The effects of Progesterone-Variation during the female menstrual cycle on Betrayal Aversion – an experimental study
Sarah Fawver 11277815
Master’s Thesis (15 ECTS)
MSc in Economics – Behavioural Economics and Game Theory University of Amsterdam
Supervision: Professor Engelmann 15th of July 2017
Outline
Abstract ... 4
1. Introduction ... 5
2. Literature Review ... 6
2.1. Behavioural gender differences – effects of hormonal fluctuations throughout the female menstrual cycle ... 6
2.2. Progesterone’s effects on mood and neuroscientific evidence ... 6
2.3. Distinction between risk preferences and trust ... 7
2.4. Oxytocin’s effects on trust ... 8
3. Methodology ... 10 3.1. Participation criteria ... 10 3.2. Experiment’s timing ... 11 3.3. Experimental design ... 13 3.4. Hypotheses ... 19 3.4.1. General hypothesis ... 19 3.4.2. Hormonal hypotheses ... 21 4. Results... 21 4.1. Sample’s idiosyncrasies ... 21 4.2. Statistical Analysis ... 22 4.2.1. General Analysis ... 22
4.2.2. Analysis - Hypothesis one and two ... 24
4.2.3. Interpretation of results ... 31 5. Critical Discussion ... 33 5.1. Experiment’s timing ... 33 5.2. Experimental Design ... 33 5.3. Hypotheses ... 34 6. Conclusion ... 35 7. Bibliography... 37 8. Appendix ... 41
8.1. Example email: Invitation to Survey Completion ... 41
8.2. Pdf form: First invitation to potential participants ... 41
8.3. Instructions – Qualtrics input ... 43
8.4. Mann-Whitney-U-Test ... 58
8.5. Regression Table 1: Simple Regression without Covariates (Period.f) ... 58
8.7. Regression Table 3: Simple Regression with non-explanatory covariates (Headache, Cramps, TenderBreasts, Education) ... 60 8.8. Regression Table 4: Simple Regression with non-explanatory covariates (Age,
Nationality, Economics) ... 61 8.9. Regression Table 6: Simple Regression with explanatory covariates (Period.f) ... 62 8.10. Regression Table 7: Complex Regression with interaction term “PMS” (period.f) .. 62 8.11. Regression Table 9: Complex Regression with interaction term “AT” (period.f) ... 63 8.12. Regression Table 10: Complex Regression with interaction term “AT” (period.b3.f)
64
8.13. Regression Table 11: Complex Regression with interaction term “CN” (period.f) .. 65 8.14. Regression Table 12: Complex Regression with interaction term “CN” (period.b3.f)
65
8.15. Regression Table 13: Complex Regression with interaction term “GB” (period.f) .. 66 8.16. Regression Table 14: Complex Regression with interaction term “GB” (period.b3.f)
67
Abstract
This Master’s Thesis investigates the effects of progesterone variations during the female menstrual cycle on the phenomenon of betrayal aversion via the performance of an online survey. Betrayal aversion is measured by investors’ (first players) Minimum
Acceptance Probability (MAP) during three different treatments, namely Decision Problem,
Risky Dictator and Trust Game. Hypothesized results could not be fully affirmed; the effects of two included covariates, namely mental state and intensity of suffrage from PMS add significant explanatory value to the model. The main results depict the following correlation:
Women’s emotional state in combination with progesterone-variations affects decision-making. Furthermore, a boost in women’s emotional state increases betrayal aversion during day nine and ten of the menstrual cycle when women are not burdened by any other influences such as PMS or menstruation’s side effects.
1. Introduction
In today’s highly specialized and globalized economy a key concept is cooperation and division of labour. We cannot personally verify that the manufacturing of a product was in fact performed according to the stated quality standards – on the contrary, we are simply required to trust other persons, mere strangers. This is the case as still a number of processes are being performed by actual humans or a machine undertakes the task but had at least been created by human kind at some point in time. Thus, nowadays we constantly have to engage in risky situations because of an interaction with other individuals.
Has nature prepared women for this task?
According to an experimental study conducted by Bohnet and Zeckhauser (2004) human interaction incurs a certain betrayal cost which is of different nature than only monetary costs. Therefore, individuals prefer the risky situation of a purely probabilistic lottery to for instance a trust game with “social” risk. A wide range of conducted research confirms that trust and risk preferences are behaviourally distinct (e.g.: Houser et al., 2010, Kosfeld et al., 2005).
Hormone-free women are guided by constant hormonal variations which prepare females every month for a potential pregnancy.
