Difference in risk preferences between couples and individuals when large stakes are at risk

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Difference in Risk Preferences

between Couples and Individuals

when large Stakes are at Risk

Master’s Thesis

supervised by the

Faculty of Economics and Business at the

University of Amsterdam

Dr. Adam Booij

to obtain the degree of

Master of Science UvA (in Business Economics)

Author: Batuhan Kalyoncu

Course of Studies: Business Economics Student ID: 11374667

Address: Plantage Muidergracht 20 C5 1018 TV Amsterdam

E-Mail: kalyoncubatuhan@gmail.com

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Statement of Originality

This document is written by student Batuhan Kalyoncu, who declares to take full responsibility for the contents of this document.

I declare that the text and the work presented in this document is original and that no sources other than those mentioned in the text and its references have been used in creating it. The Faculty of Economics and Business is responsible solely for the supervision of completion of the work, not for the contents.

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Abstract

T

his thesis examines risky choices of contestants in a large-payoff TV game show called Var mısın(ız) Yok musun(uz). The main objective is to investigate differences in risk attitudes between contestants who take decision jointly as a couple and individuals who have the full decision power in their own hands. The results show a substantial difference in risk preferences with couples being less risk-averse. This difference, however, does not result in overall higher winnings for couples.

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Acknowledgments

F

irst and foremost, I want to thank my supervisor Dr. Adam Booij for his continuous feedback and unparalleled support. Also, I want to thank the production company Endemol Shine Turkey for supporting my thesis by sending me the recordings of previous seasons of Var mısın Yok musun and Ilker Co¸skun, for his support in getting in touch with the responsible people at Endemol Shine Turkey. It would have been impossible to conduct my research without these two parties. Specially, I want to mention the ongoing support of my parents, Leyla Görpe and Ibrahim Kalyoncu, without whom my studies at the University of Amsterdam would not have been possible. I am especially grateful for my fiancée Seher Ilciktay’s support and motivation in times of doubt as well as the time and effort she invested to proofread my work and to help in giving my thesis the final touch.

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Chapter 1 Introduction

M

any risky economic decisions in real life are taken by groupsrather than individuals. In companies, boards of executives, committees or working groups decide together on matters like market entry, product development, and investments. Beyond corporate settings, an important proxy for such groups are families, more specifi-cally couples. In a household, economic decisions that include risks are rarely taken without consulting with the partner. The more important the decisions are, the bigger the involved stakes and potential risks get, the more likely it is that couples will discuss options and decide jointly.

Saving or investment decisions of households have huge impacts on the economy. Therefore, it is worthwhile to study risky choices of couples. Many studies have been conducted regarding risk attitudes of individuals as well as the differences to small groups and couples, but how do the differences change when large stakes are at risk? This thesis has the objective to answer this question and to close this research gap by studying differences in risky choices of couples and individuals in a large-payoff TV show called Var mısın(ız) Yok musun(uz), which is the Turkish version of the globally known TV show Deal or No Deal. The well-defined, lab-like setting of this TV game show with known probabilities and risks, allows a proper investigation of risk preferences when the amount that can be won is very high.

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2 CHAPTER 1. INTRODUCTION Assuming myopic foresight of the contestants, this thesis can show that there is in fact a significant difference in behavior between couples and individuals. While both couples and individuals are risk-averse, contestants who have to reach a joint decision with their partner display risk preferences that are closer to risk-neutrality. This, however, does not result in overall higher winnings for one of the two groups in the sample.

The remainder of this thesis is as follows: Chapter 2 reviews former studies and prior research in this field. In Chapter 3, the game show is described in greater detail. The results are presented in Chapter 4, and Chapter 5 concludes.

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Chapter 2 Related Literature

T

With the rise in popularity of experimental economics in the lasthere is a wide variety of literature that investigates risky choices. decades, many laboratory experiments with monetary rewards were conducted to test theories like the normative expected utility theory of John von Neumann and Oskar Morgenstern (1944) and the descriptive prospect theory of Daniel Kahnemann and Amos Tversky (1992). Unfor-tunately, limited budgets restrict most of the experiments to small stakes. Some experimental studies try to overcome this issue by conducting their experiments in low-income countries to fabricate situations with high payoffs relative to the income (e.g., Hans P. Binswanger (1980, 1981) and Steven J. Kachelmeier and Mohamed Shehata (1992)). Nevertheless, pay-offs are usually not worth more than one month’s income and are therefore not particularly suited to investigate behaviour regarding life changing decisions. The biggest issue with these kind of field experiments is that it is mostly impossible to disentangle subjects’ risk preferences and their beliefs. The risk allocations as well as the distributions of probabilities are in reality not known to subjects.

