Applications (see Crawford+ 2010 review)
• Matrix steps
– Hedden, Zhang Cog 02, TICS 03
• 2D matrix beauty contest
– Chen, Huang, Wang (NatlTaiwanU) 09
• Hide-and-seek
– Crawford, Iriberri AER 06; Alec Smith, Forsell+ in prep
• Coordination games & cheaptalk (theory)
– Ellingsen, Ostling AER 12?
• Auctions
– Crawford, Iriberri Ecma 07; Gneezy MS 05; Ivanov Ecma 09;
Nunnari+ in prep
• Private-information betting games
– Brocas+ REStud in press
• Global games (theory)
– Kneeland (UBritishColumbia) 09?
• Heterogeneous CH/QRE splice
– Rogers, Palfrey, Camerer
JEcTheory 09
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2. Lowest unique positive
integer game (LUPI)
•
•
•
•
•
Swedish lottery
n=53,000 players
Choose k from 1 to 99,999
Lowest unique number wins 10,000€
If n is Poisson distributed…
– mixed equilibrium solves enp(k+1) = enp(k) – np(k)
Östling, Wang, Chou, Camerer AEJ: Micro 12
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Poisson equilibrium is a surprisingly
good approximation (week 1)…
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…but Q-cognitive hierarchy fits
deviations
CH τ=1.80
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Lab replicates direction of
field deviations
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Imitation learning produces
convergence over time (week 7)
60
40
20
0
2000
4000
6000
Number guessed
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8000
0
10000
17
18
4. Field application: Cold opened
(unreviewed) movies
(Brown, Camerer, Lovallo AEJ 12, Mgt Sci 13)
•
Film distributors choose:
– Show movie to critics before
opening
– Withhold (7% 2000-06; 25% 20072009)
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Logical “unravelling argument”
predicts no cold openings
(Milgrom Bell J 81, Grossman JLE 81 )
• Suppose quality is U ~ [0,100]
Movies below q* are opened cold
--> E(q|cold)=q*/2
Movies with q  [q*/2,q*] are misjudged
judged as bad, they are “not so bad”
….
 open all movies except very worst
• CH: Naïve moviegoers overestimate q,
box office gross is higher than predicted
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Low quality movies are cold opened
400
350
300
Cold Openings
250
200
150
100
50
0
0-20
20-40
40-60
Cold Openings
60-80
80-100
Regular Openings
Average Rating of 30 critics
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Low quality movies are cold opened
400
Number of movies
350
Sophisticated
moviegoers know
250 cold openings
have this quality
200
300
150
100
50
0
0-20
20-40
40-60
Cold Openings
60-80
80-100
Regular Openings
Average Rating of 30 critics
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Low quality movies are cold opened
Naive moviegoers
think cold openings
have this quality
400
Number of movies
350
Sophisticated
moviegoers know
250 cold openings
have this quality
200
300
150
100
50
0
0-20
20-40
40-60
Cold Openings
60-80
80-100
Regular Openings
Average Rating of 30 critics
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Why open cold?
• “If you screen [a bad movie] for critics all
they can do is say something which may
prevent someone from going to the
movie.”
• Greg Basser, CEO Village Roadshow
Entertainment Group
• “…if negative reviews are expected, the studio
may decide not to screen a picture hoping to
delay bad news.”
– Mark Litwak, Reel Power
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OLS estimation strategy
• Bm = αE(qm) + ΣkβkXmk + εm
Box office = f(expected quality,other controls)
• What is E(qm)?
–Reviewed movies: E(qm)=qm
–Cold opened movies: E(qm)> qm (from CH)
•Bm = αCCOLD + αRqm+ ΣkβkXmk + εm
•Coefficient αC > 0 indicates CH naivete
•Coefficient αC = 0 indicates sophistication
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Residuals: Cold vs. Reviewed Movies (based on log of 1st wkd BO)
2
1.5
1
Residual
0.5
0
-0.5
-1
-1.5
-2
0
10
20
30
40
50
60
70
80
90
100
Metacritic Rating
Cold Opened
Screened for Critics
Linear (Cold Opened)
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Cold opening variable is significantly positive in US
15% increase in revenue
 insignificant in UK, Mexico, US rental (DVD) markets
 Can be fit with CH model with  1.63 (Brown+ Mgt Sci in press)

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No effects in UK, Mexico, US rentals
(word leaks out)
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Propensity score matching
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PSM similar to OLS regression
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Studios learning that cold opening pays?
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frontier 2: What is level 0?
• My current view
– Level 0 is fast, salient
– Fundamentally an empirical question:
– Cf. Schelling:
• “one cannot, without empirical evidence,
deduce whatever understandings can be
perceived in a non-zero sum game of
maneuver any more than one can prove, by
formal deduction, that a particular joke is
bound to be funny.”
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But what’s salient?
•
•
•
•
“personal” numbers
ends + center of a number line
visual: Itti-Koch “low level” algorithm
Private info: Strategy = known state
– e.g. bid your value in an auction
– e.g. report state honestly in sender-receiver
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Neurally Based Models of Visual Salience
(Itti Koch Nature 05)
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Schelling (1960) map
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Fails on categorical
distinctiveness
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Meta-model approach: Level 0’s focus
on strategy features (Wright, Leyton-Brown subm 14)
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Georganas+ 14 (UG1)
Nash
(30%)
Level 1
(33%)
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Conclusions
• Cognitive hierarchy approach
– Lab, field, eyetracking, fMRI
• Many open questions
– Are there distinct types?
– Closer link to ToM regions
• Beliefs, intentions, attributions
– Disorders of strategic thinking
• Paranoia, gullibility, autism(s)
– Experience and expertise
– Endogenized steps
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