The valuation of bundles is not gain-loss context dependent.
H. K. Chung,1* A. Tymula,3 and P.W. Glimcher2.
*Correspondence at: hkc278@nyu.edu
of Psychology, 2Center for Neural Science, New York University; 3 School of Economics, University of Sydney.
Results – Gain-loss reference for decision under uncertainty.
Gain
∆U/ ∆X ↓
 Diminishing MU
Gain (α1-1)
0.4
0.2
0
-0.2
-0.4
-0.6
Loss (1-α2)
*
*
Drinks
Snacks
Gain: 24+6=30
Loss : 20+24+24+6=74
Total: 30*2+74*2=208
Loss α2 =0.8979
Methods – Certainty
Loss
Drinks
Snacks
Parametric analysis - aggregate level
N=43
N=22
1
2
3
4
7
Marginal utility
8
Drinks
Gain: 32+6=38
Loss : 30+32+30+6=98
Total: 136
𝜌1
𝜌1 1/𝜌1
U (X1,X2)=[β1X1 +(1- β1)X2 ]
𝜌2
𝜌2 1/𝜌2
U (X1,X2)= - [β2|X1| +(1- β2)|X2| ]
*
Drinks
Snacks
0.3
0.2
Prospect theory
-4
N=13
It works for decision
under uncertainty.
N=4
-5
-1
-0.8
MU↓
-0.6
-0.4
-0.2
0
Gain (α1-1)
0.2
0.4
MU↑
0.6
Non-parametric analysis
N=43
Loss (1-𝜌2Median)
Gain
0.4
Gain
0.2
Loss
1
0
-0.2
β
-0.4
0.5
0
 Diminishing
MRS
 Diminishing
MRS
Gain
0.2
Loss
1
0
-0.2
β 0.5
-0.4
0
-0.6
Prospect theory
0.9
N=5
N=2
Loss
-0.1
-1.1
-2.1
-3.1
-4.1
Prospect theory
-5.1
-6.1
Loss
-7.1
N=26
-1.5
Experimental procedure
Endowment
*
0.4
-3
Gain (𝜌1Median-1)
Gain
Comprehension
questions
0.5
-2
Loss (1-𝜌2)
-0.6
Gain
6
0.6
Loss
-1
Parametric analysis - individual level
Drinks
5
Gain
Coefficient of variation (CV)= SD/EV.
0
0.4
 Diminishing
MRS
Prospect theory
N=39
Gain (𝜌1-1)
MRSx: MUX ↓
MUY ↑
N=43
r=0.881* for α1s
r=0.808∗ for α2s
2
MU↓ Loss (1-𝜌2) MU↑
Snacks
 Increasing
MRS ?
MRSx: MUX ↑
MUY ↓
1
*
Non-parametric analysis
Results – No gain-loss reference for decision under certainty.
However, dose prospect theory also hold for
choices amongst riskless bundles of goods ?
X MUX

Y MUY
*
-1.2
 Prospect theory argues that the gain-loss reference is important
for decision-making under risky conditions .
Marginal rate of
substitution :
Loss (1-α2Median)
Goods
Introduction – Bundle and Indifference curve
8
7
6
5
4
3
2
1
 Increasing
MU
Marginal utility
Utility
ΔU
Marginal Utility:
ΔX
U(X) = Xα1 for gains
U(X) = - |X|α2 for losses
Snacks
Loss
Utility
 Increasing MU
 Diminishing
MU
α1 =0.4612
Gain (α1Median-1)
0.4
0.2
0
-0.2
-0.4
-0.6
MU↑
Gain
Outcome
∆U/ ∆X ↑
N=39
MU↓
 Kahneman and Tversky
(1979) proposed gain-loss
asymmetric utility
function to explain it.
N=43
Parametric analysis - individual level
Proportion Choose Risk
(Higher CV) option
Parametric analysis - aggregate level
Marginal utility
 Previous study found that risk preference is
gain-loss context dependent .
Methods – Uncertainty
Loss (1- α2)
Introduction – Prospect theory
Marginal utility
1Department
459.02
SS42
-1
N=6
-0.5
MU↓
0
0.5
1
Gain (𝜌1-1)
1.5
MU↑
2
2.5
It doesn’t work for
decision under certainty.
Tasks
Practice
rounds
Lottery blocks
(Gain/Loss)
Bundle blocks
(Gain/Loss)
Conclusions and Future plan
• Prospect theory holds in the lottery ─ gain-loss reference is important for decision-making under uncertainty.
