The influence of transparency on cheating behaviour – an experimental study

The influence of transparency on

cheating behaviour – an experimental

study

December 15, 2017

Abstract

The interaction between athlete, organization and sponsor is complicated and often unpredictable. Modelling this interaction as an expanded inspection game provides insights

in their cheating related behaviour. From game-theoretic analysis it follows that the presence of sponsors leads to excessive cheating. Transparency about cheating inspections,

both positive and negative, seems to be necessary to reduce cheating. An experiment is conducted to observe the actual behaviour in a controlled setting and to study the effects of increased transparency. In contrast to the prediction from the game theoretical model most

athletes choose to play fair, while the majority of organizations inspect the athlete. The experiment gives little reason to make results of cheating inspections public, as it is not

found that this reduces cheating.

Master Thesis –Behavioural Economics and Game Theory 15ECTS

2 Statement of Originality

This document is written by Student Merel Bruijnsteen who declares to take full responsibility for the contents of this document.

I declare that the text and the work presented in this document are 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.

3

1 I

NTRODUCTION

1.1 M

Cheating in sports is a widespread phenomenon which is generally disapproved of by supporters. A well-known example is doping usage in physical sports. Other examples are electronical cheating in chess and hand signals in the bridge game. Arguments to reduce cheating in sports are numerous (Preston & Szymanski, 2003). Whenever an athlete cheats, he obviously disadvantages his opponents. If he cheats through the usage of doping, he puts his own health at risks and if the cheating comes to light, this may cause negative publicity for not only the athlete, but also for his sponsors, the sports federation and other athletes.

Because of these and other arguments, cheating and doping are often studied in game theory. Examples are inspection games (Rauhut, 2009) and cheating games (Breivik, 1987). In these game theoretical approaches the stakeholders include the athletes and the

organisations, who can test for cheating. In addition to the athletes and organizations, sponsors and supporters are also involved when it comes to fraudulent behaviour. When cheating comes to light, it forms a threat to the organizers of sports events. Because of a cheating scandal, sponsors and supporters can lose their interest in the event, resulting in a financial loss for the organizer. According to Buechel, Emrich and Pohlkamp (2013), the result of this threat is that organizers will choose not to test the participating athletes and the athletes can cheat without consequences. They also claim that when the outcome of cheating inspections is made public, this will result in less cheating if sponsors and

supporters adopt a critical attitude. In my research, I will experimentally test whether such an increase in transparency indeed induces a decrease in cheating. The research question follows naturally: Does an increase in transparency about the results of cheating detection

lead to a decrease of cheating?

1.2 S

The next chapter will discuss existing models that explain and predict cheating behaviour. The first model provides insights in the interaction between different athletes. It illustrates that athletes have strong incentives to cheat. The second model introduces an organization that can inspect if the athlete cheated. As inspection is costly and athletes prefer not to get

4 caught cheating, this model predicts a mixed strategy equilibrium. When subsequently a sponsor is introduced to the model, behaviour shifts dramatically, resulting in a highly undesirable situation in which athletes cheat and organization do not preform inspections.

This model, which includes an athlete, an organization and a sponsor, can be altered using different information structures. Different levels of transparency predict different behaviour by the actors. To answer the research question, I designed an experiment based in this model. The experimental design is presented in chapter 3. Additional information on the experimental procedures is included and the chapter concludes with hypotheses on the results of the experiment.

The results of the experiment are presented in chapter 4. The chapter starts with an

exploratory analysis, to continue with a summary of the behaviour of the different actors in the experiment. It is confirmed that in contrast to the prediction from the game theoretical model most athletes choose to play fair, while the majority of organizations inspect the athlete.

The experiment gives little reason to make results of cheating inspections public, as it is not found that this reduces cheating. This statement needs an explanation though, which can be found in chapter 0, accompanied by some limitations for the external validity of the results and some suggestions for further research.

To complete the paper, the experimental instructions can be found in Appendix A. Also, a paragraph on the data is included and the statistical code is presented. References are presented in chapter 7.

5

2 T

HEORETICAL FRAMEWORK

The previous chapter illustrated the motivation behind this research. This chapter will discuss existing models that explain and predict cheating behaviour. The actors in these models are athletes, organizations and sponsors. The athletes can choose between playing fair and cheating. Cheating improves their chances at winning, but when an inspecting authority is introduced, there is a chance of getting caught. This inspecting authority will be referred to as the organization1_{. The sponsor plays an important role in the finances of both} athletes and organizations.

2.1 T

:

’

To start, we will consider a model that includes two athletes, who compete for a prize. Their interaction can be modelled as a prisoner’s dilemma (Breivik, 1987).

The athletes can choose to play fair or they can cheat, giving them a comparative advantage that leads to a higher chance of winning if the other athlete chooses to play fair. If both players cheat, their chances at winning are unaffected. As cheating is not risk free and may involve costs, the players prefer to outcome in which both play fair over the outcome in which both cheat. If the (expected) cost of cheating is smaller than the expected advantage, cheating is the dominant strategy.

To be consistent throughout this paper, let the prize be €8 and let the players be equally likely to win this prize if they both play fair2_{. If one athlete cheats, while the other athlete} plays fair, his chance to win increases to 75%. The other athlete’s chance to win is thus reduced to 25%.

The expected advantage of cheating is equal to €2, regardless of the strategy of the other player, as cheating always increases the chance of winning by 25%. Let the expected cost of cheating be €1. This game can be represented in matrix form:

1_{In some sports, the institution that organizes the tournament is responsible for the cheating (doping)} inspection. In other sports, the inspecting authorities work autonomous. However, a demand for cheating inspection is driven by the organization of tournaments. Therefore, the interests of organizations and inspecting authorities are related and both benefit from a thriving competition.

2_{If the expected profit of cheating is higher than the cost of cheating, the amount of prize money and the}

6 Athlete 2

Cheat Play fair

Athlete 1 Cheat (3,3) (5,2)

Play fair (2,5) (4,4)

As the expected benefit of cheating is larger than the expected cost involved, cheating is the dominant strategy and the Nash Equilibrium is the outcome in which both athletes cheat. As can be seen in the matrix, if the athletes would commit to playing fair, this would result in a welfare improvement for both athletes. The model is a prisoners’ dilemma: both athletes have strong incentives to cheat, whereas they would be better off if they both play fair.

2.2 THE INTERACTION BETWEEN ATHLETE AND ORGANIZATION: THE INSPECTION GAME

In the previous section the interaction between two athletes was modelled as a prisoner’s dilemma. In this section an inspecting authority will be introduced in the form of an organization. The chance of getting caught increases the expected cost of cheating.

The simplest and most commonly used model to describe the interaction between an athlete and an organization that can choose to inspect the athlete is the inspection game (Rauhut, 2009).

