Cognitive Load and Strategic Sophistication

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 (2014), 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 (2014), 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

6. 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. 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 • Low Load • 3 digit number • of 0’s and 1’s

9. Timeline across periods • Ten 3x3 games • Version of 11-20 Game • Version of Beauty Contest • Randomly matched every period • Memorization task strongly incentivized • Related to number of randomly selected paid periods • No feedback

10. What we found out • Two effects of cognitive load 1. Reduced ability to make computations 2. Subjects realized they were disadvantaged in distribution of cognitive resources • Believed opponents more sophisticated • Work in opposite directions

11. Control for beliefs? • Control for beliefs of opponents? • ??? • Obtained new data • Told subjects the load of their opponent • before subjects were under load

13. Experiment Details • 308 Subjects • Rutgers-New Brunswick • 144 told load of opponent • 164 not told • z-Tree • Fischbacher (2007)

14. 3x3 Games • 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

17. 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

18. Repeated measures regressions • Logistic regressions • Exchangeablecovariance matrix within subjects • And across observations • Provide coefficient estimates and p-values

19. 3x3 games-L2 Action Difference in behavior given opponent has high or low load High load subjects Less likely to play L2 if high load opponent (p=0.04) Difference for low load subjects Not significant High load subjects less sensitive to own dominated strategies

20. 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 • Some subjects reminded • About 50% of subjects are high load • and 50% low load

21. High load subjects less sophisticated Beauty Contest Game Response High load subjects less sophisticated High load subjects more sophisticated High load subjects better use information Higher GPA, more sophisticated GPA, and BC choice not related

22. Our version of 11-20 Game • Adapted from Arad and Rubenstein (2012) • Subjects are matched • 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

23. 1-10 Game Response High load subjects are more strategic GPA not related to choice Information about opponent’s load not significant

24. 1-10 Game Response • High load more sophisticated! • (Not less!!!!!) • High Load subjects • expect to face more cognitively able opponent

25. 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 (2014)

26. What we found out • Two effects of cognitive load 1. Reduced ability to make computations 2. Subjects realized they were disadvantaged in distribution of cognitive resources • Believed opponents more sophisticated • More likely to use available information • About load of opponent • Prompt to think harder

27. Future Work • More with cognitive load • Observe timing of the • Action and belief decisions • Do not solicit beliefs • Perhaps prompts subjects to be more strategic • Games involving judgments

28. 3x3 games-Best Respond to Beliefs High load subjects less sensitive to own dominated strategies High load subjects less able to take advantage of easier problems