• However, there is no gain-loss reference for choice of riskless bundles .
• The marginal utility of each good in a bundle was diminishing not only in the gain domain, but also in the loss domain.
• We need both brain data and a more general model that will explain gain-loss asymmetric valuation for lottery and the
mechanism of the disappearance of reference for the decisions over riskless bundles.
Reference: Kahneman, D., and Tversky, A. (1979). Prospect theory: An analysis of decision under risk. Econometrica, 47(2), 263-291. Varian, H.R. (1992). Microeconomic Analysis (3rd Edition). New York, NY: W. W. Norton & Company.
Fixed Probe
option option
(5,3);(6,3);(7,3);(8,3);(5,2);(6,2);(7,2);(8,2);
(5,1);(6,1);(7,1);(8,1);(5,0);(6,0);(7,0);(8,0);
Gain (4,4)
(3,5); (3,6);(3,7);(3,8);(2,5);(2,6);(2,7);(2,8);
(1,5); (1,6);(1,7);(1,8);(0,5);(0,6);(0,7);(0,8).
(-4,-2);(-5,-2);(-6,-2);(-7,-2);(-8,-2);
(-4,-1);(-5,-1);(-6,-1);(-7,-1);(-8,-1);
(-4,0);(-5,0);(-6,0);(-7,0);(-8,0);
(-3,-3)
(-2,-4);(-2,-5);(-2,-6);(-2,-7);(-2,-8);
(-1,-4);(-1,-5);(-1,-6);(-1,-7);(-1,-8)
;(0,-4);(0,-5);(0,-6);(0,-7);(0,-8).
(-5,-3);(-6,-3);(-7,-3);(-8,-3);(-5,-2);(-6,-2);(-7,-2);(-8,-2);
Loss
(-5,-1);(-6,-1);(-7,-1);(-8,-1);(-5,0);(-6,0);(-7,0);(-8,0);
(-4,-4)
(-3,-5); (-3,-6);(-3,-7);(-3,-8);(-2,-5);(-2,-6);(-2,-7);(-2,-8);
(-1,-5); (-1,-6);(-1,-7);(-1,-8);(0,-5);(0,-6);(0,-7);(0,-8).
(-6,-4);(-7,-4);(-8,-4);(-6,-3);(-7,-3);(-8,-3);
(-6,-2);(-7,-2);(-8,-2);(-6,-1);(-7,-1);(-8,-1);
(-5,-5) (-6,0);(-7,0);(-8,0);(-4,-6);(-4,-7);(-4,-8);
(-3,-6);(-3,-7);(-3,-8);(-2,-6);(-2,-7);(-2,-8);
(-1,-6);(-1,-7);(-1,-8);(0,-6);(0,-7);(0,-8).
Fixed
option
Gain
(4,40%)
(-3,30%)
Loss
(-4,40%)
(-5,50%)
Probe
option
(5,30%);(6,30%);(7,30%);(8,30%);(5,20%);(6,20%);
(7,20%);(8,20%);(5,10%);(6,10%);(7,10%);(8,10%);
(3,50%);(3,60%);(3,70%);(3,80%);(2,50%);(2,60%);
(2,70%);(2,80%);(1,50%);(1,60%);(1,70%);(1,80%).
(-4,20%);(-5,20%);(-6,20%);(-7,20%);(-8,20%);
(-4,10%);(-5,10%);(-6,10%);(-7,10%);(-8,10%);
(-2,40%);(-2,50%);(-2,60%);(-2,70%);(-2,80%);
(-1,40%);(-1,50%);(-1,60%);(-1,70%);(-1,80%).
(-5,30%);(-6,30%);(-7,30%);(-8,30%);(-5,20%);(-6,20%);
(-7,20%);(-8,20%);(-5,10%);(-6,10%);(-7,10%);(-8,10%);
(-3,50%);(-3,60%);(-3,70%);(-3,80%);(-2,50%);(-2,60%);
(-2,70%);(-2,80%);(-1,50%);(-1,60%);(-1,70%);(-1,80%).
(-6,40%);(-7,40%);(-8,40%);(-6,30%);(-7,30%);(-8,30%);
(-6,20%);(-7,20%);(-8,20%);(-6,10%);(-7,10%);(-8,10%);
(-4,60%);(-4,70%);(-4,80%);(-3,60%);(-3,70%);(-3,80%);
(-2,60%);(-2,70%);(-2,80%);(-1,60%);(-1,70%);(-1,80%).