Some researchers try to circumvent these issues by analysing risk pref-erences of contestants in television game shows like Card Sharks (Gertner, 1993), Jeopardy! (Metrick, 1995), Illinois Instant Riches (Hersch & McDougall, 1997), Lingo (Fullenkamp et al., 2003), and Who Wants to be a Millionaire?

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4 CHAPTER 2. RELATED LITERATURE (Hartley et al., 2006). Game shows are predestined to be analysed with their lab-like framework and potential large payoffs. These games are often set up in a way to present well defined decision problems that opens opportunities to get insights about human behaviour.

One of the most successful TV shows, which at the same time provides an excellent setup for analysis of risky choices, is Deal or No Deal?. This TV show, which has its origins in the Netherlands, was broadcast in more than 80 different countries around the world. With simple stop or go decisions and potential payoffs that range from a few cents to half-a-million, it provides an ideal platform for behavioural economic research.

Many researchers used this game show to investigate risk preferences of individuals. Andersen et al. (2008) used the UK edition of the show while Post et al. (2008) compared results of the Dutch, UK, and German editions. Bombardini and Trebbi (2005) and Botti et al. (2006) focussed on the Italian version, and based on the UK and Italian editions, Blavatskyy and Pogrebna (2008) showed that contestants do not display lower risk aversion when the probability of winning a large prize is small. Finally, Deck et al. (2008) used the Mexican episodes and De Roos and Sarafidis (2010) as well as Mulino et al. (2006) used the Australian version of Deal or No Deal to study risk preferences of contestants under potential large-payoff conditions.

In all these game shows, however, the contestants competed on their own, which leaves a substantial research gap regarding risky choices of couples. In fact, because it is hard to observe risk preferences of groups in real-life settings (for an exception, see Prather and Middleton (2002) using data from mutual fund management), most studies have used lab experiments to examine risky choices of groups.

These experiments suggest that groups are more risk-averse in lotteries in which the probabilities of winning the largest payoff are low, but less risk-averse when the probabilities are high (e.g. Bone et al. (1999), Baker et al. (2007), Shupp and Williams (2008), Masclet et al. (2009)). Their results are in line with findings from Kocher and Sutter (2002) as well as Cooper and Kagel (2005), who state that group choices are in general more rational

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5 than individuals.

The groups in the mentioned experiments were randomly assigned students, which poses the question of external validity. It is not clear that artificially created groups act in a similar way as endogenously formed groups with a long-lasting history or as couples that know each other very well. This potential issue has been recognized and recent studies examined risky choices of couples (He et al. (2012), with students; Bateman and Munro (2005), Carlsson et al. (2009), De Palma et al. (2011), with general population). The result of these experiments are in line with the ones mentioned above from Masclet et al. (2009). Individuals and groups are on average both risk-averse, but groups’ risk preferences are less divergent. The results are also in line with Shupp and Williams (2008), with groups being less risk-averse for lotteries with high probability of winning and the opposite results for lotteries with low probabilities of winning. These results suggest that neither does it seem to make a difference if groups are randomly assigned, nor does it play a role if couples are drawn out of a student population or the general public.

This thesis has the objective to combine the endeavors in the field of research of behavior when huge winnings are possible and the study of differences in risk preferences between individuals and couples. The goal is to contribute to research by answering the question how risk preferences of couples differ from individuals when large stakes are at risk. Following prior research, three hypotheses will be tested:

Hypothesis 1 Couples are on average less risk-averse than individuals when large stakes are at risk.

Hypothesis 2 Couples outperform individuals.

Hypothesis 3 The variance of risk preferences is smaller for couples than indi-viduals.

The data are drawn from the Turkish TV game show Var mısın(ız) Yok musun(uz), which is a slight variation of the Dutch original Deal or No Deal?. Contestant decisions of two seasons are examined, one with individuals

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6 CHAPTER 2. RELATED LITERATURE competing alone, and one with participating couples, who have to decide jointly. Using data from one country alone will mitigate differences caused by different behavior of the ’bank’1 as well as cultural differences between the contestants.

