“Constructed” preferences
SS200 Colin Camerer

Preferences: “complete, transitive” u(x), tradeoffs among goods


“Constructed” suggests expression of preference is like problemsolving:



Will you vote for John Kerry?
Answered by rapid intuition (tall, good hair) and/or deliberate logic
(positions on issues)
Alternative views of preference:



Historical note: Axioms not empirically well-founded. They were
designed to provide simple mathematical framework for aggregation
(utility demand) and because Pareto won the “what is utility?” battle
Learned (reinforcement, “locked in a closet” story)
“Discovered” (Plott, implies path-independence)
Hybrid view: Combination of predisposition (e.g., language,
“preparedness”), learning and logic
“Constructed” preference: effects






Context-dependence (comparative)
Description-dependent “framing
(descriptions guide attention)
Reference-dependence (changes, not levels; anchoring)
Some values “protected”/sacred (health, environment)
Is too much choice bad?
Open questions:





Are effects smaller with familiar choices?
Experts?
Markets?
New predictions (e.g. “big tip” labor supply experiment)
Cross-species (pigeons, rats, capuchins)
Preferences and utility theory:
A guide for neuroscientists
Colin Camerer, Caltech

Utility theory: numerical accounting for choices




Bundles of goods
Risky and ambiguous “gambles” (EU, SEU)
Choices over time (discounted utility)
Representation theorems:


Find mathematical structures that map onto
(“represent”) observable choices
U(x) > U(y)
iff
xy
numbers
preferences
EU: Preferences over risk

How do people weigh and combine
likelihoods and outcomes?





Gambling
Risky investment (stocks, college, mates)
Insurance
Social risks (terrorism, global warming)
Notation: f(x) is a risk with probability
f(x) of outcome x
Where utility theories come from

Axiomatic



Empirical


What preference structures would have adapted? (e.g., Robson
JEcLit 01, JEcPers 02)
Neural


What mathematical functional forms fit choice data?
Evolutionary


Decompose representations into logical “bones”
Find sets of axioms that are mathematically equivalent to
numerical representations
Do brain structures obey axioms?
Ideal: All four criteria should cohere
Possible decision rules

Maximin



Safety-first/VAR



Choose best EV with p(loss) below a threshold
f*=argmaxg Σxxg(x) subject to Σx<0 g(x)<p*
Mean-variance



Choose risk with the best worst outcome
f*=argmaxg [minx x]
Prefer high EV, low variance
f*=argmaxg E(g)-bσ2(g)
Expected utility


Choose risk with highest probability-averaged
outcome utility
f*=argmaxg Σxg(x)u(x)
The rise (and fall?) of expected utility

Why EU?

EV-maximization Σxxg(x) easily disproved


St. Petersburg paradox
…but EU is a simple generalization of EV
Axioms:


Completeness of preference (including transitivity)
Continuity (“solvability”)


Cancellation (independence)


If fgh then there exists p such that pf+(1-p)hg
If fg then pf+(1-p)z  pg+(1-p)z for all z, p>0
Axioms imply EU form U(g)=Σxu(x)g(x)

Degree of risk-aversion: -u’’(x)/u’(x)
(Arrow-Pratt)
What’s wrong with the axiomatic approach



Axioms are useful if they are more transparent
than equivalent representations
Easier to judge normative content than
descriptive
Is generality a seductive illusion?




Thou shalt not kill
Always cancel common consequences
Always tell the truth
Competing axioms are difficult to compare

E.g. independence versus betweeness
if fg then f pf+(1-p)g  g for all 1>p>0
Cancellation is logically sensible but
perceptually unnatural

Allais common consequence problem:


A: $1 M or? (.10, $5 M; .89, $1 M; .01, 0)
B: (.11, $1 M; .89,0) or? (.10,$5 M; .89,0; .01, 0)
Cancellation is logically sensible but
perceptually unnatural

Allais common consequence problem:




A: $1 M or? (10, $5 M; .89, $1 M; .01, 0)
B: (.11, $1 M; .89,0) or? (.10,$5 M; .89,0; .01, 0)
Majority choose $1M in A
and (.10,$5M) in B
Violates EU


