eeking, or either risk-averse; to overweight the probabilities, whether small one or large one. To make decisions faced of risk, in fact placed decision-makers is an aspect of prospect theory, while they have framed already some expectations. Deal or No Deal, is popular television game show in United Kingdom, which data we will utilize to explore whether the real and high stakes have changed the reference point and whether is variable the risk aversion. The prospect theory proposed by Kahneman and Tversky cover the offers and remarks of model, which is alternative. The main concept in the sciences of decision is risk preferences, which usefully explore making decisions under uncertainty and risk.

## CHAPTER 1

## Introduction

The uncertainty and risk have significant role not only in important economic decisions, but also in our everyday life. The way when we take decisions is different when involve uncertainty or risk. Risk as a risk itself cannot be exactly specified, but could be defined in terms of uncertainty, too. If we have formula to measure could be much easier, but we cannot predict the future. Nature of human is to be uncertain in the decisions. The risk is everywhere around us, risk is to cross the street on red led, which can lead to car accident, but that is human sense. Most of our decisions we think are rational, but sometimes there are irrationals, that is because the human behaviour is unpredictable. The possibility of given activity or action will lead to a loss is risk. It implies that the existence of possible income have influence over our choices. Risk is carried by every human endeavour, some are less risky, some not.

This paper will look into different literature (journal, articles and books) to find more about perspective of behavioural finance; will explore the United Kingdom version of Deal or No Deal. It is convenient to study the risk decision-making of high-stakes, which involve real people and real situations. In the context of prospect theory, whether risk aversion is affected by decision frame.

Behavioural finance represents collection of explanations and theories of making financial activity and decisions, which are based on phenomena and concepts of psychology. It examines the factors, sociological and psychological, which influence decision making. The beliefs and preferences are the two typically broad psychology aspects.

There are plenty of previous literatures, which prove and show how people are susceptible of regular aptitude about future uncertain expectation of outcome and their beliefs. Kahneman, D. and Tversky, A. (March, 1979) have the concepts of behavioural representativeness and the anchoring.

In this paper we will have a look into how risky we are, how the risk affects us to make a decision and what change them; what influence have the risk to our decisions. Risk is determinative factor for taking decisions. Among the risk we can separate into three categories of basic behaviours risk preferences – risk neutral, risk seeking and risk averse. Those categories specify the level of risk, which is generally acceptable. Risk is variable, because of the expected return; it is chance to win or loss. The higher return is in the base of risk-seeking. There are likely to take riskier decisions with expected high return. Risk neutral people look over the risk, because they are concern about the return. Risk-averse people dislike risk; prefer the safe, lower return. If they have two opportunities with expected return, which is similar (but different risks), will prefer the lower risk one.

When there is loss, people tend to be risk-seeking, and then they prefer to risk more than moderate, so in case of win can cover the loss. That is the way how gamblers get addicted. They continue to gambling once they lose, to avoid the loss. Therefore, if it comes to gains, they try to avoid risk, because once they have something do not want to lose it. It is much easier to play with someone else’s money. Once you are chosen to play Deal or No Deal you do not have what to lose, so the contestants take more risky decisions. Two important words are gathered in this game – risk and luck, due to the potential of winning large amount, which could change your life. Real game, real people, real decisions … they made the game more interesting as case study for exploring.

Deal or No Deal (DOND) game began originally in 2002 in Netherlands and was the first game with no question (except one – Deal or No Deal?), game where no knowledge or extra skills are need. On 31st October 2005 started in United Kingdom and until today this game is played in more than 66 countries around the world (Endemol, 2011). This game show is mainly used to examining people’s behaviour, which are forced to make uncertainty decisions, because of the high stakes. The degree of risk aversion in Deal or No Deal depends on how during the game contestant is an affected prior loss. There are very large possibilities of winning high amount. This game show in fact is convenient for examination of decision making risky high-stakes, which involved real people.

To understand the subject of the research I will introduce the game rules of Deal or No Deal. There is no knowledge need to know how to play and there are no good or bad decisions. No one game play is the same order as other, neither with the same result – everything is individual. The rules are one for all contestants.