The athlete competes for a prize and he can choose to cheat or to play fair. Cheating

increases his chance to win, but he risks getting caught by the organization, who chooses to inspect the athlete or not. The athlete will not receive any prize money if he is caught cheating. Therefore, the athlete prefers to cheat only if the organization does not inspect.

The organization decides whether to inspect the athlete or not. Inspection involves costs, such as wages or material costs. When the organization discovers that the athlete cheated, the organization is rewarded with money. As there is no profit in inspecting if the athlete played fair and inspection is costly, the organization prefers to inspect only if the athlete cheats.

To be consistent with the previous paragraph and the experiment, let there be a prize of €8. If the athlete plays fair, he has a chance of 50% to win this prize. If the athlete cheats, his chance to win is 75%. Let the cost of inspection be €1. If the organization inspects and the

7 athlete is caught cheating, the organization will obtain €4. This game can be represented in matrix form:

Athlete

Cheat Play fair

Organization Inspect (3,0) (-1,4)

Do not inspect (0,6) (0,4)

This game has no dominant strategies and no equilibrium in pure strategies. There is a mixed equilibrium though. In this mixed equilibrium, the athlete cheats with chance ¼ and the organization inspects with chance ⅓. The expected payoff for the athlete is €4 and the expected payoff for the organization is €03_.

This model can be expanded by adding one or more athletes. In such expanded models, behaviour in equilibrium is similar to the behaviour in the given model. There are no dominant strategies and an equilibrium in mixed strategies exists (Berentsen, Bruegger, & Loertschen, 2008).

2.3 T

:

So far, the models discussed only included athletes and organizations. Professional sports would not be economically viable without supporters, media and sponsors. Therefore, this section will add this important group of stakeholders to the inspection game.

The relation between athletes, organizations and sponsors is clear. Athletes depend on sponsors for funding of materials, traveling, training camps and salaries. Organizations are unable to organize major sporting events without the financial aid of sponsors.

The interaction between sponsors, media and supporters is a bit more complicated. An important reason for sponsors’ interest in sports is the publicity that is involved. Through the media, they can reach fast amounts of supporters, which in turn may buy their products or services. These supporters however are usually not interested in what the sponsor has to

3_{If the athlete increases his chances of winning by cheating and the reward of catching a cheater is higher} than the inspection costs, the only equilibrium of the game is a mixed equilibrium. The amount of prize money, the inspection costs and the reward for the organization when catching a cheater do influence the location of the equilibrium, but neither its existence nor its uniqueness, as long as these conditions are met.

8 offer, but in the sporting events. They need the media for accessibility to these events. The media in turn depend on sponsors for their revenues but they can charge higher prices if more supporters watch their broadcasts.

Buechel, Emrich and Pohlkamp (2013) propose an extension of the inspection game with a third actor: the customer. This customer can be either a supporter, a medium or a sponsor. This customer can choose between continuing his support or withdrawing his support after receiving information about the cheating behaviour of the athlete. Whenever an athlete cheats and the organization finds out through inspection, the result is a scandal, which will most likely lead to the withdrawal of customers.

As the organizations and athletes are directly depending on sponsors, I will focus on the role of the sponsor in the expansion of the model. As the sponsor is in turn depending on both the media and the supporters, their behaviour is strongly linked to the behaviour of the other customers. I will expand the game in the same way as Buechel, Emrich and Pohlkamp (2013) do, but I will refer to the third actor as the sponsor.

The extended game involves three players: one athlete, one organization and one sponsor. As in the inspection game, the athlete can either cheat or play fair and the organization can either inspect or not. As the athlete and organization have no information on the other player’s decision, their decisions can be regarded as simultaneously. After the sponsor receives some information about the inspection, he decides whether to continue his sponsorship or withdraw his sponsorship4_{. The behaviour of the sponsor depends on the} information structure of the game.

First, I will explain some assumptions about the behaviour of the players. Then I will discuss the equilibrium of the game with two different information structures. The first information structure is derived from the situation as it is in most sports nowadays. The second, more transparent, information structure follows from a desire to reduce cheating.

4 _{Remark that the sponsor wants to anticipate on the behaviour of the supporters. If supporters withdraw} their support, the publicity involved with sponsorship diminishes and the sponsor will be inclined to withdraw his sponsorship. If the supporters continue their support, the sponsor has incentives to continue his sponsorship.

9 2.3.1 Assumptions on the preferences of the different actors

To create a game with representative pay-offs some assumptions about the preferences of athletes, organizations and sponsors are needed. In this section these assumptions are introduced and explained.

For the athlete it is assumed that he prefers to cheat if the organization does not inspect, as cheating gives the athlete a comparative advantage. Furthermore, it is assumed that the athlete prefers to play fair and be inspected while the sponsor continues the sponsorship over cheating and be inspected while the sponsor withdraws the sponsorship. This

represents the case in which financial support from the sponsor is larger than the increase in prize money associated with cheating.

For the organization it is assumed that undetected cheating while the sponsor continues his sponsorship is preferred over detecting cheating while the sponsor withdraws his

sponsorship. This means that the financial support from the sponsor is larger than the benefit of detecting cheating. Furthermore, the organization prefers to inspect fair athletes while the sponsor continues the sponsorship over not inspecting fair athletes while the sponsor withdraws his sponsorship. The cost of inspection is lower than the financial aid from sponsors.

For the sponsor it is assumed that he prefers to withdraw the sponsorship after the athlete is caught cheating. This is justified as supporters are expected to withdraw support for a

cheater, resulting in negative publicity if the sponsor would continue his sponsorship. If the athlete is not caught cheating (which is the case whenever the athlete plays fair or the organization does not inspect), the sponsor prefers to continue his sponsorship. If the athlete is not caught cheating, the supporters have no reason to withdraw their support, so neither does the sponsor.

2.3.2 The intransparent treatment

In most sports the outcome of cheating inspections is revealed only when the athlete is caught cheating. If this is the case, the sponsor cannot distinguish whether the athlete played fair, or the organization decided not to inspect the athlete. This information structure will be referred to as the intransparent treatment. The result is a game with imperfect information as shown in Figure 1. The pay-offs that are indicated are in accordance with the assumptions in section 2.3.1 and the experimental design as explained in chapter 3.

10 Figure 1: structure of the game in the intransparent treatment.

The choices and pay-offs for the athlete are indicated in red, for the organization in blue and for the sponsor in green. Dotted lines indicate that the decision is within the same information set. The player cannot distinguish between the choices by the other players that may have led to this point in the game.

This game has a subgame perfect Nash Equilibrium in which the athlete cheats, the

organization does not inspect and the sponsor withdraws support after the athlete is caught cheating and continues support whenever this is not the case. This means that the

sponsorship is continued if either the athlete played fair or the organization did not inspect the athlete. In the equilibrium there is no scandal, so the sponsor will continue his support. This equilibrium is unique.

In the inspection game as described in section 2.2, the athlete was best off when choosing a mixed strategy. Sometimes the athlete cheats, sometimes he plays fair. After introducing a sponsor to the model, the equilibrium predicts that the athlete will always cheat. This result is both remarkable and undesirable.