A pair is (.11,$1M) or (.10,$5M) with common (.89,$1M)
B pair is (.11,$1M) or (.10,$5M) with common (.89,0)
Cancellation is logically sensible but
perceptually unnatural

Allais common consequence problem:




A: $1 M or? (10, $5 M; .89, $1 M; .01, 0)
B: (.11, $1 M; .89,0) or? (.10,$5 M; .89,0; .01, 0)
A’: (.11,$1M; .89, $1M) or? (.10, $5 M; .89, $1 M; .01,
0)
Brain craves whole gestalts, not decompositions
Compliance with axioms often depends
on unnatural representations

58% choose C over D
Sensible?

Source: Kahneman-Tversky JBus 86

Axioms require unnatural representations




BUT! D “first-order stochastically dominates” C (FOSD)
A and B rearrange C and D to make dominance transparent
KT: B chosen 100%, D chosen 42%
FOSD is only detectable if a table is constructed (or compare
CDF’s). Mas-Collel: But they would be fired!”
Choice is a psychological process
Will depend on many factors


Description-invariance (framing, referencedependence)
Actual study with n=792 docs (Harvard Med, Brigham
&Women’s, Hebrew U; McNeil et al JAMA ’80s)



Surgery
Radiation



treatment
10%
0%
treatment
Surgery
Radiation
90%
100%
1 yr
32%
23%
1 yr
68%
77%
5 yrs
66%
78%
5 yrs
34%
22%
choice
53%
47%
choice
82%
18%
both frames
60%
40%
Choice is a psychological process

Procedure-invariance (pref. reversal)

Prefer p-bet (.95, $4) over $ bet (.30,$16)
…but price p-bet higher

Context-invariance


Disappointment (across states [columns])
Regret (between choices [rows])
A
B

1/3
10
0
1/3
0
5+e
1/3
5
10
Is regret an overadapted learning signal?
(Gilovich-Medvec Olympic medalists study)
Many variants of expected utility

Source: Camerer JRiskUnc 88, Edwards (Ed) Utility Theories, 92
Useful tool: Marschak-Machina triangle for
representing 3-outcome gambles



Outcomes
x3>x2>x1
Each point is a
gamble
Theories dictate
indifference
curve shape

EU is equivalent to



Linear indiff curves
Parallel
Allais common
consequence
effect curves get
steeper toward
upper left
Different theories predict different
indifference maps
Facts from experimental studies:

Betweenness (linear indiff curves) often
violated (Prelec, 90 JRU, Camerer-Ho JRU 94):
If you prefer (.34,$20k)  (.17,$30k)
…should prefer (.34,$20k) to any mixture
But most pick (.01,$30k.;.32,$20k)  (.32,$20k)

Sensitive to compound lottery reduction though
More facts from experiments



Violations are larger when some probabilities are
low [inside the triangle]  nonlinear w(p) is
crucial
Animal behavior (rats) similar to humans (Kagel
et al)
Small effect of experimental stakes


Paying real money reduces noise, creates more
significant EU violations
Source: Camerer, 95; Harless-Camerer 94 Econometrica
Prospect theory, I

Key features:


Nonlinear weighting of probability





Reference-dependence, nonlinear w(p)
Zeckhauser bullet example, 6 5 and 1 0
Inflection (sensitivity), elevation (risk attitude)
KT (’92 JRU)
w(p)=pγ//(pγ+(1-p)γ)1/γ
Prelec (98 E’metrica) w(p)=1/exp((ln(1/p)γ)
 Large overweighting of low probabilities
 γ=.7
w(1/10)=.165, w(1/100)=.05, w(1/1,000,000)=.002
Morgenstern 79 J Ec Lit:

[Like Newtonian mechanics] The domain of our axioms on utility theory
is also restricted…For example, the probabilities used must be within
certain plausible ranges and not go to .01 or even less to .001, then be
compared with other equally tiny numbers such as .02 etc.”
Prospect theory value function:
Note kink at zero and diminishing marginal sensitivity
(concave for x>0, convex for x<0)
Empirical weighting functions
SEU: Ambiguity and risk



Derive subjective (“personal”) probabilities from
bets between “states” s
SEU form is Σsu(x(s))p(s)
Ellsberg paradox:


