Risk preferences

by

TABLE OF CONTENTS

CHAPTER # 4: RESULTS1

The Bank Offer1

Econometric Analysis2

Random Effects Logit Model4

CHAPTER # 5: DISCUSSION6

Summary8

REFERENCES10

CHAPTER # 4: RESULTS

People make decisions daily, decisions which often involve risk and sometimes large sums of money. The game show Deal or No Deal offers a unique opportunity to evaluate theories on decision making under uncertainty. It is also ideal for measuring risk aversion among contestants, and may give insight into the coefficient of risk aversion for the general population. Using data from the UK version of the game, in this research the researcher uses a random effects logit model under the assumption that Expected Utility Theory (EUT) is the correct model of decision making under uncertainty. This yields an estimate for the parameter of risk aversion. This research then seek evidence against EUT by repeating the random effects logit model for three subsamples which are created based on outcomes in the game (i.e. path dependence). If EUT is the correct specification, the models should not significantly differ.

The Bank Offer

Table below shows descriptive statistics of the bank offers by round. From this information, it is difficult to determine how the Banker may make his offers, since we are unable to tell anything about the cases that remain in play. It is interesting to note, however, that very few players accept offers before the sixth round, and most offers are accepted between the sixth and eighth rounds. This suggests that the Banker may be setting his offer in a manner as to encourage players to stay in the game until this point. Possible reasons for this are discussed below.

Descriptive Statistics of Bank Offers

Round

Obs

Females/Males

Mean

Standard Deviation

Min

Max

Acceptance Rate (%)

1

169

1.16

29502.98

20046.01

3

94000

0

2

169

1.16

44863.91

28536.3

7000

153000

0

3

169

1.16

58491.13

36993.74

9000

187000

0.6

4

168

1.18

75697.92

49834.32

250

292000

3.6

5

162

1.18

81292.28

62794.3

150

411000

7.4

6

150

1.27

92552.93

74064.95

40

349000

20.7

7

119

1.16

100443.9

96326.17

30

464000

42

8

69

1.23

79963.84

97689.21

20

375000

50.7

9

34

1.62

26105.53

43821.54

2

198000

35.3

All

1209

1.2

66650.5

62945

2

464000

X

Twenty-two players never accept any offers. It may be important to note, however, that of these twenty-two players, nineteen have a case with an expected value of less than £5,013 in round nine. It is also interesting to note how the average bank offer increases round on round until round seven, after which the average bank offer begins to decline. In special games, however, bank offers continue to increase even after the seventh round. With only this information, it is difficult to explain why this occurs, but it is likely because large cases are being eliminated, which becomes more likely as the game progresses due to the initial distribution of prizes.

Econometric Analysis

A strategic Banker who has similar objectives as the producers of the show may want to keep contestants in the game for early rounds and also build excitement in order to boost ratings. Subsequently, in later rounds his objectives would change so as to minimize the amount that the show must pay out. These objectives alone would explain the increasing bank offers (as a fraction of the case's expected value). However, a truly strategic banker would use all information available to him to determine the optimal offer he should make in each round. This includes not only descriptive statistics of the cases remaining in play, but also contestants' individual characteristics such as age, occupation, and even ...