11 2.3.3 The transparent treatment

According to Buechel, Emrich and Pohlkamp (2013), cheating can be reduced by a small alteration in the information structure. If the sponsor is not only informed after a scandal, but also after an inspection was conducted and the athlete was found to be playing fair, a doping free equilibrium arises.

This alteration enables the sponsor to distinguish between the cases in which the athlete played fair and was inspected and the cases in which there was no inspection. If there was no inspection, the sponsor does not know whether the athlete cheated or not. This finer information structure will be referred to as the transparent treatment. The new game is represented in Figure 2.

Figure 2: structure of the game in the transparent treatment.

The choices and pay-offs for the athlete are indicated in red, for the organization in blue and for the sponsor in green. Dotted lines indicate that the decision is within the same information set. The player cannot distinguish between the choices by the other players that may have led to this point in the game.

Under the same assumption on the preferences of the players, there exist two Nash Equilibria. The first equilibrium is equal to the one in the game with less information. The

12 athlete cheats, the organization does not inspect and the sponsor only withdraws support after the athlete is caught cheating. The second equilibrium however is cheating free. The athlete plays fair, the organization inspects and the sponsor only continues support if the organization inspected the athlete and the athlete played fair. As it is costlier for the organization to lose the sponsor than it is to inspect the athlete, the sponsor can create a threat by withdrawing support if there was no inspection. This is an unbelievable threat as it leads to a lower payoff for the sponsor when there was no inspection. However, critical sponsors may have moral arguments to prefer athletes who play fair. This can influence their pay-offs enough to change their preferences and to withdraw their sponsorship if there was no inspection.

2.4 C

According to Buechel, Emrich and Pohlkamp (2013), the finer information structure in the transparent treatment may lead to fewer cheating. The aim of this research is to test in an experimental setting if this effect is achieved. Therefore, groups of three participants are formed, one athlete, one organization and one sponsor. They will play the game as described in the previous paragraph with the two different information structures. In chapter 3 the experimental design will be explained. The outcomes of the experiment will be presented in chapter 4.

13

3 M

ETHODOLOGY

Previous chapters gave an overview of the importance of this research and the literary framework. This chapter will make explicit how the research question can be answered through an experiment. First, the experimental design and procedures are explained. Subsequently, hypotheses on the outcome of the experiment are presented.

3.1 E

To answer the research question, I conducted an experiment. The instructions as given to the participants can be found in Appendix A.

Participants randomly received one out of three roles: athlete, organization or supporter. After all data was collected participants were randomly placed in a group of three members, one for each role. The decisions of every group member influence the pay-off of the other group members.

Every participant has two options. The athlete chooses to play fair or to cheat5_{. The} organization chooses to inspect whether the athlete cheated or not. The athlete and

organization decide simultaneously. Subsequently, the sponsor decides upon continuing his sponsorship or withdrawing his sponsorship.

The athlete can win a prize of €8. If he plays fair, the chance of winning is 50%. If he cheats, the chance of winning is 75%. If the athlete cheats and the organization inspects the athlete, he will not receive any prize money.

Additionally, the athlete receives €1 if the sponsor continues the sponsorship. This additional amount is independent of the choice of the athlete and the organization.

The organization receives €1 if he does not inspect the athlete. If instead the organization inspects the athlete, the organization receives €4 if the athlete cheated and receives €0 if the athlete played fair.

5_{Remark that cheating in this experiment is merely a strategy label. No actual cheating is involved, as}

14 Additionally, the organization benefits from the investment by the sponsor. He receives €4 if the sponsor continues his sponsorship. This additional amount is independent of the choice of the athlete and the organization.

The sponsor has an initial endowment of €1. If the sponsor continues his sponsorship, he will invest €1 in the athlete. If the athlete cheated and the organization inspected the athlete, the investment is lost. Else, the investment is doubled, and the sponsor earns €2. If the sponsor withdraws his sponsorship, no money is invested in the athlete and the sponsor will hold on to his initial endowment of €1.

All pay-offs are in compliances with the assumptions on the preferences of the different actors as explained in section 2.3.1.

3.2 T

The experiment has two treatments, the intransparent treatment and the transparent treatment.

The intransparent treatment is chosen to represent the current course of action. The athlete and organization decide simultaneously, unaware of the other’s decision. Only if the athlete cheated and the organization inspected, the sponsor is told that the athlete cheated. In all other outcomes, the sponsor is told that the athlete was not found to be cheating. Thus, the sponsor cannot distinguish whether the athlete played fair or the organization did not inspect.

The transparent treatment is chosen in accordance with the alteration as suggested by Buechel, Emrich and Pohlkamp (2013). As in the intransparent treatment, the athlete and organization decide simultaneously, unaware of the other’s decision. Subsequently the sponsor is told whether the athlete cheated, played fair, or the organization did not inspect. Therefore, the sponsor can distinguish whether the athlete played fair or the organization did not inspect, which is the only difference in comparison with the intransparent treatment.

3.3 P

The experiment was conducted through an online questionnaire as this facilitated the collection of data. This may have resulted in a loss of control, which is accounted for by the increase in statistical power.

15 The treatment effect can be investigated through a within or between subject comparison. A within subject comparison eliminates the effects of omitted variables that differ over

participants but are constant over time. However, order effects may be present at a within subject comparison as the first decision is not independent of the second. Therefore, all participants will be asked to decide in both treatments. Half of the participants will begin with the transparent treatment. The other half begins with the intransparent treatment. This makes it possible to investigate if order effects are present. If this is the case, a between subject comparison offers an outcome, as the choices of different participants are independent.

To obtain information on the choice of the supporter in different situations, the strategy method will be used. The supporter will be asked to decide for every possible outcome. Using the strategy method gives as an additional advantage that it is not necessary to know the choices of the athlete and the organisation prior to the decision of the supporter and therefore the participants do not have to be placed in a group at the start of the experiment, but they can be randomly placed into groups afterwards.

When the data collection has ended, one athlete, one organisation and one sponsor will be randomly selected for payment. They will be paid according to their decisions for one of the treatments, which is also determined randomly.

3.4 H

As described in chapter 2, the game induced by the intransparent treatment has only one Nash Equilibrium. The athlete cheats, the organization does not inspect, and the sponsor continues sponsorship when the athlete is not found to be cheating. The finer information structure in the transparent treatment results in a game with two Nash Equilibria. One equilibrium is equal to the one in the intransparent treatment. In the other equilibrium the athlete plays fair, the organization inspects the athlete and the sponsor only continues his sponsorship when the organization inspected and the athlete played fair. This last

equilibrium involves non-optimal behaviour outside the equilibrium path. Therefore, it’s occurrence depends on the moral considerations of the participants and their beliefs about others’ considerations.