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Chapter 3 Description of the Show

T

he TV show Deal or No Deal has its origins in the Netherlands andwas first produced in 2002 by a company named Endemol. Its huge success led to exports to many different countries, one of them being Turkey, where the show first aired in 2006 called Büyük Teklif1 and continued running from 2007 until 2013 under the name Var mısın Yok musun2. After a three-year break, the show was picked up in 2016 introducing new features, with the most obvious being that instead of individuals, couples were competing together. The name was slightly changed to Var mısınız Yok musunuz, in order to adjust the verbs to plural form.

This thesis focusses on decisions of two seasons. The only season containing couples aired from June 16, 2016 until November 5, 2016, and is henceforth called V MYM2. The second most recent season before the

format changed aired from November 11, 2011 until March 29, 2012, and is henceforth called V MYM13. First, V MYM1 will be explained followed

by changes in V MYM2.

In V MYM1, all 24 contestants were randomly assigned to 24 sealed

and numbered boxes containing 24 randomly allocated, fixed and known

1_{This means Big Offer.}

2_{This means Are You In or Are You Out.}

3_{The season in between these two seasons is left out, because it aired only 8 episodes}

before the show was cancelled.

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8 CHAPTER 3. DESCRIPTION OF THE SHOW monetary amounts ranging from 1 to 500’000. One of the contestants was then randomly selected by a computer to play the game, while all other candidates remained having a chance to be selected in the next episodes. The chosen contestant kept her box, which was kept closed until the end of the show.

The game had a maximum of eight rounds. In each round, the contes-tant needed to choose which boxes she liked to have opened, before Mr. Hamdi, a person who watched the show from an undisclosed location and represented the bank, called and made an offer to buy the contestant’s box. The contestant was given some time to decide whether or not she wanted to accept (Deal) the sure amount offered. In case of refusal (No Deal), the game continued and one or more boxes were being opened.

The number of boxes that needed to be opened in the eight consecutive rounds were 5, 3, 3, 3, 3, 3, 2 and 1. This means that the number of prizes in each round have been reduced to 19, 16, 13, 10, 7, 4 and 24. Every opened box was automatically giving more information about the contestants own box. The offers were always based on the remaining prizes in the game and if the contestant rejected all offers, she was ultimately opening her own box at the end of the show and won the amount revealed by it. Mr. Hamdi’s offers started low (mostly less than 10 percent of the expected utility of all remaining prizes) and usually increased in each round, while they sometimes decreased in the last round depending on the remaining prizes5. To illustrate the rounds more clearly, Figure 1 provides a graphical description of the game.

In V MYM2, a few changes were made in order to make the show more

attractive. The game still contained 24 boxes, but was reduced by one round. The number of boxes opened in the seven consecutive rounds were

4_{The number of boxes has been reduced to 22 after episode ten, which reduced the}

maximum number of rounds to seven. The number of boxes to be opened were then 6, 3, 3, 3, 3, 2 and 1. While shortening the game, this change does not affect our study of risk preferences, since offers in the first few rounds have never been accepted.

5_{A decrease in terms of percentage of the expected outcome were occasionally}

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9 9, 3, 3, 3, 2, 2 and 16. The couples always had to agree on which boxes to open next and whether or not to accept the offer.

Moreover, in the first round, the competing couples faced 3 challenges, which were small games they needed to master. These games had to be played after opening 3, 6 and 9 boxes. Reaching the predefined goal in a game turned the biggest amount in the game that was smaller than 500’000 into 500’000 on the scoreboard. In the first episode, the goal of the contestants was to shoot a tennis ball through each of the three holes in a wall, using a big slingshot. They were allowed 30 attempts and they managed to shoot a ball through each of the holes and in consequence turned 250’000 to 500’000, meaning that if the couple would have rejected all offers and revealed 250’000 in their own box, they would have won 500’000. Another added feature was that the person who opened the box with the smallest amount ( 1) would win a car, if the competing couple would win the maximum amount of 500’000. While the added feature with the games changed the skewness of the prizes and thus the amounts offered by Mr. Hamdi, it is assumed that it had no effect on a couple’s risk preferences. Also, one could argue that a non-selected contestant who opened the box containing 1 could influence a couple in their decision process to raise her chances to win the car. This, however, never occurred in the 29 studied episodes.

6_{Similar to V MYM}

1, the number of boxes was reduced to 22 after episode 14, but

keeping the number of rounds equal. This reduced the amount of boxes that needed to be opened in the first round to seven.

