Deal or No Deal: Determinants of Preferences Under Risk

Deal or No Deal: Determinants of Preferences Under Risk Neslihan Aldogan

Ebru Ceylan

Onuralp Demiralp

Can Kuseyri

Cansu Peker

Abstract This research aims to state the determinants of risk aversion under a high-payoff game. Episodes from the television show “Var misin Yok musun” were watched and recorded the sequence of the play with offers and laps to form the data. Opposed to the mathematical explanation of the expected utility theory, it is believed that socioeconomic conditions and the course of the game can have huge impacts on the risk preference.

JEL code: D81. Keywords: Decision making, risk, path-dependency, socio-economic determinants, probit analysis

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Introduction

The television show “Var misin Yok musun” this research depends on is the Turkish version of “Deal or No Deal”, a Dutch originated game show where one of the 24-26 suitcases or boxes is assigned to a contestant. After the audience gets to know the personal information related to the contestant, the game begins. 5 boxes in the first lap, 3 boxes in second to sixth lap and 2 boxes in the last lap are picked by the contestant and the value in it is crossed out of the “money tree”. At the end of each lap, an offer is made by the bank according to the values opened. The offer mainly refers to the price the bank accepts to pay to buy the box s/he holds during the game from the contestant in order to end the game. The contestant either declines the offer and keeps opening boxes, which is related to a risk lover’s behaviour, or accepts the offer and the game ends, which is related to risk aversion. The offers happen to be relatively low in the first laps and they get closer to the expected value of the remaining boxes as the laps proceed. The contestants, as observed, often decline the offer in the first four laps and they generally accept it in the last three laps. Due to patent related issues, the episodes are not open to public access. The researchers contacted the Turkish broadcaster and got authorization to watch the episodes in the office and obtain the data. This data consists of the episodes of three seasons of the show that are aired between 2007 and 2010. Every episode available is watched and relevant information is gathered by the researchers. The total adds up to 308 episodes, 308 decision making contestants and 2007 observations. The binary dependent variable is set to be contestants accepting the bank offer, in other words saying “deal” (Deal=1 No Deal=0). The independent variables consist of personal information such as gender, birthplace, application place, age, marital status, duration of the marriage, number of children and socioeconomic conditions such as occupation and education. Other than these information, numerical observations such as average value and the standard deviation of the boxes opened in that lap, of the total boxes opened, of the boxes that are left are noted at the end of each lap, as well as the offers. It is hypothesized that the demographic variables related to the contestant’s personal 2

information and socioeconomic conditions have statistically low or no significance whereas the path dependent variables formed by the numerical observations are hypothesized to have higher significance in affecting the contestants’ behavior on accepting or declining the offer. The rest of the paper is organised as follows: The following section features the literary review process, in section 3, we give the in-depth explanation of our analysis and finally in section 4 we give the results obtained and the points concluded after this research.

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Literary Review

In economics, examining risky choice has been a debated topic and many theories have been developed on it. Prominently, in 1947, Von Neumann and Morgenstern derived the “expected utility theory” which stated that under uncertainty, individuals will behave as if to maximize the expected value of their utility function. Later on, in 1979 Kahneman and Tversky, in their study “Prospect Theory: An Analysis of Decision under Risk” opposed the expected utility theory asserting that under a risky situation decision makers behave accordingly their potential gains or loses rather than the final outcome. Despite popularity of preference under risk, the real life testing of these theories has never been easy. Since the true probability distribution are not always clear to individuals and their beliefs are not known to the researchers, research was rather aimed answering hypothetical question. Although risky choice experiments are caught on as experimental economics become more recognized, the amounts at risk were small because of the limited budget. Therefore these experiments didn’t reflect the risk behavior thoroughly. In order to overcome this problem, in their article “Deal or no deal? decision making under risk in a large-payoff game show”, Post, T., Van den Assem, M. J., Baltussen, G., & Thaler, R. H. observed TV shows called “Deal or No Deal” from three different countries with 151 participants. Considering the fact that format of the shows from different countries is significantly same with the Turkish version, this research is taken as a guide to our study conveniently. Moreover, our study had the opportunity of enhancing of number of participants. In their study, the data of remaining and eliminated prize, bank offers and deal or no deal 3

