Dynamic Choice Behavior in a Natural Experiment

1. Dynamic Choice Behavior in a Natural Experiment Steffen Andersen, Glenn W. Harrison, Morten I. Lau* and Elisabet E. Rutström *Durham Business School, Durham University

2. 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

3. 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.

4. 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.

5. 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

6. The Proto-Typically British “Trevor”

7. 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

8. 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

9. Estimates Assuming EUT

11. 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)

12. Rank-Dependent Preferences

13. Cumulative Prospect Theory

14. 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.