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10 CHAPTER 3. DESCRIPTION OF THE SHOW open 5 boxes

24 boxes

Round 1 1st_{bank offer}

19 boxes

Round 2 open 3 boxes ₂nd _{bank offer}

16 boxes

Round 3 open 3 boxes ₃rd _{bank offer}

13 boxes

Round 4 open 3 boxes ₄th _{bank offer}

10 boxes

Round 5 open 3 boxes ₅th _{bank offer}

7 boxes

Round 6 open 3 boxes ₆th _{bank offer}

4 boxes

Round 7 open 2 boxes ₇th _{bank offer}

2 boxes

Round 8 open 1 box open contestant’s box

the game ends Deal No Deal Deal No Deal Deal No Deal Deal No Deal Deal No Deal Deal No Deal Deal No Deal

Figure 1: Example of a flow chart of the game show

In each round, the contestant needs to choose a number of boxes she wants to open. This is followed by an offer from the bank. Does the contestant choose to take the offer (Deal), she wins that offered amount and the game ends. In case of rejection (No Deal), she enters the next round and opens more boxes. The game continues in the same way and if the contestant chooses to reject all seven offers from the bank, she will finally win the amount that was hidden in her own box.

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Chapter 4 Results

4.1 Preliminary Analysis

T

his thesis examines 395 decisions of 69 contestants of two seasons of the Turkish version of Deal or No Deal?, one with competing individuals (244 decisions, 40 contestants) and one with competing couples (151 decisions, 29 contestants1). Seven episodes of V MYM1 and

six episodes of V MYM2were omitted, because the contestants were

Turk-ish celebrities, who donated their winnings. By selecting seasons from the same country as well as the same production company, differences in risk attitudes that could have been due to differences in wealth or cultural background between contestants, different behavior of the bank, or different selection procedure of contestants were mitigated.

For each round and contestant, data about eliminated and remaining prizes in the game, the bank offer and the contestants’ decisions were collected. The dataset also contains the contestants’ age, gender and their education. The contestants’ age and education are often revealed during parts of the show, in which private pictures of the contestants are shown and their life’s stories are told. Education is coded as a dummy variable, which takes the value 1 if the contestant has obtained a university degree or is currently studying and zero otherwise, following closely Post et al.

1_{A competing couple is counted as one contestant.}

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12 CHAPTER 4. RESULTS Table 1: Summary Statistics

Individuals Couples Diff. P-Value

Mean Std. Dev. Mean Std. Dev.

Age (years) 29.97 7.24 34.97 9.92 -5.00 0.018** Education (high=1) 0.48 0.51 0.41 0.48 0.07 0.615 Stop Round 5.90 0.36 5.45 1.15 0.45 0.042** Best Offer Rejected 0.26 0.13 0.43 0.24 -0.17 0.000*** Offer Accepted 0.43 0.30 0.63 0.40 -0.20 0.018** Amount Won ( ) 42’600 30’946 35’444 35’727 7156 0.378 * p < 0.1, ** p < 0.05, *** p < 0.01.

Notes: Diff. stands for the difference in means between the two independent samples Individuals and Couples. P-Value shows the statistical significance of Diff.. Age is measured in years. Education is a dummy variable that takes the value one if the contestant has a at least a university degree (or is a student). Stop Round shows the round number in which the bank’s offer was accepted (Deal). The ten episodes for V MYM1, in which the game could last one round longer, were

adjusted by -1. Best Offer Rejected displays the highest certainty-equivalent ratio (CER) (= bank offer / expected value of remaining prizes) the contestant chose to reject (No Deal). Offer Accepted is the ratio of offer the contestant accepted (Deal) or it is 1 if the contestant chose to win the amount in her own box.

and their methods. For contestants for whom the age or education is not explicitly mentioned, the values are imputed based on their physical appearance and additional information like age of their children or date of when one of the displayed pictures of the candidate was taken. For the competing couples, the averages of their age and education were used2.

The summary statistics of the gathered data is shown in Table 1. The competing couples were in general 5 years older than the individuals and similarly educated. The competing individuals played on average more rounds, therefore, rejecting more offers, while accepting on average lower certainty-equivalent ratios (CER = bank offer / expected value of remaining prizes). Furthermore, the Best Offer rejected for couples is also much higher than for individuals. This difference is statistically significant on the 1% level. In fact, the highest rejected CER for couples has on average the same value as the CER of accepted offers for individuals. These results

2_{There were 2 couples with one partner having a higher education than the other,}

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4.1. PRELIMINARY ANALYSIS 13 combined with the higher average number of rounds for individuals, suggests that the bank offers for V MYM1 were generally lower than

for V MYM2. Nevertheless, the mean of the amount won is higher for

individuals than for couples, despite the fact that couples were given chances to replace amounts in some boxes by an additional 500’000 and therefore having the chance to win even higher prizes. Couples do clearly not outperform individuals and in consequence Hypothesis 2 can be rejected. The results of Offer Accepted indicate risk-awareness for both group of contestants. Both means are well below a value of one, which symbolizes the preferred value of a risk-neutral contestant. The difference in means is statistically significant on the 5% level with couples being closer to one.

