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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