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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. Introduction. Deal or No Deal provides a wonderful opportunity to examine dynamic choice under uncertainty.

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dynamic choice behavior in a natural experiment

Dynamic Choice Behavior in a Natural Experiment

Steffen Andersen, Glenn W. Harrison,

Morten I. Lau* and Elisabet E. Rutström

*Durham Business School, Durham University

introduction
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
introduction1
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.
introduction2
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.
game format
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
game play
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 contestant’s 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
bank offers
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 banker’s “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
rank dependent preferences
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)
conclusions
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.
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