In Table 2, it is apparent that the bank offers are more generous in the couples edition. While the average CER increases gradually in both seasons, the highest overall percentage (38%) in V MYM1, is almost reached

(37%) by V MYM2 in its forth round and clearly surpassed in the last two

rounds (49% & 72%). Although there is a discrete change in bank behavior, this shift does not have an impact on contestants’ risk preferences under the assumption of myopia. A contestant that is confronted with an offer that is worth less to her than the ’lottery’ of continuing to play with the remaining prizes in the game, should always reject an offer which will ultimately lead to shows that end in later rounds. Examining Table 2, one can see that in fact for V MYM1, not a single episode ended before

round five, whereas in V MYM2, there was an episode that ended already

in round three.

In order to test whether there is a difference in behavior between couples and individuals in different risk regions, the CER is graphically displayed for different probabilities of winning a high prize. All prizes that are bigger than or equal to 50’000 are defined as a high prize and are also highlighted with a red background in the show to emphasize their high value. Moreover, whenever one of these prizes got eliminated, a sad background music was played. In consequence of these measures, it is safe to state that the contestants consider these prizes as high as well.

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14 CHAPTER 4. RESULTS Table 2: Offers and Decisions

All Deal No Deal

Rnd Nr. Stakes %CER Nr. Stakes %CER Nr. Stakes %CER

Individuals(N=40) 0 10 68’508 7 0 - 7 10 68’508 7 1 40 79’002 7 0 - 7 40 79’002 7 2 40 82’639 12 0 - 7 40 82’639 12 3 40 88’673 17 0 - 7 40 88’673 17 4 40 102’730 21 0 - 7 40 102’730 21 5 40 125’573 27 6 95’959 37 10 130’799 25 6 34 158’124 38 27 171’526 35 10 106’430 49 Couples(N=29) 1 29 84’885 13 0 - - 29 84’885 13 2 29 96’169 19 0 - - 29 96’169 19 3 29 99’602 25 1 101’073 46 28 101’476 24 4 28 103’011 37 5 86’378 63 23 103’145 33 5 23 87’451 49 10 102’612 39 13 75’789 57 6 13 66’363 72 6 113’243 65 7 26’180 80 Notes: This table follows closely the design of Post et al. (2008). For each game round (Rnd), the number of contestants who accept (Deal) and reject (No Deal) the bank offer is reported. Stakes determines the expected value of the remaining prizes and %CER is the certainty-equivalent ratio shown as a percentage. The rounds for the first ten episodes of V MYM1 are adjusted by -1 to correct for the initial larger amount of total

rounds. In two episodes of V MYM2, there was no offer in the last round, because the

Stakes were lower than 1’000 and the contestants automatically won the prize in their boxes. %CER was adjusted for this irregularity. The high percentage of 63 in the Deal condition in round 4 of the couples edition is a result of one exceptional high offer of 4’000, when the expected prize was roughly 2’000, otherwise the number would have been at 28%.

All offers were clustered to the closest multiple of 10% and the average CER for each cluster is displayed. Figure 2 shows impressively that the CER of the two samples highly correlates over the range of probabilities, with couples always rejecting as well as accepting higher CERs. Dividing the decisions results in support of the previous insights of this Chapter and reveals that the difference in behavior between the groups is similar over the spectrum of probabilities. Only if winning a high prize is certain, couples show higher risk-averseness. These results, however, need to be treated with caution, since only very few observations had a probability of

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4.1. PRELIMINARY ANALYSIS 15 winning a high prize of one. Nevertheless, these results are contradicting to the findings of Shupp and Williams (2008), in which couples are more risk-averse when the probability of winning a high prize is low and less risk-averse when it is big.