(One) resolution: p(A)+p(not-A) < 1



p(s) cannot express both likelihood and “weight of
evidence” or ambiguity
P(A)/p(not-A) is likelihoood
1-p(A)-p(not-A) is reserved belief
Caution: Updating given new information is
tricky…
Ambiguity-aversion
with knowledge questions
1. Ambiguity Aversion (with Ming Hsu et al)



Ambiguity is uncertainty about probability,
created by missing information that is relevant
and could be known
Does “weight of evidence”/ambiguity matter?
Longstanding debate
 Savage: No



Logic overrides discomfort of not knowing
Keynes, Knight, Ellsberg, experiments: Yes
Many new theories (Gilboa-Schmeidler et al)
Pessimism over sets of beliefs
 Nonadditive beliefs (“missing” probability is
“reserved belief”)

Historical suggestion: Distinct neural
processes in ambiguity vs risk
"But if certain uncertainties in the problem were in cloudy
or fuzzy form, then very often there was a shifting of gears
and no effort at all was made to think deliberately and
reflectively about the problem. Systematic decomposition of
the problem was shunned and an over-all 'seat of the pants'
judgment was made which graphically reflected the
temperament of the decision maker.“ (Raiffa, 1963)
Ambiguity vs risk is important in social science


Home bias in equity markets (1-2%/yr), insurance,
incomplete contracting, entrepreneurship, “rolloff” in
voting, political incumbency advantage, brand loyalty,
law (“not proven” in Scottish law), game theory
Ambiguity-aversion  pure demand for information
even if it doesn’t affect a decision



E.g. medical overtesting, “sunshine laws” in politics
Inflames hindsight bias in manager-worker “agency”
relationships
Permits encoding bias:

US Senate Iraq report; “…led intelligence community to
interpret ambiguous evidence as conclusive of a WMD
program…”; Bush: “it might come in the form of a mushroom
cloud”
Ambiguity-aversion as emotion-driven pessimism

Risk case:


P(red)=P(blue)=.5
Ambiguous case




w(red)=w(blue) but don’t add to 1
1-w(red)-w(blue) is “reserved belief”
…a “vigilance” signal expressed by limbic system?
Bet on red is valued



w(red)u($10)= P(red)u($10) - [P(red)-w(red)]u($10)
risky part
pessimism
 look for neural dissociation

Measure strength of ambiguity aversion by w(red)=P(red)γ

γ>1 ambiguity-aversion, γ=1 neutrality γ

Logit “softmax” model P(bet red>x)=1/(1+exp[λ*[xρ-10ρP(red)γ]])
Description-dependent “framing” (descriptions
guide attention)


Analogy to figure-ground in perception
Actual study with n=792 docs (Harvard Med,
Brigham &Women’s, Hebrew U; McNeil et al
JAMA ’80s)



Surgery
Radiation






Surgery
Radiation
10%
0%
treatment
90%
100%
1 yr
32%
23%
1 yr
68%
77%
5 yrs
choice
5 yrs
choice
66%
78%
34%
22%
53%
47%
82%
18%
both frames
60%
40%
Asian disease problem (-200 vs (1/3) of -600 / +400 vs (2/3) 600
Pro-choice vs pro-life
Politics: “spin” (Lakoff)




treatment
e.g. aren’t we better off w/ Hussein gone?
Liberation vs. occupation
…other examples?
Supply-side response: Competitive framing; which frame “wins”?
Some new frontiers

Animal model



Animals exhibit all EU violations humans do
Field studies
Imagined vs. learned probabilities
Weber et al Psych Sci)

Emotion and nonlinear w(p)
Rottenstreich Psych Sci)

Neural foundations
(Hsee-
(Erev,
Prospect theory, I

Key features:


Reference-dependence, nonlinear w(p)
Reference-dependence

Extension of psychophysics (e.g. hot-cold)
U(x-r)
U(.) “reflects” (gamble over losses)

