Dynamic Choice Behavior in a Natural Experiment

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Dynamic Choice Behavior in a Natural Experiment

• Steffen Andersen, Glenn W. Harrison,
• Morten I. Lau and Elisabet E. Rutström
• Durham Business School, Durham University

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Introduction

• Deal or No Deal provides a wonderful opportunity
  to examine dynamic choice under uncertainty.
• Advantages of the television game show
• The show constitutes a controlled natural
  experiment
• Real and large stakes (from 1p to 250,000 in the
  UK version)
• Tasks are repeated in the same manner from
  contestant to contestant
• No strategic aspects are involved

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Introduction

• We examine two general issues in the
  specification of dynamic choice.
• (i) the characterization of this behavior
  assuming EUT
• Like Holt and Laury AER, 2002, we find that
  more flexible functional forms than CRRA or CARA
  are needed.
• One must also allow some flexibility about the
  arguments of the utility function (Cox and
  Sadiraj GEB, 2006).
• However, allowing for asset integration leads to
  choices consistent with CRRA.

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Introduction

• (ii) the characterization of behavior using
  alternatives to EUT
• We find that there is some probability weighting
  undertaken by the contestants, particularly in
  the gain domain (Quiggin JEBO, 1982)
• And there is no evidence of loss aversion using a
  natural assumption of the reference point
  (Kahneman and Tversky Econometrica, 1979)
• We employ data from the UK, reflecting 1,074
  choices by 211 contestants.

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Game Format

• Game format
• One contestant is picked at random from a group
  of 22 preselected people
• A known list of 22 monetary prizes (from 1p to
  250,000) is randomly placed in 22 boxes
• One box has been randomly allocated to the
  contestant before the show
• The contestant is informed that the money has
  been put in the box by a third party
• Any unopened boxes at the end of play are opened
  so that the contestant can confirm that all
  prizes were in the boxes

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The Proto-Typically British Trevor
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Game Play

• Game play
• In round 1, the contestant picks 5 boxes to be
  opened and the prizes are displayed
• At the end of round 1, the host is phoned by a
  banker who makes an offer to buy the
  contestants box
• If the contestant accepts the offer the play is
  over
• If the contestant rejects the offer he will pick
  3 boxes in round 2 to be opened, and so on...
• At the end of round 6 there are only two unopened
  boxes left, and 39 of the contestants reach that
  point

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Bank Offers

• Bank offers
• The typical offer in the first round is low
  compared to the average value of the prizes in
  the remaining 17 boxes
• We estimate the bankers offer curve, and he
  starts out at roughly 15 of the expected value
  of the unopened boxes
• This offer increases to roughly 24, 34, 42,
  54 and then 73 in rounds 2 through 6
• This trend is significant, and serves to keep all
  contestants in the game for at least 3 rounds
• Hence, it is clear that the box that the
  contestant owns has an option value in future
  rounds

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Estimates Assuming EUT
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(No Transcript)
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Rank-Dependent Preferences

• One can use non-linear transformations of the
  probabilities instead of non-linear utility
  functions (Yaari Econometrica, 1987).
• Quiggin JEBO, 1982 presented a more general
  case with probability weighting and non-linear
  utility.
• We consider two alternatives
• Rank-Dependent Utility by Quiggin (RDU)
• Rank-Dependent Expected Value by Yaari (RDEV)

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Rank-Dependent Preferences
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Cumulative Prospect Theory
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Conclusions

• The Deal or No Deal game incorporates many
  dynamic, forward-looking decisions in natural
  counterparts.
• We confirm the results from Holt and Laury AER,
  2002 that one must account for IRRA to explain
  behavior.
• We also show that the arguments of utility are
  not just the prizes of the lotteries, and that
  CRRA is a reasonable assumption when one allows
  for asset integration.
• Finally, we find no evidence of loss aversion.