16 Nash equilibria assume that all players behave like rational self-centred agents. From

behavioural economics it is known that this is not always the case. Bounded rationality and social preferences may cause participants to behave differently. In this experiment about cheating, private and social norms play an important role.

Many studies have shown that people have strong private and social norms against lying and cheating (Abeler, Nosenzo, & Raymond, 2016). Because of these norms it may be expected that most athletes will choose to play fair in both treatments. However, as the transparent treatment involves a cheating-free equilibrium while the intransparent treatment does not, I expect to see that more athletes play fair in the transparent treatment, when compared to the athletes in the intransparent treatment.

For the organizations, the same norms are of importance. In both treatments, a substantial part of the organizations may choose to inspect the athlete. This is not only because of moral considerations, but also because catching a cheater will be awarded with €4. This reward is considerably larger than the cost of inspection, which is €1. On the other hand, some organizations might be unwilling to inspect the athlete, as they do not want to be the whistle-blower (Magnus, Polterovich, Danilov, & Savvateev, 2002). Because of the cheating-free equilibrium in the transparent treatment, I expect that in this treatment, relatively more organizations will choose to inspect the athlete, prompted by the threat of sponsors

withdrawing their support if there was no inspection.

Regarding the sponsors, I expect that almost all of them will withdraw their sponsorship if the athlete is caught cheating because of private and social norms. In the intransparent treatment, sponsors have little incentives to withdraw support after they are informed that the athlete was not found to be cheating, as they cannot know whether the athlete played fair or there was no inspection. Therefore, most sponsor will probably continue the

sponsorship in this case. In the transparent treatment though, sponsor can distinguish these cases. I may expect that sponsors will continue the sponsorship after they hear that the athlete played fair, whereas some sponsors will withdraw the sponsorship if there was no inspection. The fraction of sponsors withdrawing their sponsorship when no inspection occurred provides a measure of the critical attitude of participants.

17

4 R

ESULTS

In the previous chapter the experimental design and hypotheses on the results were

explained. This chapter will point out the most important results of the experiment and their consequences.

Throughout the analysis a significance level of 10% will be used. The cost of higher

transparency is little and even a small decrease in cheating can be considered an important improvement. A Type 2 error is therefore more undesirable than a type 1 error, which justifies a higher significance level.

4.1 E

The experiment was conducted through an online survey. The respondents were informed about the experiment through my personal network. A total of 289 respondents completed the survey. They were randomly sorted into six groups. Two groups of athletes, two groups of organizations and two groups of sponsors. For every role, one group started with the transparent treatment, followed by the intransparent treatment. The other group started with the intransparent treatment and ended with the transparent treatment. Every group will be referred to with a two-letter-combination. The first letter indicates the role of the participants, A for athletes, O for organizations and S for sponsors. The second letter indicates with which treatment the group started, T for transparent and I for intransparent. The six groups are thus referred to as AT, AI, OT, OI, ST and SI, see Table 1.

Group reference Role First treatment

AT Athlete Transparent AI Athlete Intransparent OT Organization Transparent OI Organization Intransparent ST Sponsor Transparent SI Sponsor Intransparent

Table 1: overview of the reference used for every group

Of the 289 respondents, 61 (21.1%) were female, 226 (78.8%) were male and two (0.6%) respondents did not specify their gender. See Figure 5 for the male-to-female ratio per group.

18 Of the 275 (95.2%) participants who indicated their age the average age was 47.09 with a standard deviation of 16.79. See Figure 7 for the age distribution per group. A majority of 209 of 288 (72.6%) participants indicated that they participate in competitive sports themselves. See Figure 6 for the participation rate per group.

One athlete, one organization and one sponsor were selected for payment. They received payment according to their decision in one of the treatment. The total amount that was paid amounted to €16, -.

4.2 G

As displayed in Figure 3 in both groups of athletes the majority plays fair in both treatments. This behaviour is consistent with social norms as discussed in section 3.4. The part of

athletes that cheats varies from 10% to 30%. Within a group, the difference in behaviour between treatments appears to be minimal, but we do observe a difference between the behaviour of the two groups.

Figure 3: summary of the behaviour of the athletes in different groups and treatments.

As displayed in Figure 4 in both groups of organizations the majority inspects the athlete, while a small minority does not. Differences in behaviour between and within groups appear to be small. At most we might observe that the group of organizations that started with the

0% 10% 20% 30% 40% 50% 60% 70% 80% 90% 100% AI intransparent

treatment AI transparenttreatment AT intransparenttreatment AT transparenttreatment

Behaviour of the athletes

19 transparent treatment inspect slightly more in both treatments than the group that started with the intransparent treatment.

Figure 4: summary of the behaviour of the organizations in different groups and treatments.

In Table 2, Table 3, Table 4 and Table 5 the behaviour of the two groups of sponsors during the different treatments is presented. We see that in all groups organizations continue the sponsorship even if the athlete is caught cheating. This is not beneficial for the sponsor as he will lose his initial endowment without any return. This behaviour is very beneficial for the other players though. If the sponsorship is continued, the cost to the sponsor is €1, while the athlete gains €1 and the organization gains €4. If the sponsor is aiming at maximizing the joint pay-off, the best strategy to do so is by always continuing the sponsorship.

Nevertheless, in both treatments most sponsors withdraw the sponsorship when the athlete is caught cheating. As stated in chapter 3.4 the fraction of sponsor that withdraw their sponsorship if the organization did not inspect provides a measure for the critical attitude of the participants. Of 88 sponsors, 10 sponsors (11,4%) withdraw the sponsorship if they discover that the organization did not inspect the athlete. This means that approximately this fraction of participants has the critical attitude that is necessary to arrive at the cheating free equilibrium of the game.

0% 10% 20% 30% 40% 50% 60% 70% 80% 90% 100% OI intransparent

treatment OI transparenttreatment OT intransparenttreatment OT transparenttreatment

Behaviour of the organizations

20

Continue sponsorship Withdraw sponsorship

The athlete cheated 1 38

The athlete played fair 38 1

The organization did not inspect 34 5

Table 2: behaviour of the SI group during the transparent treatment.

Continue sponsorship Withdraw sponsorship

The athlete cheated 9 40

The athlete played fair 49 0

The organization did not inspect 44 5

Table 3: behaviour of the ST group during the transparent treatment.

Continue sponsorship Withdraw sponsorship

The athlete cheated 4 35

The athlete was not found to be cheating 37 2

Table 4: behaviour of the SI group during the intransparent treatment.

Continue sponsorship Withdraw sponsorship

The athlete cheated 4 45

The athlete was not found to be cheating 45 4

Table 5: behaviour of the ST group during the intransparent treatment.

4.3 W

The data obtained from the experiment are twelve distributions of strategies, one for every group and treatment. The experiment was executed in a way that the conclusions can be based on either a within subject design or a between subject design. Both have up- and downsides.