Loss-aversion



Q: Is loss-aversion a preference or a forecasting mistakes
(underestimates emotional “immunity” a la Tim Wilson-Dan
Gilbert)?
Loss-aversion in savings decisions
(note few points with y-axis actual utility <0) Chua & Camerer 03
Actual Utility Vs Optimal Utility
Actual Utility Gains/Losses
50
40
30
20
10
-50
-30
0g
-10
-10
10
-20
-30
-40
-50
Optimal Utility Gains/Losses
Data Points
Jack Knife Regression
30
50
Reference-dependence modelling (Koszegi-Rabin, 05)

Two problems in prospect theory:



KR solution




Is v(c-r) the only carrier of utility? Probably not…
How is r “chosen”? Perceptual? Expectations? How are expectations
chosen?
U(c|r)= m(c)+µ(m(c)-m(r))
separable into consumption
and “surprise” utility
For distributions F, F*=argmaxF∫cu(c|r)dF(c)
For reference distribution G, F*=argmaxF∫c∫ru(c|r)dF(c)dG(r)
Axioms:



A0: µ(x) continuous, twice differentiable (for x≠0), µ(0)=0
A1: µ(x) strictly increasing (µ’(x)>0)
A2: If y>x>0, then µ(y)+µ(-y)<µ(x)+µ(-x)




(convexity of disutility is weaker than concavity of utility)
A3: µ’’(x)≤0 for x>0 and µ’’(x)≥0 for x<0
(reflection effect)
A3’: For all x≠0, µ’’(x)=0
(piecewise linear utility)
A4: limx-->0 µ’(-|x|) / limx-->0 µ’(|x|) = λ > 1 (coef. of loss-aversion)
Economic domain
citation(s)
Type of data
Estimate
λ
Instant endowment effects for goods
Kahneman-Knetsch-Thaler
(1990)
Field data (survey), goods
experiments
2.29
Choices over money gambles
Kahneman and Tversky
(1992)
Choice experiments
2.25
Asymmetric price elasticities for consumer product
increases & decreases
Putler (1992), Hardie-FaderJohnson (1993)
Supermarket scanner data
2.40, 1.63
Loss-aversion for goods relative to money
Bateman et al (2004) ADD
NAMES
Choice experiments
1.30
Loss-aversion relative to initial seller “offer”
Chen, Lakshminarayanan,
Santos (2005)
Capuchin monkeys trading tokens for
stochastic food rewards
2.70
Reference-dependence in two-part distribution
channel pricing
Ho-Zhang (2005)
Bargaining experiments
2.71
Aversion to losses from international trade
Tovar (2005)
Non-tariff trade barriers, US 1983
1.95-2.39
Surprisingly few announcements of negative EPS
and negative year-to-year EPS changes
DeGeorge, Patel and
Zeckhauser (1999)
Earnings per share (EPS) changes
from year to year for US firms
Disposition effects in housing
Genesove & Mayer (2001)
Boston condo prices 1990-97
Disposition effects in stocks
Odean (1998)
Individual investor stock trades
Disposition effects in stocks
Weber and Camerer (1999)
Stock trading experiments
Daily income targeting by NYC cab drivers
Camerer-BabcockLoewenstein-Thaler
(1997)
Daily hours-wages observations (three
data sets)
Equity premium puzzle
Benartzi-Thaler (1997)
US stock returns
Consumption: Aversion to period utility loss
Chua and Camerer (2004)
Savings-consumption experiments
Monkey loss-aversion




(a,b,c) means display a,
then pay b or c
One: stochastic
dominance
Two: referencedependence (risky)
Three: referencedependence (riskless)
Reference-dependence

Sensations depend on reference points r

E.g. put two hands in separate hot and cold water, then
in one large warm bath


Loss-aversion ≡ -v(-x) > v(x) for x>0 (KT 79)


Hot hand feels colder and the cold hand feels hotter
Or v’(x)|+ < v’(x) |- …a “kink” at 0; “first-order riskaversion” aka focussing illusion?
Requires theory of “mental accounting”



What gains/losses are grouped together?
When are mental accounts closed/opened?
Conjecture: time, space, cognitive boundaries matter

Example: Last-race-of-the-day effect (bets switch to longshots
to “break even”, McGlothlin 1956)
Reference-dependence modelling (Koszegi-Rabin, 05)

Prop 1: If µ satisfies A0-A4, then “reference
point preference” follows


Big move: What is reference distribution?




