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. 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


  • 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


  • 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.


  • (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)


  • 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.