An advantage of a within subject design is that every subject will decide in every treatment, while the circumstances per subject will vary only slightly. This eliminates the influence of omitted variables. However, order effects may be at issue. As the question in both

treatments is very similar, subjects may not notice that the question changed and give the same answer in the second treatment. Learning may also have an effect, even though the participants did not receive feedback between treatments.

21 An advantage of a between subject design is that the distributions obtained are

independent. A disadvantage is that external factors may influence their behaviour, which may lead to omitted variable bias. As the data obtained from the experiment is a distribution of strategies per group, it is not possible to control for omitted variables properly. Randomly assigning participants to a group is important because this averages out the effects of any omitted variables.

As discussed, a within subject design has the advantage that there is no or little influence of omitted variables. Therefore, this method is preferred if the influence of order effects is insignificant. However, if order effects are found, a between subject design will be used.

4.4 O

If the order of the treatments does not influence the behaviour of participants, the decisions of the groups within one treatment must be equally distributed, whether the group began or ended with the treatment. Therefore, I compared the answers of the two groups per role. Athletes and organizations make two decisions, one decision per treatment. Sponsors make two decisions in de intransparent treatment and three in the transparent treatment. This results in a total of nine comparisons.

To test if the two distributions that I compare originate from the same distribution I may use either a Fisher’s exact test or a Chi-squared test for contingency tables. The Chi-squared test relies on a Chi-square limit distribution that only applies if the expected number of

observations in a cell is large enough. As it is unclear whether this is the case, Fisher’s exact test is preferred. As no order effects are expected, a two-sides test is performed.

In Table 6 and Table 7 the choices of the athletes are presented. There is no significant difference in the distribution in the intransparent treatment. However, with a 10%-significance level, there is a significant difference in the distribution in the transparent treatment. Significantly more athletes choose to play fair if they started with the transparent treatment, in comparison to the athletes that started with the intransparent treatment. This is an indication that order effects are present.

22

AI AT

Cheat 8 14

Play fair 40 40

Table 6: comparison of the athletes’ decisions in the intransparent treatment.

Fisher’s exact test indicates no order effects, p = 0.3363.

AT AI

Cheat 15 6

Play fair 39 42

Table 7: comparison of the athletes’ decisions in the transparent treatment.

Fisher’s exact test indicates order effects, p = 0.08494.

In Table 8 and Table 9 the choices of the organizations are presented. There is no significant difference in the distribution in the intransparent treatment. Neither is there a significant difference in the distribution in the transparent treatment.

OI OT

Inspect the athlete 30 32

Do not inspect the athlete 21 16

Table 8: comparison of the organizations’ decisions in the intransparent treatment.

Fisher’s exact test indicates no order effects, p = 0.5334.

OT OI

Inspect the athlete 34 29

Do not inspect the athlete 14 22

Table 9: comparison of the organizations’ decisions in the transparent treatment.

Fisher’s exact test indicates no order effects, p = 0.2096.

In Table 10 and Table 11 the decisions of the sponsors in the intransparent treatment are presented. Table 10 shows the decision whether to continue the sponsorship after the athlete was caught cheating. Table 11 shows this decision after the athlete was not found to be cheating, which means that either the athlete played fair or the athlete cheated, but the organization decided not to perform an inspection. There is no indication of order effects.

SI ST

Continue sponsorship 4 4

Withdraw sponsorship 35 45

Table 10: sponsors’ decisions in the intransparent treatment if the athlete cheated.

23

SI SO

Continue sponsorship 37 45

Withdraw sponsorship 2 4

Table 11: sponsors’ decisions in the intransparent treatment if the athlete was not found to be cheating.

Fisher’s exact test indicates no order effects, p = 0.6893.

In Table 12, Table 13 and Table 14 the decisions of the sponsors in the transparent treatment are presented. Table 12 shows the decision whether to continue the sponsorship after the athlete was caught cheating. Table 13 shows this decision after the athlete was found to be playing fair. Table 14 shows the decision after the athlete was not inspected by the

organization.

ST SI

Continue sponsorship 9 1

Withdraw sponsorship 40 38

Table 12: sponsors’ decisions in the transparent treatment if the athlete cheated.

Fisher’s exact test indicates order effects, p = 0.03804.

ST SI

Continue sponsorship 49 38

Withdraw sponsorship 0 1

Table 13: sponsors’ decisions in the transparent treatment if the athlete played fair.

Fisher’s exact test indicates no order effects, p = 0.4432.

ST SI

Continue sponsorship 44 34

Withdraw sponsorship 5 5

Table 14: sponsors’ decisions in the transparent treatment if the organization did not inspect the athlete.

Fisher’s exact test indicates no order effects, p = 0.7452.

There is no significant difference in the distributions after the sponsor is told that the athlete played fair or the sponsor is told that there was no inspection.

If the sponsor is told that the athlete cheated, the sponsors that started with the transparent treatment are more likely to continue the sponsorship nevertheless, if compared to the sponsors that participated in the transparent treatment after they had participated in the intransparent treatment earlier. This result is remarkable as it is not in the financial benefit of the sponsor to continue the sponsorship if the athlete is found to be cheating. Perhaps

24 sponsors opted for this to stimulate organizations to inspect the athletes. Even though this might theoretically not be the best way to achieve this, it might result in more inspections, which in turn might stimulate athletes to play fair.

To summarise this section, strong evidence for the influence of order effects on the decisions of both athletes and sponsors was found. Because of these order effects, the decisions in the second round are not identically distributed as decisions in the first round. Therefore, a within subject comparison fails.

In the remainder of this chapter, I will focus on a between subject approach. As the subject differ in many aspects, omitted variables may influence the results. The next section is dedicated to test if the subjects were randomly assigned to a group successfully.

4.5 R

In Figure 5 the ratio of men and women per group is displayed. With a p-value of 0.4765 a Chi-squared test confirms that it is plausible that these samples originate from the same distribution.

Figure 5: ratio of men to women per group.

A Chi-squared test confirms that the distribution of men and women is similar in all groups, p = 0.4765.

0% 10% 20% 30% 40% 50% 60% 70% 80% 90% 100% AI AT OI OT SI ST Total

Male-to-female ratio per group

25 In Figure 6 participation in competitive sports per group is displayed. With a p-value of 0.7432, a Chi-squared test confirms that it is plausible that these samples originate from the same distribution.

Figure 6: participation in competitive sports per group.

A Chi-squared test confirms that the participation in competitive sports is similar in all groups, p = 0.7432.

In Figure 7 the age distribution per group is displayed. When comparing the age distribution of the two groups of athletes, it seems unlikely that these samples originate from the same distribution. A Kolmogorov-Smirnov test with p-value 0.006133 confirms that this is indeed very unlikely. However, the comparison of the two groups of organizations and the two groups of sponsors using the Kolmogorov-Smirnov test does not give an indication that they do not originate from the same distribution. Also, a comparison of any group with the total population does not give reason to conclude that they originate from different samples.