decision; and contestants’ traits were collected for each contestant. However, it is stated that contestants’ traits did not have an explanatory power on their analysis. Notwithstanding that, in our study characteristics were not passed over because the previous study’s number of observation may not be enough to have the variation of characteristics. In their research, the results based on these three shows did not hold with the orthodox interpretation of risk aversion. The preferences rather followed a “path-dependent” way, which is explained by previous outcomes during the show. The first path was “break-even effect” that is the risk aversion decreased after the high value boxes had been opened; and the second path was “house money effect” stating the risk aversion decreased after low value of boxes had been opened. As a result of decreased risk aversion, the ratio of bank offer over remaining average prize increased as the laps went on. This result is also consistent with our findings. In order to analyze these two effects separately, Post et al categorized contestants as “losers” and “winners”. A contestant is categorized as “loser” if the average remaining price after eliminating the lowest remaining price is the among worst 1/3 of all contestants in the same game round, and categorized as “winner” if the average after eliminating the largest remaining prize is among the best 1/3. Throughout this classification, it was observed that compared to winners, losers tend to reject the bank offer more likely. They generally exhibited a risk seeking behavior by rejecting bank offers which were more than the average prize. Therefore house money effect was concluded to be weaker. But above all, supporting break-even and house money effect, losers and winners had a strong inclination to play whereas neutrals tended to give up at early laps. Their study concluded that the decisions are made upon previous outcomes and this result is not consistent with traditional interpretation of expected utility theory saying that choices of the individuals are not dependent on previous events. On the other hand, prospect theory is more convenient to explain this path-dependent way of behavior. Because under the prospect theory, at first the individual sets risky outcomes according to a reference point then he chooses one of the risky preferences. In other words their decision depends on different kind of settlements. In 2010, Ren Yu Ku widened the scope of the research of Baltussen, Post and Van den

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Assem and published “A Study of Risk Aversion: Comparing Contestant Behaviour on Deal or no Deal”. The regression model of our study is motivated by the probit model of Ku that explained in the following. In this study, the measure of risk was set to be the tendency of the contestant to say “deal” in a probit model. Therefore, the dependent variable in this probit regression model was constructed to be binary as taking the values 1 and 0 for deal decision and no deal decision respectively. Thus the regression model was applicable to each lap which rendering each lap an individual observation. As regressors, personal traits of contestants and path dependent variables such as relative stakes, bank offer over average prize left, and standard deviation ratio were included as in the model of Post et al. Furthermore, it was suggested that the each contestant had their own “individual idiosyncrasy” that effected their risky decision makings. Considering the independency of these idiosyncratic characteristics, there were no need to use a fixed effect model. Rather, for the aim of explaining the clustering effect of each contestant an identifier was introduced into the dataset.

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Data & Methodology

For every 308 contestant, we have calculated and derived the following variables and finally prepared our data. We observed some variables which are individual specific like age, gender, region, marital status, number of child and duration by watching the introductory videos of the game show and composed our data. We have generated and calculated remaining variables to make specific commands. Since we have started to identify Turkish version of Deal or No Deal TV show by inspiring from the article of Thierry Post, Martijn J. van den Assem, Guido Baltussen, and Richard H. Thaler, in our summary statistics part we will compare those four countries outcomes.

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3.1

Summary Statistics

The following table shows the summary statistics from the data we have created. 55% of the contestants are female which means all contestants were chosen almost equally from both sexes. Age is around 31 with standard deviation 11,76. Almost 70% of the contestants said no to bank offer. Average of the gain around 53.000 but standard deviation is high. Best offer rejected is a variable that among all offers if contestant said no deal to the best one which is 54% of contestants said no to their best offer.

Secondly, the comparative summary statistics obtained from the article mentioned in Literary Review are below. Information gathered from three different competitions in Germany, Netherlands and US is presented on the following table. 6

We have made further analysis across different determinants such as demographics, education, gender and so on (based on average gains). 3.1.1

Demographics

The most of the contestants applied the TV show from Marmara (48%) not surprisingly we can say that they gained the bigger prices. Other results lying below.

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3.1.2

Education and Profession

There is no strong difference between education and average gain. On the other hand people who working on private sector gained more than the other professions.

3.1.3

Gender and Marital Status

Male contestants earn more than females which may give us further information for our regression analysis. Additionally, divorced people gain more relatively than other but their number (12) is not enough to say something certain.

