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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