It is unclear why the group of athletes that started with the intransparent treatment is significantly younger than the group of athletes that started with the transparent treatment. Random assignment of participants to one of the groups was ensured by using a randomizer in Qualtrics. As the results only include the answers of participants who finished the survey, self-selection may occur. As both groups performed identical tasks, it remains uncertain why one of the groups is younger. The order of the tasks should not influence the age of the participants who finish the survey, especially since the tasks are very similar.

0% 10% 20% 30% 40% 50% 60% 70% 80% 90% 100% AI AT OI OT SI ST Total

Participation rate in competitive sports per group

26 As there is no obvious reason why age should influence the decision of an athlete, I will continue with a between subject comparison. However, when analysing the results, I will have to keep in mind that the group of athletes that started with the intransparent treatment is significantly younger than the group of athletes that stated with the transparent treatment.

Figure 7: age distribution per group.

Kolomogorov-Smirnov tests confirm that the distribution of ages if different in the two groups of athletes, p = 0.006133, whereas this distribution is similar in the groups of organizations (p = 0.8618) and sponsors (p = 0.8078).

4.6 B

In this section the treatment effect will be investigated through a between subject

comparison. As the results in the second round are biased because of the order effect, only the results of the first round are used. To test for significant differences, Fisher’s exact tests will be used.

AT transparent treatment AI intransparent treatment

Cheat 15 8

Play fair 39 40

Table 15: comparison of the decisions of the athletes in the first round.

A one-sided Fisher’s exact test invalidates the hypothesize that athletes cheat less in the transparent treatment (p = 0.9437). A two-sided Fisher’s exact test provides no indication of any significant difference (p = 0.2368).

27

OT transparent treatment OI intransparent treatment

Inspect athlete 34 30

Do not inspect athlete 14 21

Table 16: comparison of the decisions of the organizations in the first round.

A one-sided Fisher’s exact test provides not enough evidence to confirm that organizations inspect more often in the transparent treatment, when compared to the intransparent treatment (p = 0.1494).

ST transparent treatment SI intransparent treatment

Continue sponsorship 9 4

Withdraw sponsorship 40 35

Table 17: the sponsor’s decisions in the first round if the athlete cheated.

The two-sided Fisher’s exact test provides no indication of a significant treatment effect on the number of sponsors that continue the sponsorship after the athlete is caught cheating (p = 0.369).

In Table 17 we see that after hearing that the athlete cheated, a larger fraction of the sponsors in the transparent treatment decided to continue the sponsorship. This difference is not significant according to a two-sided Fisher’s exact test.

In the transparent treatment, the sponsor is told whether the organization performed an inspection and, if this is the case, the outcome of that inspection. In the intransparent treatment the sponsor is only told if the athlete cheated and the sponsor cannot distinguish the cases in which the athlete played fair and the cases in which there was no inspection. As the decision of the sponsor is influenced by the information provided, I cannot compare these decisions in the different treatments.

In Table 16 we see that in the transparent treatment, a larger fraction of the organizations inspects the athlete. This is in accordance with the hypothesis as stated in section 3.4, which was based on (Buechel, Emrich, & Pohlkamp, 2014). When testing this hypothesis with a one-sided Fisher’s exact test, we find that the difference is not significant. Therefore, I must conclude that an increase in transparency on the outcomes of cheating detection does not necessarily lead to an increase of investigation.

From Table 15 it can be concluded that there was a larger fraction of athletes who cheated in the transparent treatment, than in the intransparent treatment. This is not in accordance with the hypothesis in section 3.4, based on (Buechel, Emrich, & Pohlkamp, 2014). The prediction was that the transparent treatment would give rise to a cheating-free equilibrium

28 as sponsors can pose a threat to organizers when they withdraw the sponsorship if no

inspection was performed. This would lead to more inspections and less cheating due to the increased chance of getting caught. A one-sided Fisher’s exact test (p = 0.9437) confirms that the difference is not in accordance with the hypothesis. A two-sided Fisher’s exact test (p = 0.2368) gives no indication of any significant difference between cheating in the transparent and intransparent treatment.

As observed in Table 17 more sponsors continued the sponsorship after the athlete was caught in the transparent treatment than in the intransparent treatment. Even though this difference might not be significant, if this behaviour was expected by the athletes, it is an explanation for the increase in cheating, as it reduces the costs of getting caught.

4.7 L

As discussed, the group of athletes that started with the transparent treatment was

significantly older than the group of athletes that started with the intransparent treatment. If there is a significant effect of age on cheating behaviour in adults, the between subject comparison suffers from omitted variable bias. Although research on the effects of age on cheating behaviour in children indicate that age is an indicator of cheating (Kanfer & Duerfeldt, 1968), it cannot be concluded that this is also in indication of cheating in adults.

I must emphasize that the respondents were informed about the online survey through my personal network. As many of my friends and acquaintances play bridge at a high level, a large part of the participants consists of professional and competitive bridge players. This has some consequences for the external validity of the results that were obtained in this experiment.

A large fraction of participants consisted of males. With the knowledge that the high-level bridge community consists mainly of men, this is not surprising. As men are more likely to lie in competitive environments (Dato & Nieken, 2015), it seems plausible that the large

fraction of men influences the obtained results. In a population with more female

participants, you might encounter less cheating. This influences the behaviour of athletes directly. As the behaviour of organizations and sponsors depends on the believes of the other players’ behaviour, their decision might be influenced as well.

29 Furthermore, a large part of participants indicated to be participating in competitive sports. This indicates that a substantial part of the participants is very competitive and might be more willing to cheat if this increases their chances at winning, when comparing them with less competitive people. As athletes are also highly competitive, this group represents athletes quite well. It is not so clear though whether organizations and sponsors are also competitive in general. This may vary from one sport to another. In bridge, organizations are often led by former bridge players and the sponsors often compete on the highest levels of bridge themselves. However, this does not apply to all sports. Therefore, when extrapolating the results from this experiment to other sports, it is important to realize that this group of participants was very competitive.

Also, remark that throughout the experiment, no actual cheating is involved. The athlete has to choose whether to cheat or to play fair, but these words are nothing more than a label for a strategy. However, the results show that most of the participants did classify this strategy as actual cheating, which is indicated by the small fraction of participants that chose for “cheat”.

As always with controlled experiments, the situation as considered is a simplification of reality. In this experiment, participants played a one-shot game whereas in reality athletes, organizations and sponsors often meet again. Reputation did not play a role in this

experiment but does matter in reality. If athletes are caught cheating once, they are usually suspended, and they often must return the medals and prize money received earlier.

30

5 D

ISCUSSION AND CONCLUSION

5.1 M

Due to the presence of order effects, a between subject design was adopted to answer the research question. The downfall of this method is that omitted variables may enlarge or diminish the treatment effect. Specifically, the influence of age on cheating behaviour of adults is of importance, as one group of athletes is significantly older than the other group.