0 10 20 30 40 50 60 70 80 90 100 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

Lottery Win Percentage

CER = Bank Of fer / Expected V alue of Prizes IndividualsDeal IndividualsNoDeal CouplesDeal CouplesNoDeal

Figure 2: Certainty-Equivalent Ratio (CER) Comparison

Notes: All accepted Deal and rejected No Deal offers were split and clustered to the closest multiple of 10%. The average CER for every cluster of lottery win percentage is shown. The fewer number of displayed marks for the Deal condition is a combination of an overall fewer amount of accepted offers and offers being accepted in similar rounds facing similar probabilities of winning a high prize.

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16 CHAPTER 4. RESULTS

4.2 Risk-Aversion and Differences

The main objective of this thesis is to determine whether there is a sig-nificant difference in risk preferences between individuals and couples. The true mean of the risk preferences of each independent sample is not the focus. Therefore, one of the biggest challenges that confronted many researchers analyzing this type of game shows is here of secondary interest.

Most researchers face the obstacle of not knowing the magnitude of a contestant’s foresight. This aspect plays an essential role in determining risk preferences. This thesis argues that the magnitude of foresight is the same for couples and individuals. This means that defining the magni-tudes wrongly, will shift the values for the parameter of risk-averseness, but the parameters for both groups will be shifted by a similar non-linear amount. This will leave the difference in risk preferences between the groups unchanged and ultimately result in more reliable outcomes.

In order to estimate the contestants’ risk parameters, a standard Con-stant Relative Risk Aversion (CRRA) with a myopic foresight is assumed, in which the contestants only face a binary decision between two lotteries, without considering future rounds.

It is assumed that the utility of income is defined by

U(x) = xr (1)

where x is the bank offer or the expected value of the remaining prizes and r the risk parameter that needs to be estimated. The expected value under the expected utility theory is simply the probability weighted utility for each prize

EU(x) = ∑n i=1

(pi×ui) (2)

for n outcomes. The expected utility for each pair of bank offer and expected value of prizes is calculated for each contestant’s estimated value

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4.2. RISK-AVERSION AND DIFFERENCES 17 of r, to calculate the difference between the Deal and No Deal option:

OEU =EU(NoDeal) −EU(Deal) (3)

Following the contextual utility theory of Wilcox (2011), this difference needs to be supplemented by a denominator, resulting in

OEUW = EU

(NoDeal)−EU(Deal)

(EU(HPrize))−(EU(LPrize)) (4) where HPrize stands for the highest remaining prize in the game and LPrize for the lowest one. OEUW, which is based on the risk preferences of

the contestants, is then linked to their observed choices of Deal or No Deal using a standard cumulative normal distribution functionΦ(OEUW). This

is a probit function that transforms every value between±∞ into a value

between 0 and 1. In order to achieve more reliable results, the standard deviation of the error term σ in the probit function is not fixed to one, but kept variable and is estimated as well:

NoDeal=    1 if OEUW+e ≥0 0 if OEUW+e <0 , with e∼ N(0, σ) (5)

For the maximum likelihood estimation, Stata has been used and the 395 decisions have been clustered by individual contestants to obtain robust standard errors. The Stata code can be examined in the Appendix. The results of the estimation are summarized in Table 3.

Table 3 shows that the contestants are on average risk-averse with a coefficient of 0.699 which is significantly lower than 1 at the 1% level. A risk parameter of 1 defines risk neutrality, in which a contestant is indifferent between an offer that is equal to the average of the remaining prizes in the game.

Column (2) presents a statistically significant difference at the 1% level in risk attitudes between couples and individuals. Couples are less risk-averse than individuals. This also does not change after the addition of observable control variables Age and Education in column (3), which both

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18 CHAPTER 4. RESULTS Table 3: Maximum Likelihood Estimation

r (1) (2) (3) (4) (5) Couple 0.468*** 0.462*** 0.584*** 0.592*** (0.082) (0.085) (0.098) (0.12) Age (years) 0.001 0.000 0.000 (0.003) (0.003) (0.003) Education (high = 1) 0.031 0.045 0.045 (0.047) (0.044) (0.043) Time -0.231* -0.231* (0.108) (0.107) Constant 0.699*** 0.462*** 0.420*** 0.487*** 0.487*** (0.045) (0.026) (0.114) (0.104) (0.103) Couple 0.004 (0.031) σ 0.201*** 0.138*** 0.137*** 0.135*** 0.133*** (0.018) (0.016) (0.016) (0.016) (0.023) Contestants 395 395 395 395 395 * p < 0.1, ** p < 0.05, *** p < 0.01. Standard errors in parentheses.

(Clustered standard errors at contestant level.)

have no significant effect on the variables of interest.

