Why Do People Under-Search? —The Effects of Payment Dominance on

Individual Search Decisions And Learning

Gong, BinglinShanghai JiaoTong University

Ramachandran, VandanaUniversity of Maryland

June 2007@ ESA Rome

Outline

• Research Questions• Literature Review• Theoretical Background• Discussion of Payoff Functions• Experimental Design• Experimental Results• Conclusions

Research Question

• Why do people under-search, as observed in previous sequential search experiments?

• Does payment dominance play a role here? If so, how and how much?

Literature: Theory of Search

• Optimal search—reservation value strategyKeep searching if the expected gain from search is higher than the search cost, and stop otherwise.--Stigler (1961)

• If the distribution is known, and search costs are constant, the optimal search strategy is to use a reservation value, and recall should not matter (should never be used).

Literature: Experiments on Search• Schotter and Braunstein (1981): optimal search—

reservation value strategy• Kohn and Shavell (1974): With increased search

costs, players become less selective • Sonnemans (1996), (1997): subjects write down

strategies instead of realized points• Cox and Oaxaca (1989), (1996), (2000): finite

horizon, unknown distribution• Hey (1981), (1987): individual behavior, rules of

thumb • They found that search is highly efficient (in terms

of earnings) and there is some tendency to recall. Lower reservation values than risk neutral predictions were observed.

Why Do People on Average Search Less Than Predicted?

• Risk Posture– All the above predictions are based on risk neutrality. If people

are risk averse, then accepting current value is safer than searching

– Risk posture may not be a sufficient explanation (Rabin 2000 - all experiments offer very low monetary prizes, over which one may assume that subjects are locally risk neutral. Cox and Oaxaca get different “risk preferences” estimates for the same subjects in different treatments.)

• Extra cost for search– Other than the costs assigned in the experiment, people need to

take time and effort to search and figure out best strategy.• Flat payoff

– Stopping rules that give rise to too little search perform rather well in most cases (Sonnemans 1998)

Literature: Payment Dominance• Glenn Harrison (1989)• Comments by Friedman, Kagel and Roth, Cox, Smith, and

Walker, Merlo and A. Schotter (1992 )• Reply by Glenn Harrison (1992 )• When an economic problem is complicated but

people can learn from the history, a flat payoff function can limit the information people get from experience and lead to noisier behavior.

• Economists should look at not only the “message space”, but also the “payoff space”.

• Experimenters should design experiments carefully to avoid the payment dominance problem.

Example of A Sequential Search Problem (Known Distribution, with Recall)

• In each period, one can randomly draw one award from the uniform distribution between 0 and 2, after paying the search cost s=0.2. These are known to the searcher.

• After each draw, one can decide whether to stop or to keep searching.

• If one stops after n draws, her total payoff is the highest draw minus the total search cost, s*n.

Theoretical Predictions for Risk Neutral Individuals

• Using optimal search strategy, when distribution is known, the reservation value r should satisfy:

• The expected number of draws n will be

• The expected earning in each round is

• If optimal strategy is used, the expected earning should be equal to reservation value.

tsearchrdyyfrygainEr

cos4

)2()()()(22

r-22...)

2r(

2r-23

2r

2r-22

2r-2)( 2 nE

rsr

22

22sE(n)-)E(acceptedE(earning)

Estimate The Reservation Value 0 r/2 r 1+r/2

2

• Award~U[0,2]• Reservation Value r• E(accepted draw)=1+r/2• E(rejected draw)=r/2• Estimator of reservation value:

2*average(accepted-1, rejected)• We get an estimated reservation value for each

subject in each round.

What We Learn About Payoff

• The bigger the award (price, wage, etc.) dispersion is, the steeper the payoff function is.

• The smaller the search cost is, the steeper the payoff function is.

00.5

1

1.5

2 0

0.5

1

1.5

2

-10

-5

0

00.5

1

1.5

2Reservation value

E(earning)

Search cost

Experimental Test of Payoff Dominance

• Use plat payoff and steep payoff as treatments, look at the difference of deviation from optimal strategy.

Treatment 1 2 3

Distribution U[0,2] U[0,2] U[0,10]

Search Cost 0.05 0.50 0.05

Slope of E(Payoff)(left, right)

0.3, -20 0.1, -0.1 0.45, -30

Diff. in Payoff in the relatively flat area

0.6 0.086 4

Predicted Reservation Value

big varianceserious under-

search

very big variance

under-search

r*, maxE(payoff) 1.553 0.586 9

Alternate Order of Treatments

Subject ID Treatment Order

1-4 1 2 3

5-8 1 3 2

9-12 2 1 3

13-16 2 3 1

17-20 3 1 2

21-24 3 2 1

Strategy Method And Real Search

• We use a mix of strategy method and real search in this experiment

1. Reading instructions (reveal distribution of awards)2. Subjects choose strategy (reservation value +)3. Subjects make decisions in real sequential search

(repeat for 10 rounds)4. Subjects revise strategy (reservation value +)5. All decisions are paid.

Why?

• By using strategy method - real searches - strategy method , we can measure the effect of learning from real search experiences.

• When we use strategy method and pay subjects the expected payoffs, we can eliminate risk aversion as a reason for under-search.