Throughout the experiment, a large majority of athletes chose to play fair in all treatment, which is consistent with current social norms. A between subject comparison showed that in the transparent treatment more athlete cheated than in the intransparent treatment, but this difference was not significant.

Most organizations chose to inspect the athletes, even though inspection is costly.

Most sponsors withdraw the sponsorship if the athlete is caught cheating and continue the sponsorship else. Approximately 11% of sponsors withdraw the sponsorship if the

organization did not inspect the athlete. This proves that some sponsors adopt a critical attitude towards cheating. However, this group is not large enough to ensure cheating can be eradicated.

A between subject comparison showed no significant treatment effect on the behaviour of organizations and sponsors. This gives us enough information to answer the research question.

Does an increase in transparency about the results of cheating detection lead to a decrease of cheating?

The results from the experiment indicate that providing sponsors with both positive and negative outcomes of cheating inspection does not lead to a decrease of cheating. To complete this conclusion some important remarks need to be taken into consideration.

As the effect of age on cheating attitude is unclear, the difference in age between the two groups of athletes may influence the treatment effect that was found. If older people are more likely to cheat, the treatment effect is counteracted by the age difference, resulting in

31 an underestimation of the treatment effect. If older people are less likely to cheat, the treatment effect is overestimated.

When extrapolating results obtained in an experiment to real life situations, it is important to consider the composition of the test group. This group consisted mainly of men (78.8%) and most participants indicated that they participate in competitive sports (72.6%).

This experiment does not predict behaviour impeccably, but it does provide an empirical substantiation that a more transparent inspection does not lead to significantly less cheating and more drastic method are necessary to achieve results.

5.2 F

The results from the experiment do not support the view that transparency leads to less cheating. The reason for this might be that not enough sponsors adopt a critical attitude against cheating, which is a necessary condition. Thus, transparency may not lead to less cheating in the short run. However, it could contribute to a change of attitude. It would be interesting to investigate whether this is indeed the case and if so, this would be an important reason to publicize the results of both positive and negative cheating detection tests. However, before publicizing these results, an investigation into possible negative effects, including violation of privacy, must be conducted. Eradicating cheating in professional sports at short notice is not a realistic goal. Keeping up with new methods of cheating is a recurrent challenge and an immense job by itself. Hence, the focus should be on increasing success rates of cheating detection methods. This can be achieved through specialization of inspecting authorities and the use of modern technology.

32

6 A

PPENDIX

A. Instructions a. Welcome

Welcome to this online experiment. Please read these instructions carefully.

There will be three types of players: Athletes, Organizations and Sponsors. Your role will be assigned randomly after these instructions. Then you will be randomly placed in a group with one player of every type.

You can earn money in this experiment. When the experiment has ended, one group will be selected for payment. The amount of money you earn, depends on your own choices and the choices of the other participants in your group.

There will be three parts of the experiment. In the first and second part you will make one or multiple decisions, depending on the role you are given. The third part is a short questionnaire.

b. General instructions

Explanation of the types of players

The athlete has no initial endowment. He/she can win an amount of €8. The athlete has to choose if he/she will play fair or cheat. If he/she plays fair, the chance of winning is 50%. If he/she cheats, the chance of winning is 75%. The athlete has to decide whether to play fair or to cheat.

The sponsor has an initial endowment of €1. He/she can invest this money in the athlete. If the athlete cheated and the organization found out, the investment is lost. Else, the investment is doubled and the sponsor earns €2. The sponsor has to choose if he/she will invest or not.

33 The organization has an initial endowment of €1. This money can be used to perform a test to check if the athlete cheated. If the athlete cheated, and the organization performed this test, the organization wins €4 and the athlete will not receive the prize money of €8. The organization has to choose if he/she will test for cheating or not. If the sponsor invested €1 in the athlete, the organization receives €4.

To summarize the payoffs:

The athlete receives €8 if he/she wins. The chance of winning is 50% if the athlete plays fair and 75% if the athlete cheats. If the athlete cheats and the organization finds out, he will not receive any prize money.

Additionally, the athlete receives €1 if the sponsor invests his/her money. This additional amount is independent of the choice of the athlete and the organization.

The sponsor receives €1 if he does not invest his/her money in the athlete. If the sponsor does invest his/her money in the athlete, he/she receives nothing if the athlete cheated and the organization found out. Else, the sponsor receives €2.

The organization receives €1 if he/she chooses not to check if the athlete cheated. If the organisation chooses to check if the athlete cheated, he/she will receive €4 if the athlete cheated and receive €0 if the athlete played fair.

Additionally, the organization receives €4 if the sponsor invested in the athlete. This additional amount is independent of the choice of the athlete and the organization.

If you have carefully read and understand these instructions, please continue to receive your role. You can always read these instructions again.

c. Intransparent treatment

In this part of the experiment, the athlete and organization make their decision without knowing what the other player did. If the athlete cheated and the

organization tested this, the sponsor will be told that the athlete was found to be cheating. If the athlete played fair, and/or the organization did not test if the athlete

34 cheated, the sponsor will be told that the athlete was not found to be cheating. The sponsor can thus not distinguish between the outcomes (Cheat, No test), (Play fair, No test) and (Play fair, Test). The sponsor will decide to invest his/her money after he/she is told whether the athlete was found to be cheating or not.

Please indicate your choice: Athlete: Play fair or Cheat Organization: Test or No test Sponsor:

If the athlete is found to be cheating: Invest or Do not invest If the athlete is not found to be cheating: Invest or Do not invest

d. Transparent treatment

In this part of the experiment, the athlete and organization make their decision without knowing what the other player did. If the athlete cheated and the

organization tested this, the sponsor will be told that the athlete was found to be cheating. It the athlete played fair and the organization testes this, the sponsor will be told that the athlete was found to be playing fair. If the organization did not test if the athlete cheated or played fair, the sponsor will be told that the organization did not perform a test. The sponsor can thus not distinguish between the outcomes (Cheat, No test) and (Play fair, No test). The sponsor will decide to invest his/her money after he/she is told whether the organization performed a test and if so, the outcome of the test.

Please indicate your choice: Athlete: Play fair or Cheat Organization: Test or No test Sponsor:

If the athlete is found to be cheating: Invest or Do not invest If the athlete is found to be playing fair: Invest or Do not invest

35 If the organization did not test if the athlete cheated or played fair: Invest or Do not invest

e. Questionnaire

What is your gender? Male, female, I prefer not to tell

What is your age? … I prefer not to tell

Do you participate in competitive sports yourself? Yes No I prefer not to tell

Thank you for participating in this experiment. If you want to be eligible for payment, please indicate you e-mail address below. This e-mail address will only be used for payment and, if indicated, to send information about the outcomes of the

experiment. Your answers will remain strictly anonymous and will never be made public.

Do you want to receive information about the outcomes of this experiment? Yes/No

Please feel free to share the link to this experiment with friends or family if desired.