(If A3’), then for F and F’, U(F|F’) ≥U(F’|F’)  U(F|F)
≥U(F’|F)
Impose “personal equilibrium”: r=F*
Pro: Ties reference point to expected actions
Con: If µ(x) is a “prediction error” designed for
learning, r=F* means there is nothing to learn
Implication: Can get multiple equilibria (buy if
you plan to buy, don’t buy if you don’t)

Role for framing/advertising etc. in choosing an
equilibrium (supply side response)
Endowment effects (KKT JPE ’90)
KKT “mugs” experiment (JPE ‘90)
Reference-dependence and
endowment effects


Koszegi-Rabin applied to pens (xp), $ (xd)
Utility is direct plus “transition utility” t(.)
u ( x p , x d ; y p , y d )  bx p  x d  t ( y p )  t ( y d )
if y p  0,

  v( y p )  ω  b  y p
t( y p )  

     v(| y p |)    ω  b  y p if y p  0,

ω is weight on ref-dependent utility, λ is
strength of loss-aversion
Endowment effects analysis


Choosing (choice-equivalent Pc)
 Reference points r(p)=r(d)=0
 U(gain pen)=b+ωb
U(gain Pc)= Pc+ ωPc
 Equating gives Pc=b
Selling (selling price Ps)
 Reference points r(p)=b, r(d)=0
 U(“lose” pen, gain $)  PS      b  1    PS
 U(keep pen, gain 0)= b
b(1   )
 Equating gives Ps=
1 
b(1   )
b =
1  

Buying price P

Prices ordered by Ps>Pc >Pb iff λ, ω>0
Plott-Zeiler review
Data from young (PCC) and old (80 yr olds) using
PZ instructions (Kovalchik et al JEBO in press 04)
Plott-Zeiler (AER 05) results:
replication (top) vs mugs-first (bottom)
“Status quo bias” and defaults in organ
donation (Johnson-Goldstein Sci 03)
Disposition effects in housing (Genesove and
Mayer, 2001)


Why is housing important?
It's big:


It’s likely that limited rationality persists






Residential real estate $ value is close to stock market value.
most people buy houses rarely (don't learn from experience).
Very emotional ("I fell in love with that house").
House purchases are "big, rare" decisions -- mating, kids, education, jobs
Advice market may not correct errors
buyer and seller agents typically paid a fixed % of $ price (Steve Levitt
study shows agents sell their own houses more slowly and get more $).
Claim:

People hate selling their houses at a "loss" from nominal [not inflationadjusted!] original purchase price.
Boston condo slump in nominal prices
G-M econometric model
Model: Listing price L_ist depends on “hedonic terms” and m*Loss_ist
(m=0 is no disposition effect)
…but *measured* LOSS_ist excludes unobserved quality v_i
…so the error term η_it contains true error and unobserved quality v_i
…causes upward bias in measurement of m
Intuitively: If a house has a great unobserved quality v_i, the purchase
price P^0_is will be too high relative to the regression. The model will
think that somebody who refused to cut their price is being loss-averse
whereas they are really just pricing to capture the unobserved
component of value.
Results: m is significant, smaller for investors (not
owner-occupants; less “attachment”?)
Cab driver “income targeting” (Camerer et al QJE 97)
Cab driver instrumental variables
(IV) showing experience effect
Capuchins obey law of demand
(K. Chen et al 05)
“Arbitrary” valuations


Stock prices?
Wages (what are different jobs really worth?)





Depends on value to firm (hard to measure)
& “compensating differentials/disutility (hard to
measure)
Exotic new products
Housing (SF Pittsburgh tend to buy “too much
house”; Simonsohn and Loewenstein 03)
Exec comp'n (govt e.g. $150k for senator, vs
CEO's, $38.5 million Britney Spears)
Anchored valuation: Valuations for listening to
poetry framed as labor (top) or leisure (bottom)
(Ariely, Loewenstein, Prelec QJE 03 and working
paperhttp://sds.hss.cmu.edu/faculty/Loewenstein/downloads/Sawyersubmitted.pdf
What econ. would happen if valuations are arbitrary?