The game consists of 22 boxes and 22 contestants. Only independent adjudicator knows the amounts in every box. On random walk it is chosen one contestant to play, either for East or West Wing. The game can go up to 7 rounds, where the 7th round is final, but occasionally may have additional round. In the first round five boxes are open, then banker offer cash amount for the contestant’s box and the question Deal or No Deal? Waiting for respond – accept or not from contestant and continue with the game, because he need to choose between known amount (banker’s offer) and unknown one – its box. Therefore, in between rounds two to six are opened 3 boxes in each round. After the opening of every three boxes follow banker offer, and the question Deal or No Deal. If they player accept the banker’s offer, the game do not finish – continue the same order of how he would play, but if he decline – continue until in the game remain only two boxes. Then Banker will give his final offer, and even then if the contestant reject, the banker may offer it to swap the boxes, so finally player can see did he make good deal. Next two tables are to provide clear idea of all amounts in the boxes and how the game runs.

Table 1: All 22 amounts in the boxes

1p

£1,000

10p

£3,000

50p

£5,000

£1

£10,000

£5

£10

£50

£100

£250

£500

£750

£15,000

£20,000

£35,000

£50,000

£75,000

£100,000

£250,000

Table 2: Simple structure of TV game “Deal or No Deal”

### Round

### No of boxes open

### No of boxes remaining at offer

### Offer accepted

### Offer rejected

1

5

17

Game ends

Go to round 2

2

3

14

Game ends

Go to round 3

3

3

11

Game ends

Go to round 4

4

3

8

Game ends

Go to round 5

5

3

5

Game ends

Go to round 6

6

3

2

Game ends

Open your box

The study in the paper is based on present UK data from TV game show Deal or No deal. In order to develop analysis of risk preferences, the research has looked the games structure, the game play of every contestant, the banker’s offer and the deal accepted/rejected.

The next Chapter 2 will look into different literature. Expected Net Present Value (ENPV) is the used method for the analysis and interpretation for the aims include comparison between different game episodes, which involved real contestant’s game play. Later on in Chapter 3, 4 and 5 follow respectively methodology, data and the findings – results. Then in the final chapter will be the conclusion.

## CHAPTER 2

## Literature review

1) Related to the topic, the available previous literatures help this study in order to establish discussion of the issues. There are many previous publications for risk preferences, risk-aversion and risk-seeking. This chapter will examine the earlier discussions of other authors, where the the majority finance behaviour researches are based on the findings of Kahneman, D. and Tversky, A. from 1979 and 1992.

The review of the article of Kahneman, D. and Tversky, A. (March, 1979) Econometrica critique the theory of Expected Utility Theory (EUT) as descriptive model of decision making under risk, which develop an alternative model, called Prospect Theory (PT).

There is no specific question, and respectively answer given. They used students to examine how people take decisions under uncertain risky prospects. The article of Kahneman and Tversky (March, 1979) critique and review more specific the Certainty, Probability and Possibility; Reflection effect; Probabilistic Insurance; Isolation effect; the value function and the weighting function. They examine 14 problems with 2 examples each, which are comparable. As the study give hypothetical choice problems in questionnaire form.

They recommend the use of target or reference as risky choices measurement. It does not mean that people (individuals) are risk averse constantly. They just copy the behaviours of risk-averse and risk-seeking, and mix in their own view. The article of 1979, Kahneman, D. and Tversky, A. give proven examples that when returns are below our expectation point, we are more risk-seeking, and respectively opposite for risk-averse.

The theory is able to adapt effects of framing, because everything what counts (gain or loss) make the frame. Prospect Theory is as puzzle, can contain so many different pieces – in our case different human behaviours. Because of EUT limitations, during the years researchers have been developed different alternative theories. Prospect theory developed by Kahneman, D. and Tversky, A. is one of the most known alternative theories.

In same pattern were results of testing series of thought experiments. Different frames, involved prizes as vacations, money and other were given for the problem. In EUT, outcome utilities are weighted by their probabilities. They used variation example of the French economist Maurice Allais. The certainty effect – where there are certain to overweight outcomes, in comparison to merely probable outcomes. Can lead to preferences of risk averse for sure gain, than large one, but with merely probable. When the prospects are in domain, which are negative, people explore the preferences of risk-loving for larger losses, more probable then certain ones.

