1 behavioral game theory: cognitive hierarchy and level k approaches colin camerer, caltech...
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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 09RSF 4.July.2014
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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 but Q-cognitive hierarchy fits deviationsdeviations
CH τ=1.80
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Lab replicates direction of Lab replicates direction of field deviationsfield deviations
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Imitation learning produces Imitation learning produces convergence over time (week convergence over time (week
7)7)
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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% 2007-2009)
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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*/2Movies 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
Average Rating of 30 critics
Col
d O
peni
ngs
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Low quality movies are cold opened
Average Rating of 30 critics
Num
ber
of m
ovie
s
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Sophisticated moviegoers know cold openings have this quality
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Low quality movies are cold opened
Average Rating of 30 critics
Num
ber
of m
ovie
s
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Sophisticated moviegoers know cold openings have this quality
Naive moviegoers think cold openings have this quality
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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 sophisticationRSF 4.July.2014 42
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Cold opening variable is significantly positive in US15% 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)
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?
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)
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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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