In column (4), a continuous time variable with the same weight for both seasons of the form of

Time=s1(0.5×#episode₄₀ ) +s2(0.5+0.5×#episode₂₉ ) (6)

has been introduced, where si are dummy variables taking the value one

if the episode aired in V MYMi and zero otherwise. This variable Time is

negatively significant at the 10% level and captures some of the changes in behavior of the bank over time. Interestingly, it neither changes the coefficients for the risk parameters for couples and individuals much, nor does it change the significance of their effect, which supports the robustness of the estimated values. The results from column (4) for the coefficients of Couple and the Constant support Hypothesis 1. Couples are significantly closer to risk-neutrality than individuals when large stakes are at risk.

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4.2. RISK-AVERSION AND DIFFERENCES 19 added when estimating σ. Couple is insignificantly positive and very close to zero. σ, which represents the standard deviation of the error term in the probit function, can be considered as equal for both group of contestants, unlike Hypothesis 3 had predicted. This result could be due to a small sample size though, especially using clustered standard errors.

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Chapter 5 Conclusion

T

his thesis had the goal of finding an answer to the question whetheror not risk preferences differ between individuals and couples when large stakes are at risk. Although decisions in game shows do not strictly match decisions in real-life for various reasons, it is still worthy studying behavior in these environments, as they can give valuable insights to human actions. Contestants are time constrained in their decisions, while this is rarely the case in real life. Nevertheless, they had a considerable amount of time prior to the game show to think about various decisions in different situations during the game. Another difference that needs to be noted is that probabilities and risks are rarely as transparent as in a game show. For these reasons as well as the pressure of standing in the spotlight, one needs to be careful when generalizing behavior in TV shows to everyday life.

Assuming similar magnitudes of foresight for couples and individuals as well as myopia for contestants in general, it was possible to answer the research question positively. Couples are less risk-averse than individuals when large stakes are at risk. Although both groups show clear risk-averse behavior, couples’ risk preferences are more moderate. By accepting less unfair offers, couples display a more rational behavior that is align with the results of Cooper and Kagel (2005) and Kocher and Sutter (2002). However, Baker et al. (2007) and Masclet et al. (2009) argue that groups

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22 CHAPTER 5. CONCLUSION are more likely to choose the safe option, which is not supported by this data. Individuals are more likely to choose the safe option. Shupp and Williams’ (2008) argument, that couples are more risk-averse in high-risk situations, but less risk-averse in low-risk situations, is also not supported by the dataset at hand.

The results show that couples cannot outperform individuals in terms of average amount of winnings. This contradicts with the findings of Cooper and Kagel (2005) and Kocher and Sutter (2002). However, it needs to be noted that this could be due to a small sample size. The same applies to the findings that the variances of risk preferences are not significantly smaller for couples than individuals. This contradicts with the results of Shupp and Williams (2008), who found smaller variances for groups.

This thesis focusses on two seasons of the Turkish version of Deal or No Deal?. For further studies, it would be interesting to include more seasons or to use other settings with similar attributes to test the robustness of the results. It was not possible to get the recordings from the production com-pany Acun Medya, who owns all seasons before Endemol Shine Turkey purchased the rights from them. The study of seasons with individual con-testants and similar CERs to the ones from V MYM2 would allow a more

reliable investigation of risk preferences in different probability regions of winning a high prize. At the time of this thesis, to the best of the author’s knowledge, there were no other game shows that involved couples and would have allowed to conduct a study like this. Moreover, future research could relax the assumption of myopia and use models that include path dependent behavior of contestants to test whether the results change.

The findings of this thesis close a long-lasting research gap by giving insight to differences in behavior between couples and individuals when large stakes are at risk.

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Appendices

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Appendix A

Stata Code

1 _{*DEFINE L i k e l i h o o d} program d e f i n e ML_eut1 3 * S p e c i f y t h e arguments o f t h i s program 5 a r g s l n f r sigma 7 _{* D e c l a r e t h e temporary v a r i a b l e s t o be used} tempvar c h o i c e prob m1 m2 m3 m4 m5 m6 m7 m8 m9 m10 m11 m12 m13 m14 m15 m16 m17 m18 m19 m20 m21 m22 m23 m24 m25 m26 m27 m28 m29 o f f e r euD euND e u D i f f xmin xmax

9

q u i e t l y { 11

* I n i t i a l i z e t h e data

13 g e n e r a t e i n t ‘ c h o i c e ’ = Accept g e n e r a t e double ‘ prob ’ = 1/SumBox 15

