Ming Hsu

Meghana Bhatt

Ralph Adolphs

Daniel Tranel

Colin Camerer

Neural Systems Responding to Degrees of Uncertainty in

Human Decision-Making

What is Neuroeconomics

Neuroeconomics seeks to ground economic theory in details about how the brain works.

Adjudicate competing models Debates between rational-choice and behavioral models

usually revolve around psychological constructs E.g. loss-aversion and a preference for immediate rewards. Before, these constructs have typically been unobservable.

Provide new data and stylized facts to inspire and constrain models.

Example: Dual-self models A number of them in recent years

Bernheim & Rangel 2004 Benahib and Bisin 2004 Benabou and Pycia 2002 Brocas and Carrillo 2005 Fudenberg & Levine 2005 Miao 2005

“This is consistent with recent evidence from MRI studies, such as McClure et al. [2004], that suggests that short-term impulsive behavior is associated with different areas of the brain than long-term planned behavior.” (Fudenberg & Levine)

The notion of a dual-self has been around since Plato. Neuroscientific data new.

Tools of Neuroeconomics

These (and other) tools enable us to study economic behavior at the neural level Functional magnetic resonance imaging (fMRI)

Indirect observation of neuronal activity Temporal resolution: 2-3 secs Spatial resolution: 2-3 mm3

Lesion patients Assess the necessity of brain region for certain behavior. Spatial resolution: varies with size of lesion.

Modularity: this organizing principle of the brain is what allows us to use these tools.

Decision Making Under Risk and Ambiguity Ambiguity and ambiguity aversion is a long-standing topic in

decision theory. Knight, Keynes, Ellsberg, and co.

There is a large theoretical and empirical literature to draw upon. Schmeidler 1989 Gilboa & Schmeidler 1988 Camerer & Weber 1992

Invoked to explain a number of economic phenomena Home bias Equity premium Entrepeneurship

The behavioral phenomenon is robust Camerer & Weber reviews experimental evidence.

Decision Making Under Risk and Ambiguity Ambiguity is uncertainty about probability, created by missing

information that is relevant and could be known. Risk: Probability of head on a fair coin toss (known p, p = 0.5) Ambiguity: Probability of head on a biased coin of unknown bias

(unknown p, p = ?)

Ellsberg Paradox Urn A with n balls: n/2 red, n/2 green. Urn B with n balls: k red, n-k green (k unknown). Lottery: choose color, then ball from urn. If match, win $x. If mismatch,

$0. Most people indifferent between choosing red or green in either urn A or

urn B. Non-trivial proportion prefer urn A.

Approaches to Decision-Making Under Ambiguity

Deny existence of ambiguity/risk distinction

Models of ambiguity aversion Non-additive probabilities (capacities and Choquet

integrals) set-valued probabilities (min-max) 2nd order prior and nonlinear weighting State dependent utility models Overgeneralization of a rational aversion to asymmetric

information

What Neuroeconomics Can Say?

Are risk and ambiguity distinguished at a neural level.

If so, are the underlying neural circuitry Two systems

Competing Independent

One system

Can this data be used to constrain the existing models.

fMRI Experiment Design

Ellsberg type gambles Canonical example of decision-making under ambiguity

World knowledge questions Control for possible framing effects of numerical information Closer analog of “real-world” decisions

Adverse selection “Unnatural habitat” hypothesis. Betting against agent who has better information.

Ellsberg Type Questions

Yes NoYes No

Real World Questions

Betting Against Informed Opponent

0

Ambiguous condition

Risk condition

Experimental Sequence

Self paced trials48 trials totalStimuli present for 2 sec after choiceBlank screen 4-10 secEach session about 10-15 min

Statistical Analysis of fMRI DataImage time-seriesImage time-series

RealignmentRealignment

Statistical parametric map (SPM)Statistical parametric map (SPM)

General linear modelGeneral linear model

Parameter estimatesParameter estimates

Design matrixDesign matrix

TemplateTemplate

NormalisationNormalisation

SmoothingSmoothing

KernelKernel

StatisticalStatisticalinferenceinference

Gaussian Gaussian field theoryfield theory

p <0.05p <0.05

Courtesy of http//:www.fil.ion.ucl.ac.uk/spm

Data Analysis

Linear model 64x64x32 time series

Dummies damb: ambiguity trial

drisk: risk trial

dpost: post-decision interval : Hemodynamic response

convolution operator

1. Individual Analysis Ambiguity > Risk: i

amb > i

risk

Risk > Ambiguity: irisk >

iamb

2. Group Analysis: Random Effects

amb > risk

risk > amb

( )( ) ( )

.1

,,

,

ti

ti

tposti

posti

triski

riski

tambi

ambiii

t

y

dd

dy

εδ

ββ

βα

++

Λ+Λ+

Λ+=

−

Results

We find three main clusters of activation Amygdala: Fear of the unknown Lateral orbitofrontal (OFC): integration of Dorsal striatum

They appear to separate into two processes A fast-responding, “vigilance” signal process (amygdala + OFC). A slower-responding, anticipated reward region (dorsal striatum). Constitute a generalized system for decision-making under

uncertainty (including both risk and ambiguity). Behavioral experiments with lesion patients show that the

OFC is necessary for distinguishing risk and ambiguity.

Ambiguity > Risk

QuickTime™ and aTIFF (LZW) decompressor

are needed to see this picture.

Risk > Ambiguity

QuickTime™ and aTIFF (LZW) decompressor

are needed to see this picture.

Correlation of Behavior with Imaging

QuickTime™ and aTIFF (LZW) decompressor

are needed to see this picture.

€

u(x) = x ρ

π p, j ∈ {a,r}( ) = pγ j

U(x, p) = π ( p)u(x)

Pr(y =1) ≡1

1+ exp λ U(x, p) − u(c)( )( )

€

LogLik(y ) = y Pr(y =1)y∈y

∑

+(1− y) 1− Pr(y =1)( )

Lesion Patient Experiment

Lesion patients allow us to assess the necessity of a brain region for behavior.

Two groups OFC lesion: location of damage overlaps with

OFC activation. Control lesion: temporal lobe patients, lesions do

not overlap with activation. Groups matched on IQ, verbal abilities,

etiology.

Lesion Patient Experiment

QuickTime™ and aTIFF (LZW) decompressor

are needed to see this picture.

Risk and Ambiguity Attitudes

QuickTime™ and aTIFF (LZW) decompressor

are needed to see this picture.

Conclusion

Our results suggest Risk and ambiguity are product of a single system Produced by two possibly competing processes To distinguish between levels of uncertainty With ambiguity and risk being limiting cases The OFC is necessary for proper functioning of

the system.

Future Research Behavioral Typing (Ellsberg 1967)

There are those who do not violate the axioms, or say they won’t, even in these situations; such subjects tend to apply the axioms rather their intuition.

Some violate the axioms cheerfully, even with gusto. Others sadly but persistently, having looked into their hearts, found

conflicts with the axioms and decided, in Samuelson’s phrase, to satisfy their preferences and let the axioms satisfy themselves.

Still others tend, intuitively, to violate the axiom but feel guilty about it and go back into further analysis.

Further establish direction of causality Exogenously stimulate the amygdala. Look in special populations of striatal differences.

END