Finally, conclude that decision problems involve such as gains and losses possibility. While people are risk-averse over gains prospects, in the same way become risk-loving over loss prospects.

The examples given in article are lottery-choice problems, with choice between values with probability. Interpretation of their finding is that people exclude components, which might be shared by alternatives, and concentrate on those who separate them, to make the choice simple between alternatives. The above inconsistent preferences come from decomposed different choice problem in different ways. That is the phenomenon – isolation effect.

The effects observed in the article by Kahneman and Tversky in 1979 designed the Prospect Theory, theory of decision-making under risk. There are many fundamental ways, which diverse Prospect theory from Expected Utility Theory.

2) Prospect theory has some theoretical problems, which were solve with the next version – Cumulative Prospect Theory (CPT), it is known as Rank-Dependent Utility Theory, too. The journal of 1992 from Tversky, A. and Kahneman, D. introduced new explanatory model of decisions under risk. It is new developed variant of prospect theory. The original model of Prospect Theory weighted each of outcomes by probability, where Cumulative Prospect Theory (CPT) applies weighting to probability distribution function.

CPT applies to risky and unsure prospects with number of payoff. For gains and losses allows different weighted functions. The authors mention five choice phenomenons, confirmed in many experiments with hypothetical and real outcomes. They are framing effects, non-linear preferences, source dependence, and risk seeking and loss aversion.

The main problem with PT, where the `stochastic dominance` was break. It requires the probability mass shift from bad to better outcomes leads to improve prospect. In response to another literature the theory combines the functional of rank-dependent and then satisfies the stochastic dominance, where previous theory (PT) does not do. The possible crucial features are as follow: 1. Losses and gains

Gains and losses, i.e. income is the carriers of value, not final assets or wealth.

The value of each outcome is multiplied by a decision weight, not an additive probability.

CPT observation tend of people’s thinking that there is relative from possible outcome to a certain point of reference.

Framing effect

Moreover, they have different risk attitudes towards gains (i.e. outcomes above the reference point) and losses (i.e. outcomes below the reference point) and care generally more about potential losses than potential gains (loss aversion). Finally, people tend to overweight extreme, but unlikely events, but underweight “average” events. The last point is in contrast to Prospect Theory which assumes that people overweight unlikely events, independently of their relative outcomes.

CPT incorporates these observations in a modification of Expected Utility Theory by replacing final wealth with payoffs relative to the reference point, replacing the utility function with a value function that depends on relative payoff, and replacing cumulative probabilities with weighted cumulative probabilities. In the general case, this leads to the following formula for subjective utility of a risky outcome described by probability measure p:

Both authors made modification to Prospect Theory that it transformed cumulative probabilities.

This leads to the aforementioned overweighting of extreme events which occur with small probability, rather than to an overweighting of all small probability events. The modification helps to avoid a violation of first order stochastic dominance and makes the generalization to arbitrary outcome distributions easier.

The current CPT is expansion over PT. CPT is useful to separate different situations, which in comparison to standard economic rationality come out non consistent, in detail puzzle of: equity premium, allocation of assets, different betting and gambling; the status quo bias; the endowment effect and intertemporal consumption.

Published in December 2007 the article of Gee, C.

The author use data from 129 Deal or No Deal – UK episodes between the period October 2005 to April 2006

The article give example of scenario-based game, which as result prove that when the banker is uncertain about the contestant’s risk attitudes, he increase the offer function, which came from optimal behaviour.

The article of Post, T., Assem, M. J., Baltussen, G. And Thaler, R. (2008) examine games from United States, Germany and Netherlands from the period 2002-2007, because of the format of the game, which is similar, except the prizes. In total they look to 151 contestants’ games. The collection of data was through the official website of research country. They called “moderate” risk aversion level, because of the analysis, which is made on average. When the offer excess 75% of expected value, many contestants not accept deals with thousands of Euros. They examine the banker behaviour and state four rules. First rule is that the value of remaining boxes set the offer of the banker, when the average amount of unopened boxes decrease (increase) the offer get worse (better). Rule two states that typically the banker’s offer it is low percentage of the average remaining amount.