B. Data

All data was collected using an online survey which was created in Qualtrics. 546 responses were recorded, of which 289 were completed. This fast difference is due to web crawlers (robots that randomly surf on the world wide web in search of new pages) and respondents who tried to participate after the data collection had ended.

The data will be made available upon request.

C. Statistical test code

All statistical tests were performed in R. Files with the statistical test code will be made available upon request.

36 intransparent_order_athlete = matrix(c(8, 14, 40, 40), nrow = 2, ncol = 2,

byrow=TRUE, dimnames = list(c("cheat", "play fair"),c("first round", "second round")))

intransparent_order_organization = matrix(c(30, 32, 21, 16), nrow = 2, ncol = 2, byrow=TRUE, dimnames = list(c("inspect", "do not inspect"),c("first round", "second round")))

intransparent_order_sponsor_cheated = matrix(c(4, 4, 35, 45), nrow = 2, ncol = 2, byrow=TRUE, dimnames = list(c("continue sponsorship", "withdraw

sponsorship"),c("first round", "second round")))

intransparent_order_sponsor_playedfairornotest = matrix(c(37, 45, 2, 4), nrow = 2, ncol = 2, byrow=TRUE, dimnames = list(c("continue sponsorship", "withdraw sponsorship"),c("first round", "second round")))

intransparent_order_athlete fisher.test(intransparent_order_athlete, conf.level=0.90) intransparent_order_organization fisher.test(intransparent_order_organization, conf.level=0.90) intransparent_order_sponsor_cheated fisher.test(intransparent_order_sponsor_cheated, conf.level=0.90) intransparent_order_sponsor_playedfairornotest fisher.test(intransparent_order_sponsor_playedfairornotest, conf.level=0.90) transparent_order_athlete = matrix(c(15,6,39,42), nrow = 2, ncol = 2, byrow=TRUE, dimnames = list(c("cheat", "play fair"),c("first round", "second round")))

transparent_order_organization = matrix(c(34,29,14,22), nrow = 2, ncol = 2,

byrow=TRUE, dimnames = list(c("inspect", "do not inspect"),c("first round", "second round")))

transparent_order_sponsor_cheated = matrix(c(9, 1, 40, 38), nrow = 2, ncol = 2, byrow=TRUE, dimnames = list(c("continue sponsorship", "withdraw

37 transparent_order_sponsor_playedfair = matrix(c(49, 38, 0, 1), nrow = 2, ncol = 2, byrow=TRUE, dimnames = list(c("continue sponsorship", "withdraw

sponsorship"),c("first round", "second round")))

transparent_order_sponsor_notest = matrix(c(44, 34, 5, 5), nrow = 2, ncol = 2, byrow=TRUE, dimnames = list(c("continue sponsorship", "withdraw

sponsorship"),c("first round", "second round")))

transparent_order_athlete fisher.test(transparent_order_athlete, conf.level=0.90) transparent_order_organization fisher.test(transparent_order_organization, conf.level=0.90) transparent_order_sponsor_cheated fisher.test(transparent_order_sponsor_cheated, conf.level=0.90) transparent_order_sponsor_playedfair fisher.test(transparent_order_sponsor_playedfair, conf.level=0.90) transparent_order_sponsor_notest fisher.test(transparent_order_sponsor_notest, conf.level=0.90) b. Randomization tests

gender = matrix(c(37, 38, 43, 27, 33, 30, 11, 16, 8, 10, 6, 9), nrow = 2, ncol = 6, byrow=TRUE, dimnames = list(c("male", "female"),c("AI", "AT", "OI","OT","SI","ST"))) gender

chisq.test(gender)

competitive = matrix(c(32, 38, 36, 35, 26, 34, 16, 10, 12, 13, 13, 14), nrow = 2, ncol = 6, byrow=TRUE, dimnames = list(c("yes", "no"),c("AI", "AT", "OI","OT","SI","ST"))) competitive

38 chisq.test(competitive) age_AI=c(35, 26, 62, 31, 41, 20, 38, 29, 18, 58, 53, 36, 28, 28,63,18,23,22,46,29,52,26,63,46,70,24,38,63,32,60,38,18,59,53,65,22,64,52,71,44,2 8,50,49,66,78,36,25) age_AT=c(22,67,42,37,49,60,67,59,71,52,42,72,98,43,21,65,64,63,53,64,59,55,39,55, 36,70,61,50,39,54,23,66,47,42,58,52,64,61,68,62,74,57,28,75,57,54,22,47,29,45,62,2 6,56) age_OI=c(27,21,30,63,30,23,21,61,52,60,50,50,21,27,24,56,69,51,24,54,50,72,60,66, 63,57,64,45,41,73,26,69,23,55,19,40,24,44,76,69,58,68,71,56,15,63,44,35,67) age_OT=c(34,40,55,62,56,73,23,31,49,32,51,57,48,63,56,30,56,52,76,38,30,50,33,75, 66,35,74,27,57,49,61,56,26,46,40,59,69,24,67,37,13,58,23) age_SI=c(32,74,74,54,32,38,26,50,25,59,41,27,67,55,55,68,75,56,26,23,63,49,49,27,2 9,27,50,45,55,43,57,39,17,26,53,22,37,43) age_ST=c(17,62,24,40,40,56,72,25,31,42,55,45,47,58,44,26,24,51,61,68,23,58,42,57, 68,55,28,63,63,45,38,41,60,52,27,47,57,31,22,56,66,43,64,60,25)

age_total =c(age_AI, age_AT, age_OI, age_OT, age_SI, age_ST)

ks.test(age_total, age_AI) ks.test(age_total, age_AT) ks.test(age_total, age_OI) ks.test(age_total, age_OT) ks.test(age_total, age_SI) ks.test(age_total, age_ST) ks.test(age_AI, age_AT) ks.test(age_SI, age_ST) ks.test(age_OI, age_OT)

c. Tests for treatment effect

treatmenteffect_athlete = matrix(c(15,8,39,40), nrow = 2, ncol = 2, byrow=TRUE, dimnames = list(c("cheat", "play fair"),c("transparent", "intransparent")))

39 treatmenteffect_organization = matrix(c(34,30,14,21), nrow = 2, ncol = 2,

byrow=TRUE, dimnames = list(c("inspect", "do not inspect"),c("transparent", "intransparent")))

treatmenteffect_sponsor_cheated = matrix(c(40,36,9,4), nrow = 2, ncol = 2, byrow=TRUE, dimnames = list(c("continue sponsorship", "withdraw

sponsorship"),c("transparent", "intransparent")))

treatmenteffect_athlete

fisher.test(treatmenteffect_athlete, alternative = "less", conf.level=0.90) fisher.test(treatmenteffect_athlete, conf.level=0.90)

treatmenteffect_organization

fisher.test(treatmenteffect_organization, alternative = "greater", conf.level=0.90)

treatmenteffect_sponsor_cheated

fisher.test(treatmenteffect_sponsor_cheated, conf.level=0.90)

7 R

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