subjects less sensitive to own dominated strategies High load subjects moresensitive to opponents dominated strategies High GPA subjects more likely to be classified as L1

  28. 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

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