Published for first time on August 2009 the authors Mulino, D., Scheelings, R., Brooks, R. and Faff, R. explore the Australian version, because of the different final rounds, which are offered: Normal round, Chance round, and SuperCase round. The Chance round and SuperCase round are offered only when there are two boxes left. Chance round (exchange already won (certain) amount for 50/50 lottery of the remaining boxes. Alternatively, SuperCase round, where swap already won amount for 1 in 8 prizes may be won). Normal round goes as swap boxes between unknown amounts or known (sure) amount for contestant’s box (unknown). Those additional rounds in Australian version faced contestants with completely different decision frame. Their concern is to find out what effect change the frame of decision on risk aversion of contestant.

Usually Banker’s offer is to challenge contestant to change its box (the unknown amount) for sure amount. In the last rounds banker can offer swap, where its change unknown amount for unknown. The paper by Mulino, Scheelings, Brooks and Faff (2009) explore whether decision frame influence risk aversion of contestant. It fit a model of dynamic decision-making, where based on choices of each round it estimate risk aversion of contestant. The finding: where there is potential loss contestants are more risk averse. It is significant impact of framing turnaround to willingness of people to take risk. The special rounds in Australian version involve a reversal to reference frame of contestant, where during SuperCase and Chance rounds level of risk is high, steadily with framing effects existence. Invasive role has framing effects because of the broad range of topics for behavioural finance.

They develop unique features of the setting through the method of devising an experiment, which show that agent behaviour has descriptive framing. Additionally, the settings were one of the real high stakes, give confidence to the analysis. The findings, that framing does matter, can be use in other behaviour finance area, which rely on framing.

## CHAPTER 3

## Methodology

In this chapter is described the basic research methodology used. The study is based on present UK data from TV game show Deal or No deal.

The records of all experiments of behavioural economics (with different parameters and data) are used to generate models, which can predict performance. Series of decision between subjects must choose, is the typical experiment of behavioural economics. In order to settle what is going with subject’s brain, when need to make decision, different variables will be measure. Subject will be given choice of: to have 45%; 50/50 chance of $1 and nothing, respectively.

Expected value is used in every research. In this paper was used as well. Somewhere it is written as Expected Net Present Value (ENPV). ENPV is the mean (average) of all values, weighted by the event probability. The following equation below represents the ENPV, where is the expected value, is the probability and is possible outcome.

The ENPV does not provide criteria for an acceptable decision. It provides profitability measure applying to investment, which are risky. Then it is important the attitude towards risk.

Explanation of the above is because in this paper it is main used for the analysis of the data. The expected value of banker’s offer is the statistical mean based on the amount in the remaining unopened boxes. In the continuous game, after each round the remaining boxes shrinks. Actually in the last two rounds the actual banker’s offer it becomes much closer to our Expected Banker’s Offer.

## CHAPTER 4

## Data

There many papers written for Deal or No Deal around the world, but just a few looking to UK version. In this paper for the purpose of our research the collected data is from the original website of UK version Deal or No Deal, where it has record of all episodes of contestants’ games. The data included is from January to March 2011, including 24 episodes, with 24 real contestants (14 females and 10 males). Collected data include eliminated (opened) boxes and remaining amounts, offer of the banker and the decision – deal or no deal for every round.

From the data, there is only one game of 17th February 2011, which had additional round. Usually it is uncommon situation.

The collected data is provided in summarized table, for clear view for comparison and understanding.

## Table 3.1: Summarized data of DOND episodes from 12.01.2011 to 18.02.2011.

On the top of both tables (3.1 and 3.2) can be found the date, when the contestant play; the name of contestant and continuous number in the table. In tables 3.1 and 3.2 the grey highlighted cells represent the game between each round, the total amount of all boxes left, our expected value of banker’s offer, the actual offer of the banker and if the contestant accept the offer. The opened boxes can give more information for the contestant’s own box unknown amount. The highlighter blue cells present the continuous simulate game, after the contestant accept deal, it is only for measurement if the deal was good or not. It could be that contestant cell box for £0.01 for high amount as £10 000, which could be one very good deal or opposite, to deal high amount box for small. The cell with red font shows when the contestants accept banker’s deal, with blue font the amount in the box, which contestant own from the time it is chosen to play.

