Why Do People Under-Search?

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Why Do People Under-Search? The Effects of
Payment Dominance on Individual Search Decisions
And Learning

• Gong, Binglin
• Shanghai JiaoTong University
• Ramachandran, Vandana
• University of Maryland
• June 2007
• _at_ ESA Rome

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Outline

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

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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?

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Literature Theory of Search

• Optimal searchreservation value strategy
• Keep 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).

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Literature Experiments on Search

• Schotter and Braunstein (1981) optimal
  searchreservation 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.

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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)

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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.

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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 s0.2. 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, sn.

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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.

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Estimate The Reservation Value

• 0 r/2 r 1r/2 2
• AwardU0,2
• Reservation Value r
• E(accepted draw)1r/2
• E(rejected draw)r/2
• Estimator of reservation value
• 2average(accepted-1, rejected)
• We get an estimated reservation value for each
  subject in each round.

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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.

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E(earning)
Search cost
Reservation value
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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 U0,2 U0,2 U0,10
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 variance serious under-search very big variance under-search
r, maxE(payoff) 1.553 0.586 9
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Alternate Order of Treatments
Subject ID Treatment Order Treatment Order 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
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Strategy Method And Real Search

• We use a mix of strategy method and real search
  in this experiment
• Reading instructions (reveal distribution of
  awards)
• Subjects choose strategy (reservation value )
• Subjects make decisions in real sequential search
  (repeat for 10 rounds)
• Subjects revise strategy (reservation value )
• All decisions are paid.

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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.

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Basic Statistics on Stated And Estimated
Reservation Values
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Deviation from Optimal Reservation Value
Note devr1b r1b r1,
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Percentage Deviation from Optimal Reservation
Value
Note pdevr1edevr1e/1.553100, pdevr2edevr2e/0
.586100, pdevr3edevr3e/9100.
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Deviation from Optimal Reservation Value As
Percentage of The Upper Bound of Award
Distribution
Note phdevr1edevr1e/2100, phdevr2edevr2e/21
00 phdevr3edevr3e/10100
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Learning from Real Search
Note learn1abs(devr1b)-abs(devr1a) learn2abs(
devr2b)-abs(devr2a) learn3abs(devr3b)-abs(devr3a
)
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Treatment EffectsResults of Wilcoxon Sign-Rank
Tests Individual Treatment Level
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Learning EffectsResults of Wilcoxon Sign-Rank
TestsIndividual Treatment Level
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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.

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Future Study

• Bigger sample size ? More power
• Add a risk posture test in the experiment
• Variance of payoff
• Other distributions of awards

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Thank you!