cognitive load and mixed strategies sean duffy david owens john smith rutgers-camden haverford...
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Cognitive Load and
Mixed Strategies
Sean Duffy David Owens John SmithRutgers-Camden Haverford Rutgers-Camden
Psychology Economics Economics
Mixing is difficult for subjects Often subjects have difficulty playing mixed
strategies in the laboratory Individual mixing proportions Actions with serial correlation
O'Neill (1987), Brown and Rosenthal (1990), Batzilis et al. (2013), Binmore, Swierzbinski, and Proulx (2001), Geng, Peng, Shachat, and Zhong (2014), Mookherjee and Sopher (1994, 1997), O'Neill (1991), Ochs (1995), Palacios-Huerta and Volij (2008), Rapoport and Amaldoss (2000, 2004), Rapoport and Boebel (1992), Rosenthal, Shachat, and Walker (2003), Shachat (2002), Van Essen and Wooders (2013).
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Does experience help?
Bring in subjects who have experience mixing in other situations Examine their behavior
Levitt, List, and Reiley (2010), Palacios-Huerta and Volij (2008), Van Essen and Wooders (2013)
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Cognitive resources and mixed strategies
We seek to better understand mixing behavior By examining the role of cognitive resources
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Strategic behavior and cognitive ability Examine relationship between
measures of cognitive ability and strategic behavior
Ballinger et al. (2011), Baghestanian and Frey (2012), Bayer and Renou (2012), Brañas-Garza, Garcia-Muñoz, and Hernan Gonzalez (2012), Brañas-Garza, Paz Espinosa, and Rey-Biel (2011), Burks et al. (2009), Burnham et al. (2009), Carpenter, Graham, and Wolf (2013), Chen, Huang, and Wang (2013), Devetag and Warglien (2003), Georganas, Healy, and Weber (2013), Gill and Prowse (2015), Grimm and Mengel (2012), Jones (2014), Jones (2008), Kiss, Rodriguez-Lara, and Rosa-García (2014), Palacios-Huerta (2003), Proto, Rustichini, and Sofianos (2014), Putterman, Tyran, and Kamei (2011), Rydval (2011), Rydval and Ortmann (2004), and Schnusenberg and Gallo (2011)
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Manipulate cognitive resources
Rather than measure cognitive ability We manipulate available cognitive resources
Advantage to manipulating available cognitive resources Cognitive ability related to lots of other things
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How to think about the manipulation? Discovered crayon in Homer Simpson’s brain
Was causing cognitive shortcomings
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Homer without crayon in brainHomer with crayon in brain
How to manipulate cognitive resources? Cognitive Load
Task that occupies cognitive resources Unable to devote to deliberation Observe behavior
Require subjects to memorize a number Big number Small number Differences in behavior?
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Cognitive load and games
Milinski and Wedekind (1998) Roch et al. (2000) Cappelletti, Güth, and Ploner (2011) Carpenter, Graham, and Wolf (2013) Duffy and Smith (2014) Buckert, Oechssler, and Schwieren (2014) Allred, Duffy, and Smith (2015)
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Duffy and Smith (2014) Repeated 4-player prisoner’s dilemma
Under differential cognitive load
Given number Play game Asked to recall number
Between-subject design Subjects only in one treatment
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Duffy and Smith (2014)
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
Allred, Duffy, and Smith (2015) Play several one-shot games
under differential load
Within-subject design Subjects in both load treatments
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Allred, Duffy, and Smith (2015) 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
Work in opposite directions
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Allred, Duffy, and Smith (2015) What are the beliefs about the
distribution of the cognitive load?
What are the beliefs about the effect of the cognitive load on opponent?
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Experimental Design Play against computer opponent
Subjects told “How does the computer decide what to
play? A number of possible strategies have been programmed. Some computer strategies can be exploited by you. Some computer strategies are designed to exploit you.”