Perfect competition price=marginal cost…anchoring influences
quantity, not price; expect large Q variations for similar products
Attempts to influence the anchor (QVC home shopping, etc., "for
you just $59.95”).
Advertising!!!
If social comparison/imitation is an anchor, expect geographical,
temporal, social clustering (see this in law & medical practice)
E.g., CEO pay linked to pay of Directors on Board's comp'n
committee. Geographical differences in housing prices,
London,Tokyo, NYC, SF.
Interindustry wage differentials for the same work (Stanford
contracts out janitorial service so it doesn't have to pay as much; cf.
airline security personnel??)
Sports salaries: $100k/yr Miami Dolphins 1972 vs $10million/yr
modern football
Huge rise in CEO comp'n from 1990 (42 times worker wage) to 2000
(531 times); big differentials between US and Europe
Consumers who are most anchorable or influenceable will be most
faddish -- children and toys!!? (McDonald's happy meal etc)
1/n heuristic & partition dependence in the lab
(cf. “corporate socialism”, Scharfstein & Stein, at corporate level)
Experimental markets & prob judgment
1. Abstract stimuli vs natural events??
pro: can precisely control information of individuals
can conpute a Bayesian prediction
con: maybe be fundamentally different mechanisms than for concrete events...
2. Do markets eliminate biases?
Yes: specialization
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Market is a dollar-weighted average opinion
Uninformed traders follow informed ones
Bankruptcy
No: Short-selling constraints
Confidence (and trade size) uncorrelated with information
Camerer (1987): Experience reduces pricing biases but *increases* allocation
biases
Contingent claims markets:
Markets enforce correct prices..BUT probability judgment influences
allocations and volume of trade (example: Iowa political markets)
Choice-aversion
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How to model “too much choice”?
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Anticipated regret from making a mistake
“grass is greener”/buyer’s remorse
Direct disutility for too-large choice set (e.g. too complex)
Policy question:
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Markets are good at expanding choice…what is a good
institution for limiting choice?
Example: Bottled water in supermarkets
Limit “useless” substitution? What is the right amount?
Pro-govt example: Swedish privatized social security
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Offered hundreds of funds
Default fund is low-fee global index (not too popular)
Most popular fund is local tech, down 80% 1st yr
Is too much choice bad?
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Jams study (Iyengar-Lepper):
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Assignment study:
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Short list
Long list
40% stopped, 30% purchased
60% stopped, 3% purchased
74% did the extra credit assignment
60% did the extra credit assignment
Participation in 401(k) goes down 2% for every 10 extra funds
Shoe salesman: Never show more than 3 pairs of shoes…
Medical
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6 jams
24 jams
65% of nonpatients said they would want to be in charge of medical
treatment…but only12% of ex-cancer patients said they would
Camerer conjecture: The curse of the composite
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Paraphrased personals ad: “I want a man with the good looks of Brad
Pitt, the compassion of Denzel Washington…”
Is there “too much” mate choice in big cities?
IIlusions of transparency
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“Curse of knowledge”
Difficult to recover coarse partition from fine-grained one
Piaget example: New PhD’s teaching
EA Poe, “telltale heart”
Computer manuals
“ The tapper” study (tapping out songs with a pencil)
Hindsight bias
Recollection of P_t(X) at t+1 biased by whether X occurred
“I should have known!”
“You should have known” (“ignored warning signs”)
--> juries in legal cases (securities cases)
implications for principal-agent relations?
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Spotlight effect (Tom Gilovich et al)
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Eating/movies alone
Wearing a Barry Manilow t-shirt
 psychology: Shows how much we think others are attending when they’re not
Some references
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Camerer 1995 Handbook Expl Econ
Camerer & Harless 94 Econometrica
Camerer 1989 JRiskUnc, Edwards 92 edited book
Camerer World Congress Ec’ic Society 05 (avail 11/05)
John Hey chapter (Kreps-Wallis book) 97 (more pro-EU)
Starmer J Ec Lit 2002
John Quiggin, Duncan Luce 2000+ books
Annual Rev Psych articles on decision making (Shafir
LeBoeuf 2000 et al)
Camerer Behavioral Game Theory, Princeton, 2003