3.1.4

Lap Number and Duration of Waitlist

No one said deal before the laps 4 also except 2 person all the contestants waits to make a decision deal until fifth lap. We have a theory on that later. Furthermore, in each program there are contestant who waits for its turn. Since they are selected randomly, some of them play the game in his/her first weeks or wait more than 12 months to play. We wonder if this

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duration affects gain or not. Results are showing that long term contestants earning more than the others.

3.2

Bank Offer Attitude

We wonder how the bank offers are determined. There are different attitudes in making the offers. To analyze these attitudes, understanding the gain distribution of Turkish contestants is essential.

The reason why not even a single contestant did not accept the offers in the first three laps 9

is related to the banker’s attitude. Since the production aims for a longer time and higher rate of viewing, they arrange these bank offers accordingly. A rational risk averse person should accept the bank offer which if it is equal or bigger than expected value of average of boxes left. Bank almost never offers this amount. In other words bank almost always offers the amount which is less than the average price of boxes left. If bank is offering the bigger or too low than that (average price boxes left), it means that bank wants player to continue to play. In the table below we created a variable, bank offer percentage, “the average bank offer as a percentage of average remaining price”. Bank offer percentage calculates bank offer is how many percentage of remaining price left. Bank on average at most offers 66% of remaining price.

Furthermore, bank offer percentage changing for each lap specifically. This percentage changes also country to country. In Turkish version for example bank offers generally 12,81% of the average price left at first lap without looking if the contestant said deal or no deal. According to this average numbers bank has intervals to offer an amount for each lap. Since banks want to push the player to continue to play (because it’s TV show necessity) bank offer percentage increases as the lap increases, again without looking if the contestant said deal or no deal. Even if two cases left, bank never offers the average price left. In our data bank offers only 21 times of 2008 laps more than or equal to average price of boxes left which are mostly

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for blue (including low prices) boxes. Further information, only %16 of the 308 contestant gain more than their initial expected value. So we can say that bank does its best to pay the contestants’ case the least amount that it could give.

3.3

Regression Analysis

3.3.1

Probit Regression Framework

We will be using probit regression framework by using technique of “A Study of Risk Aversion: Comparing Contestant Behavior on Deal or no Deal, Ren Yu Ku”. Propensity to contestants to accept the bank offer in other words saying deal is a binary dependent variable (Deal=1 No Deal=0). Since our dependent variable is binary we will use probit model to make regression analysis. Regression includes following independent variables taken directly from the article that we have mentioned above. Age Gender: (female=1) Education: education high (if it is more than 12 years=1) or low (if it is less than 12 years=0) Relative Stakes: average prices of boxes left (never opened) / initial average price (payoff 11

total) Percentage bank offer (BO): bank offer / average prices of boxes left Standard deviation ratio: standard deviation prices of boxes left / average prices of boxes left Age, gender, and education is demographic variables which we introduces them in the ‘Summary Statistics’ part. Relative stakes measures that “effective relative size of stakes on behavior under risk” Help us to understand that contestant accepting the deal if he/she surpass his/her initial payoff total or not. Bank offer percentage stands for if the contestant significantly affecting from bank offer according to its average price left percentage. We are expecting that bank offer percentage definitely affect player according to proportion of average price left positively. With standard deviation ratio we will measure the how the remaining prices differences from each other affect contestants’ willingness to accept the offer. We expecting that individual specific effects to be change among individuals we do not find necessary to using fixed effect model.

As we accepted relative stakes, bank offer percentage and standard deviation ratio are statistically significant while other variables (individual specific variables) are not. Signs of 12

significant independent variables are also same with our expectations, especially bank offer percentage. Additionally keeping the first probit regression same we add marital status, duration, and employment. As we expected they are not statistically significant.