## Table 3.2: Summarized data of DOND episodes from 23.02.2011 to 31.03.2011.

## CHAPTER 5

## Results

By focusing on our data analysis this research present results of risk preferences of contestants in popular TV game show Deal or No Deal. From the tables and graphs it is clearly that with continuous play and going round after round, the closer to the end it give higher banker’s offer.

The first look of risk preferences will analyze the banker’s offer and the decision of the contestants, whether reject or accept the offer in different game rounds.

Chart 1 present how during the game moving round after round the expected value of banker’s offer (EVBO) and the actual banker’s offer (BO) change upwards together. At the end of round one, the remaining boxes are 17. The average EVBO for all 24 contestants in first round is £26,030.88, but the average real BO is £7,539.17. From the above chart can be seen that difference between EVBO and BO in from round one to round six goes in between £18,491.72 to £15,455.68. The changes in both go slightly the same until round five, where is the sharp difference upwards. The red line is about £8,117.36 total difference in BO between round one to round five, but difference between round five and six is £13,681.79. In comparison the EVBO line have difference between the five rounds less than BO with £133.40.

As the game progress the banker become more generous with his offers. Usually

In round 1, banker’s offer is only 29% of the Expected Banker’s Offer, which 3.45 times lesser than the expected offer.

### Round

### â„– of contestants

### % of contestant accept deal in round

Round 1

## –

## –

Round 2

## –

## –

Round 3

## –

## –

Round 4

## 4

0.166666667

Round 5

## 11

0.458333333

Round 6

## 3

0.125

Round 7

## 5

0.208333333

Additional round

## 1

0.041666667

## Total

## 24

## 1

From all the data, which was collected prepare for clear view a summarize table above, in which round how many contestants accept banker’s offer and percentage are they from the total number of the contestants. It can be seen that no one contestant accept Deal in the first 3 rounds, but in rounds 4 and 5, the total percentage of the contestants accept the banker’s offer is about 62.5%, respectively 17% and 46%. In round 6, only 3 contestants made deal, which is 12.5% of the total number of contestant observed.

If assume that contestants in round 4 and 5 are risk averse, round 6 – risk neutral and round 7 and additional round – risk seeking, then the proportion of them will look like that risk averse – 62.5%, risk neutral – 12.5% and risk seeking 25%. More than a half of the contestants are risk averse, preferred to deal the sure amount of money.

From the summarized table

## CHAPTER 6

## Conclusion

Related to the topic, available previous literatures help this study in order to establish discussion of the issues. The basis of modern finance and economics is analysis of decisions under uncertainty. There is developing empirical literatures, which increase rapidly and help for the focus research of individuals’ risk behaviour and preferences. The TV game show Deal or No Deal faced contestant to series of choices, where need to choose between lottery (uncertain) and sure thing. Played in more than 60 countries around the world, the data in this paper is from the British version of the show. One chosen contestant, 22 boxes with amounts from £0,01 to £250 000,00.

Of course, it cannot be compare to what is contestant’s behavior under uncertainty to those with ordinary person in everyday life. Contestants have only couple of minutes to make decision involving large amounts of money, while for most of real life decisions it can take as much time as it need.

The results from the previous chapter agree to extracted results from literature and hence reply to the confirmed objective. However, this is a small piece of research, further experiments might be needed.

## APPENDICES

### Table 4: The average amounts of our Expected Offer and the Real Offer in each round.

Average Expected Value of Banker’s Offer in Round 1

£26,030.88

Average of Banker’s Offer in Round 1

£7,539.17

0.289623917

3.452753522

Average Expected Value of Banker’s Offer in Round 2

26008.78824

Average of Banker’s Offer in Round 2

£8,404.17

0.323127959

3.094749221

Average Expected Value of Banker’s Offer in Round 3

£27,673.48

Average of Banker’s Offer in Round 3

£9,822.92

0.354957777

2.817236487

Average Expected Value of Banker’s Offer in Round 4

£29,964.21

Average of Banker’s Offer in Round 4

£12,268.79

0.409448146

2.442311705

Average Expected Value of Banker’s Offer in Round 5

£34,014.84

Average of Banker’s Offer in Round 5

£15,656.52

0.460285016

2.172566922

Average Expected Value of Banker’s Offer in Round 6

£44,794.00

Average of Banker’s Offer in Round 6

£29,338.32

0.65496085

## 1.526808816

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