*GET EU o f r i s k y p r o s p e c t

17 g l o b a l x l i s t one two f i v e t e n t w e n t y f i v e f i f t y s e v e n t y f i v e hundred twohundred threehundred fourhundred fivehundred s e v e n h u n d r e d f i f t y thousand t w o f i v e f i v e t h o u s a n d s e v e n f i v e tenk f i f t e e n k t w e n t y f i v e k f i f t y k s e v e n t y f i v e k hundredk h u n d r e d f i f t y k twohundredfiftyk fivehundredkone fivehundredktwo f i v e h u n d r e d k t h r e e fivehundredkfour 19 29

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30 APPENDIX A. STATA CODE l o c a l i 1

21 f o r e a c h x o f g l o b a l x l i s t {

g e n e r a t e double ‘m‘ i ’ ’ = ‘ prob ’ _* cond( ‘ x ’ = = 0 , 0 , ( ‘ x ’ ^ ‘ r ’ −

1^ ‘ r ’ ) ) 23

l o c a l ++ i 25 }

27 _{* C a l c u l a t e unweighted u t i l i t y o f outcome ,} s e t t o 0 i f prob=0 (

i . e . box opened ) egen ‘euND’ = r o w t o t a l ( ‘ m1’ − ‘m27 ’ ) 29 *GET EU o f s a f e o p t i o n ( bank o f f e r ) 31 g e n e r a t e double ‘euD ’ = ( O f f e r ) ^ ‘ r ’ 33 _{* Get t h e Wilcox c o n t e x t u a l u t i l i t y} l o c a l i = 1 35 f o r e a c h x o f g l o b a l x l i s t { tempvar mv‘ i ’ 37 g e n e r a t e double ‘mv‘ i ’ ’ = ‘ x ’ i f ‘ x ’ ! = 0 l o c a l ++ i 39 }

egen ‘ xmin ’ = rowmin( ‘ mv1 ’ − ‘mv27 ’ ) 41 egen ‘ xmax ’ = rowmax( $ x l i s t )

43 g e n e r a t e double ‘ euDiff ’ = ( ( ‘ euND’ − ‘euD ’ ) / ( ( ‘ xmax ’ ) ^ ( ‘ r ’ ) − ( ‘ xmin ’ ) ^ ( ‘ r ’ ) ) ) / ‘ sigma ’ 45 _{* E v a l u a t e t h e l i k e l i h o o d} r e p l a c e ‘ l n f ’ = l n(normal( ‘ euDiff ’ ) ) i f ‘ c h o i c e ’==0 47 r e p l a c e ‘ l n f ’ = l n(normal(−‘ euDiff ’ ) ) i f ‘ c h o i c e ’==1 } 49 end 51 _{* E s t i m a t e column ( 1 )}

ml model l f ML_eut1 ( r : ) ( sigma : ) , c l u s t e r ( ID ) 53 ml i n i t / r = 0 . 1 /sigma=1

e s t s t o a : ml maximize , d i f f i c u l t 55 mat b = e ( b )

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31

57 _{* E s t i m a t e column ( 2 )}

ml model l f ML_eut1 ( r : = P a i r ) ( sigma : ) , c l u s t e r ( ID ) 59 ml i n i t b , s k i p

e s t s t o b : ml maximize , d i f f i c u l t 61 mat b = e ( b )

63 _{* E s t i m a t e column ( 3 )}

ml model l f ML_eut1 ( r : = Age Education P a i r ) ( sigma : ) , c l u s t e r ( ID )

65 ml i n i t b , s k i p

e s t s t o c : ml maximize , d i f f i c u l t 67 mat b = e ( b )

69 _{* E s t i m a t e column ( 4 )}

ml model l f ML_eut1 ( r : = Age Education P a i r Time ) ( sigma : ) , c l u s t e r ( ID )

71 ml i n i t b , s k i p

e s t s t o d : ml maximize , d i f f i c u l t 73 mat b = e ( b )

75 _{* E s t i m a t e column ( 5 )}

ml model l f ML_eut1 ( r : = Age Education P a i r Time ) ( sigma : P a i r ) , c l u s t e r ( ID ) 77 ml i n i t b , s k i p e s t s t o e : ml maximize , d i f f i c u l t 79 * C r e a t e t a b l e s with a l l columns 81 e s t t a b a b c d e , se s ( )

Difference in risk preferences between couples and individuals when large stakes are at risk