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3.3.2

Ordered Logistic Regressions Framework

Since the payoffs for the contestants are not the same, using variables measured in monetary units is not reasonable. Instead, we can take the ratio between the monetary amounts and the total payoffs. Also while collecting the data, we have seen that the perception of the contestants are similar for some cluster of monetary amounts regardless of the total payoff. For instance, opening a box containing 1TL or a box containing 1000TL affects the mood of the player and the offer (that is made by the bank) very similarly because the variation in lower stakes is lower than in the higher stakes. The boxes on the payoff tree are already distinguished by the colors blue, yellow and red which represents this perception. Before making any estimation, we prefer to take them as categorical variables. We can use this categorization also for the non-distinct monetary units such as offers. However we also need to account the total payoffs for the red boxes because they are the ones which vary at most among different payoff trees. So we deduce that it is necessary to determine some thresholds for the ratios generating categorical variables. The maximum value for the blue boxes is 750TL from all payoff trees. Thus we can determine a threshold for the first category of [gain/total payoff] ratio with by considering [750TL/average total payoff]. So we get .0075 as a threshold for the first category. If we calculate the average of the maximum of the blue boxes, we get 47240TL, almost 50000TL, thus, by following the same way as before, we obtain .48 for the second threshold. Then the ratio greater than .48 corresponds to the third category.

As it can be seen on the table above, there are plenty of observations divided to each category, to run ordered logistic regressions.

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We use similar variables in the ordered logistic regression model as in previous logistic and probit models. There are few alterations such as the usage of offer variable instead of bank offer percentage and the absence of the relative stakes variable. Since we use categorized ratios of gain with respect to the average total payoff, there is no need for the bank offer percentage variable. Instead we include the variable offer in the last round that is played by the contestants. Also we include the offer from the previous round. The results of the first regression with robust standard errors are in the following table.

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However the offer from the previous round [offer1] is not statistically significant. Also the age is not significant at 5% significance level. The standard deviation ratio [stdevratio], education level [educgt121], gender [female] and the last offer [offer] are statistically significant. The Wald chi-square with 6 degrees of freedom yields a large number. Although probability is equal to zero which suggest for the overall insignificance of the model, pseudo R-square is relatively insufficient to explain the gain categories. The second ordered logistic regression is better than the previous one, almost in all respects. We include [nodeal] dummy instead of deal dummy and the interaction term observes the effect of the risk seeking attitude because it represents the contestants who rejected all offers and got the amount in their boxes. Moreover we added occupation[e]. The unemployment category [e6] is omitted, thus it can be thought as a base for the interpretation of employment. Although e1 and e7 do not seem statistically significant, they are significant together and generating an additional explanatory power. It can be seen by comparing Wald chi-square statistics and pseudo R-square with the corresponding results of the first regression.

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Besides all coefficients are statistically significant with robust standard errors except for the age again. Consequently, ordered logistic regression provides significant and successful estimation for the gain categories.

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Conclusion

The interests of the research mentioned at the beginning of the paper were: finding the determinants of risk aversion which are expected to be personal information of the contestants and the varying stakes in each round. By using probit, logit and ordered logit models, we have found that the personal information has little to do with the gain and dealing. Neither the marital status nor the number of children the contestant has, do not explain any of the dependent variables according to the test results. Also age is either insignificant or slightly significant. Gender can be considered as only significant determinant of the risk aversion related to the individuals. In coherence with the literature, it suggests that the females are risk-averse. Additionally the duration of the presence of contestants, and their employment status are not statistically significant but they increase the explanatory power of the models. Besides that, the dynamics of the game such as relative stakes, bank offer percentage, and standard deviation ratio are the most decisive factors which bring the player to the deal option and also help to estimate the range of their gains. To conclude, the generated models in the research may not be the perfect estimators but they are successful at making an impression of the decision making processes of the contestants.

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References [1] Brooks, R., Faff, R., Mulino, D., and Scheelings, R. (2009). “Deal or No Deal, That is the Question: The Impact of Increasing Stakes and Framing Effects on Decision–Making under Risk.” International Review of Finance, 9(1-2), 27-50. [2] De Roos, N., and Sarafidis, Y. (2010). “Decision making under risk in Deal or No Deal.” Journal of Applied Econometrics, 25(6), 987-1027. [3] Kahneman, D., and Tversky, A. (1979). “Prospect theory: An analysis of decision under risk.” Econometrica: Journal of the Econometric Society, 263–291. [4] Post, T., Van den Assem, M. J., Baltussen, G., and Thaler, R. H. (2008). “Deal or no deal? Decision making under risk in a large-payoff game show.” The American Economic Review, 38–71. [5] Yu Ku, R. (2010). “A study of risk aversion: Comparing contestant behaviour on deal or no deal.” (honors thesis), Duke University. [6] Wooldridge, J. (2015). “Introductory econometrics: A modern approach.” Nelson Education.

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