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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. Play “Beauty Contest”. Write a real number between 0 and 100

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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. Play “Beauty Contest” • Write a real number between 0 and 100 • Winner is the closest to • 2/3 of the average of the guesses • Earn $20 • Also write your name on paper

  3. Beauty Contest-Dominance • What is the highest possible winning guess? • 66.67 • =(2/3) of 100 • Nobody should pick a number • higher than 66.67 • Nobody should pick number higher than • 44.44 • =2/3 of 66.67

  4. Beauty Contest-Dominance • Nobody should pick number higher than • 29.62 • =(2/3) of 44.44 • This continues until… • Nobody should select a number • higher than 0 • The clear theoretical prediction is • Everyone selects 0

  5. Beauty Contest-Laboratory Outcomes

  6. Strategic Sophistication L0 • How to account for the heterogeneity? • Some people just guess • Some people play as if everyone guesses • (2/3) of 50 • Some people play as if everyone is playing against people who are guessing • (2/3) of (2/3) of 50 • Some people play as if everyone is playing against people who are playing against people who are guessing • (2/3) of (2/3) of (2/3) of 50 • And so on L1 • L2 • L3

  7. 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

  8. 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), 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)

  9. 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

  10. 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

  11. 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?

  12. Subjects given snack options: Serving of fruit Healthy Piece of cake Not healthy Big Number 7 digits Small Number 2 digits Given number Make snack choice Recall number Subjects w/ big number Selected cake Reduced ability to reason to resist temptation Shiv and Fedorikhin (1999)

  13. Failure to process information Gilbert et al. (1988) Swann et al. (1990) Less self control Ward and Mann (2000) Perform worse on gambling tasks Hinson et al. (2002) More impulsive Less Analytical Hinson et al. (2003) Make more mistakes Ryvdal (2011) More risk averse Less patient Benjamin et al. (2012) Cognitive Load Literature

  14. 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

  15. Duffy and Smith (2012) • Repeated 4-player prisoner’s dilemma • Under differential cognitive load • Given number • Play game • Asked to recall number • High Load • 7 digits • Low load • 2 digits

  16. Duffy and Smith (2012) • Between-subject design • Subjects only in one treatment • Digits range from 0 – 9 • Subjects not rematched • Subjects given feedback about game outcomes

  17. Duffy and Smith (2012)-Results • Choice of low load subjects • Differentially converged to SPNE prediction • Low load “closer” to equilibrium • Low load subjects better able to condition • on previous outcomes • Low load better able to sustain some periods of cooperation

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

  19. 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

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

  21. 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

  22. 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

  23. 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

  24. Versions of the ten 3x3 games • 2 versions of 5 games • A and B versions • A and B are strategically equivalent • A is a transposed version of B • Subjects play all 10 games in same role • But play A and B under different load

  25. Manipulation Checks • Load Time • High Load: 10.3 seconds • Low Load: 2.4 seconds • p<0.001 • Difficulty rating • 1 “very difficult” • 7 “not very difficult” • High Load: 5.86 • Low Load: 6.83 • p<0.001 • Correct Memorization Task • Low Load: 98.8% • High Load: 97.1% • p=0.004

  26. …but High Load Subjects not Stupid • Subjects performed two simple addition tasks • One under high load • One under low load • Not incentivized • 154 of 164 performed both correctly • 6 wrong under high load • 4 wrong under low load

  27. 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

  28. 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

  29. Repeated measures logits • Logistic 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

  30. 3x3 games-L1 Classification

  31. 3x3 games-L1 Classification

  32. 3x3 games-L1 Classification High load subjects more likely to be classified as L1 High load subjects less sensitive to complexity of the game

  33. 3x3 games-Best Response to Others • 82 subjects in the opposite role • 34 of one load • 48 of another load • Distribution of play • Equally weight observations • Best response to others • 1 if best response to distribution • 0 otherwise

  34. 3x3 games-Best Response to Others More best responses to distribution in easy games High load subjects are differentially affected by asymmetry

  35. 3x3 games-Correct Beliefs • Correct belief • 1 if stated beliefs identical to most common action of others • 0 otherwise

  36. 3x3 games-Correct Beliefs High load subjects have less accurate beliefs High load subjects are differentially affected by ease of game Relatively worse in complex games

  37. 3x3 games-Wrap-up • Consistent with reduction of cognitive resources • High load subjects • Less strategic • Consistent with L1 • Less accurate beliefs • Best response to action of opponents • Differentially affected by asymmetry • Accuracy of beliefs • Differentially affected by complexity

  38. 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

  39. 1-10 Game Response • Bounded above by 10 • And below by 1 • Run tobit regressions with these bounds

  40. 1-10 Game Response High load subjects are more strategic No evidence that self-reported GPA related to choice

  41. 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

  42. 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

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

  44. 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

  45. New Strategic Sophistication Papers • Strategic sophistication is the result of 1. Subject’s own ability to make computations 2. Subject’s perception of opponent • Agranov, Potamites, Schotter, and Tergiman(2012) • Alaouiand Penta (2012)

  46. 1-10 and Beauty Contest Wrap-up • Two effects of reduced cognitive resources 1. Reduced ability to make computations 2. Reduction place 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

  47. 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

  48. 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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