Reservation Values by Treatment

0

1

2

3

4

5

6

7

8

9

10

0 1 2 3 4

Treatment

Reser

vatio

nVa

lue

T1, beforeT1, estimateT1, afterT2, beforeT2, estimateT2, afterT3, beforeT3, estimateT3, afteraverage by treatmentTheoretical predictions

Basic Statistics on Stated And Estimated Reservation Values

Variable Obs Mean Std.Dev. Min Maxr1b 24.00 1.34 0.28 0.85 1.90r1e 24.00 1.44 0.23 0.91 1.80r1a 24.00 1.43 0.32 0.80 1.90r2b 24.00 0.79 0.46 0.00 1.99r2e 24.00 0.69 0.46 -0.42 1.37r2a 24.00 0.73 0.48 0.00 1.50r3b 24.00 7.64 1.67 5.00 10.00r3e 24.00 8.26 1.23 4.67 9.92r3a 24.00 8.57 0.90 6.00 9.77

Variable Obs Mean Std.Dev. Min Maxdevr1b 24.00 -0.22 0.28 -0.70 0.35devr1e 24.00 -0.11 0.23 -0.64 0.25devr1a 24.00 -0.12 0.32 -0.75 0.35devr2b 24.00 0.20 0.46 -0.59 1.40devr2e 24.00 0.11 0.46 -1.01 0.78devr2a 24.00 0.14 0.48 -0.59 0.91devr3b 24.00 -1.36 1.67 -4.00 1.00devr3e 24.00 -0.74 1.23 -4.33 0.92devr3a 24.00 -0.43 0.90 -3.00 0.77

Note: devr1b = r1b –r1*, …

Deviation from Optimal Reservation Value

Variable Obs Mean Std.Dev. Min Maxpdevr1b 24.00 -13.85 18.16 -45.27 22.34pdevr1e 24.00 -7.24 14.80 -41.25 15.94pdevr1a 24.00 -7.97 20.53 -48.49 22.34pdevr2b 24.00 34.31 78.78 -100.00 239.59pdevr2e 24.00 18.13 79.14 -171.67 132.99pdevr2a 24.00 24.29 82.66 -100.00 155.97pdevr3b 24.00 -15.14 18.53 -44.44 11.11pdevr3e 24.00 -8.25 13.72 -48.16 10.27pdevr3a 24.00 -4.76 10.05 -33.33 8.56

Note: pdevr1e=devr1e/1.553*100,

pdevr2e=devr2e/0.586*100,

pdevr3e=devr3e/9*100.

Percentage Deviation from Optimal Reservation Value

Variable Obs Mean Std.Dev. Min Maxphdevr1b 24 -10.7542 14.10287 -35.15 17.35phdevr1e 24 -5.62548 11.49451 -32.0333 12.3772phdevr1a 24 -6.19167 15.94005 -37.65 17.35phdevr2b 24 10.05417 23.08325 -29.3 70.2phdevr2e 24 5.311626 23.18909 -50.3 38.9657phdevr2a 24 7.116666 24.21851 -29.3 45.7phdevr3b 24 -13.6292 16.67374 -40 10phdevr3e 24 -7.4256 12.34909 -43.34 9.246941phdevr3a 24 -4.2875 9.042042 -30 7.700005

Deviation from Optimal Reservation Value

As Percentage of The Upper Bound of Award Distribution

Note: phdevr1e=devr1e/2*100,

phdevr2e=devr2e/2*100

phdevr3e=devr3e/10*100

Variable Obs Mean Std.Dev. Min Maxlearn1 24.00 0.02 0.19 -0.27 0.50learn2 24.00 -0.03 0.27 -0.83 0.49learn3 24.00 0.90 1.29 -1.00 3.00

Learning from Real Search

Note: learn1=abs(devr1b)-abs(devr1a)learn2=abs(devr2b)-abs(devr2a)learn3=abs(devr3b)-abs(devr3a)

Treatment EffectsResults of Wilcoxon Sign-Rank Tests

Individual Treatment Level

b Prob > |z| e Prob > |z| a Prob > |z|dev12 0.0005 dev12 0.0593 dev12 0.0101

13 0.002 13 0.052 13 0.241223 0 23 0.0027 23 0.0109

pd12 0.0036 pd12 0.1034 pd12 0.055513 0.9317 13 0.7971 13 0.886423 0.0039 23 0.0919 23 0.1529phd 0.0005 phd 0.0593 phd 0.010113 0.6475 13 0.6892 13 0.931723 0.0001 23 0.0345 23 0.0369

Learning EffectsResults of Wilcoxon Sign-Rank Tests

Individual Treatment Level

b=a Prob > |z| learning Prob > |z|dev1 0.0607 learn12 0.6233

2 0.4703 13 0.88523 0.0029 23 0.0028

pd1 0.0587 learnpd12 0.63392 0.4802 13 0.88523 0.0029 23 0.0028

phd1 0.0587 learnphd12 0.62332 0.4802 13 0.88523 0.0029 23 0.0028

Payoffs by Treatment

-2

0

2

4

6

8

10

0 1 2 3 4

Treatment

Payy

T1, beforeT1, realT1, afterT2, beforeT2, realT2, afterT3, beforeT3, realT3, afterAverage PayofPredicti on of E(pay)

Conclusions• Asymmetric expected payoff function can partly

explain under-searching.• Over-searching can happen when payoff function is

flat on both sides.• Flat payoff function leads to noisier behavior in

individual search decisions.• People learn more from real searches when payoff

function is steeper.• People sometimes make bigger mistakes in strategy

method than in real searches.

Future Study

• Bigger sample size More power• Add a risk posture test in the

experiment• Variance of payoff• Other distributions of awards

Thank you!