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Experimental Design 100 repetitions of Hide-and-Seek Game
Block of 50 under high load Block of 50 under low load Block of 50 playing naive computer
Either Up-Down-Down or 50-50 Block of 50 playing exploitative computer
Either BR to mixture or BR to WSLS
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Computer’s Actions(Pursuer)
Up Down
Your Actions(Evader)
Up 0 1
Down 2 0
Screenshot
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Experimental Design Low load
1-digit number
High load 6-digit number
Also scanned all 130 right hands Different paper
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Experimental Design Strongly incentivized memorization task Performance in memorization task
unrelated to payment for game outcome in that period
Paid for 30 randomly selected game outcomes if 100 memorization tasks correct
Paid for 29 if 99 correct … Paid for 1 if 71 correct Paid for none if 70 or fewer correct
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Experimental Design Timing within each period:
Given new number to remember Play game Receive feedback about that outcome Asked for number Repeat
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Details 130 Subjects
78 Rutgers-Camden 52 Haverford
13,000 game observations
z-Tree Fischbacher (2007)
Earned average $33 From $5 to $54
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Hypotheses
High load earn less against Exploitative computers and exploitable computers
High load farther from equilibrium proportions
High load more serial correlation
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Summary statistics Correct
High load 90.7% Low load 96.2% p<0.001
Down in Naïve 50-50 100% is “optimal” High load 61.5% Low load 58.5% p=0.07
Down in Naïve Pattern 33% is “optimal” High load 49.3% Low load 52.4% p=0.11
BR in Naïve Pattern High load 62.8% Low load 55.1% p<0.001
Down in Exp. WSLS 33% is “optimal” High load 55.9% Low load 56.8% p=0.60
Down in Exp. Mix 33% is “optimal” High load 52.3% Low load 56.1% p=0.03
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Proportions and serial correlation Binomial chi-square against exploitative opponents
High load different p<0.001
Low load different p<0.001
Not different Two-sample
Kolmogorov-Smirnov
Test of runs against exploitative opponents
One-sample K-S test High load not indep.
p<0.001 Low load not indep.
p<0.002 Not different
Two-sample Kolmogorov-Smirnov
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Earned Overall
High load 0.737 Low load 0.730 M-W not significantly
different
Naive Pattern High load 0.855 Low load 0.753 M-W p<0.001
Exploitative Mixture High load 0.664 Low load 0.602 M-W p=0.02
Exploitative WSLS Naive 50-50
Not significantly different
High load either earned more or no difference
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Earned across rounds Round: period under same treatment (1-50) Coefficient estimates and p-values
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DV: Earned
Round 0.00190 (p=0.006)
0.00190 (p=0.006)
0.00190(p=0.006)
High Load 0.0584 (p=0.04)
0.0584 (p=0.04)
0.120(0.004)
Round*High Load -0.00201(p=0.04)
-0.00201(p=0.04)
-0.00201(p=0.04)
Repeated meas? No Yes Yes
Treatment dums? No No Yes
AIC 31300.9 31270.5 31216.8
Higher earnings across periods
Higher earnings for high load
No improvement for high load
Response time across rounds Time remaining when decision was made Coefficient estimates and p-values
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DV: Time remaining
Round 0.0227(p<0.001)
0.0227(p<0.001)
0.0227(p<0.001)
High Load 0.234(p<0.001)
0.234(p<0.001)
0.664(p<0.001)
Round*High Load -0.005(0.004)
-0.005(0.001)
-0.005(0.002)
Repeated meas? No Yes Yes
Treatment dums? No No Yes
AIC 46501.9 44326.4 44299.4
Faster decisions across periods
Faster decisions for high load
Slower increase for high load
Conclusions Available cognitive resources
not related to standard measures of serial correlation not related to standard measures of mixing
proportions
No evidence that available cognitive resources related to standard results
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Conclusions
Available cognitive resources not necessarily related to increased earnings
either not significant or negative
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Conclusions
Available cognitive resources is related to improvements in earnings over time
Subjects with greater available cognitive resources will faster converge to optimal behavior
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