Buser et al. (2012) collected experimental evidence on the effect of hormonal variation on competitiveness and social preferences. The effect of progesterone rather than that of oestrogen proved to be significant for explaining variation in the striving for competitiveness. Thus, this Master’s Thesis will focus on the effect of variation in solely progesterone on betrayal aversion.
Women, furthermore, act more prosocially in the context of a trust game during their mid-cycle phases. Buser et al. (2012) made use of a between-subjects-design which
introduces a relatively large amount of noise which is further increased by having all female participants categorize themselves into their current menstrual cycle phase. Cycle length across women is subject to tremendous inconsistency, more in particular, the follicular phase can exhibit the greatest degree of variation across individuals (Young & Hampson, 2008). This Master’s Thesis implements a within-subjects-design and analyses each participant’s behaviour during three menstrual phases which decreases the level of noise. Thus, this
Master’s Thesis can add to the existing literature via studying solely the effect of progesterone and via implementing a strong experimental design.
This brief introductory piece is followed by a literature review providing an overview of the current status quo in research. Subsequently, the methodology covering the
experimental design and hypotheses is elaborated. Furthermore, results are presented and the entire study is critically discussed. This Master Thesis is completed with concluding
paragraphs.
2. Literature Review
2.1.Behavioural gender differences – effects of hormonal fluctuations throughout the female menstrual cycle
Gender differences in economic behaviour are investigated by a vast number of studies of which some attempt to search for explanations of the observed gender differences in
women’s hormonal fluctuations throughout their natural menstrual cycle. Wozniak (2009) concludes that women are less likely to engage into competitive environments during low-hormone phases than during high-low-hormone times. Buser (2012) collected experimental evidence on the effect of hormonal variation on also competitiveness and social preferences. Women are less likely to engage in a competitive environment during the luteal phase when progesterone is at its peak which can also be explained evolutionarily: during infertile phases and pregnancies, competitive behaviour is not necessary as females do not “hunt” for a genetically-favourable male, optimal for reproduction. Jones et al. (2005) deliver evidence that as progesterone levels increase; women commit to their romantic partner more strongly and perceive an increased attraction to femininity in male faces. The effect of progesterone rather than that of oestrogen proved to be significant for explaining variation in the striving for competitiveness. Women, furthermore, significantly act more pro-socially in the context of a trust game, specifically giving and acting reciprocally during their mid-cycle phases (Buser, 2012). Behavioural variations within the menstrual cycle in the context of the Ultimatum Game, Public Goods Game and Dictator Game could not prove themselves to be robust.
2.2. Progesterone’s effects on mood and neuroscientific evidence
Hammarbäck et al. (1985) were able to experimentally prove progesterone’s
provocation of cyclical mood swings similar to those observed in the premenstrual syndrome (PMS) in postmenstrual female participants. The premenstrual syndrome can occur during the luteal phase when the plasma progesterone concentration is alleviated. Furthermore, the
experimenters could successfully show that oestrogen had no effect on participants’ mental states.
Andreen et al. (2003) also recruited postmenstrual women and were able to distinguish the effect of progesterone on mood more specifically, namely only participants who suffered from PMS when having experienced their menstrual cycle were observing negative mental state effects, similar to PMS’ effects. On the other all women without any history of PMS remained emotionally unaffected by the change in their progesterone level.
Tofoletto et al. (2014) concluded based on fMRI evidence that sex steroids including also progesterone affect emotional and cognitive processing. More detailed, several brain regions including the amygdala, anterior cingulate cortex, and inferior frontal gyrus were influenced by hormonal changes when comparing results obtained during the follicular to those of the luteal phase.
Andreano & Cahill (2010) were the first to study neural reactions to negative images during the follicular and luteal phase. The Hippocampus and amygdala showed increased activity during the luteal phase compared to scans obtained during the follicular phase. The authors conclude that oestrogen and progesterone are supposedly opposing in their effects on the brain’s arousal circuitry.
Wingen et al. (2007) approached the effect of progesterone neuro-scientifically via investigating whether the hormone’s administration leads to amygdala re-activity, thus a change in the integration of the emotion-circuitry during women’s follicular phase. The fMRI- examination showed selectively increased amygdala reactivity or more specifically that
progesterone facilitates functional coupling of the amygdala with distant brain regions. The dorsal anterior cingulate gyrus (dACC) primarily evaluating stimuli of threat and controlling emotions was stronger linked to the amygdala and thereby caused a decrease in the brain area’s activity. Connections between the amygdala and the fusiform gyrus, who are involved in processing faces, were decreasingly activated.
2.3.Distinction between risk preferences and trust
Houser et al. (2010) examined behaviour in the context of an investment game and could conclude that risk preferences do not predict individual investment decisions in a trust game but in a risky environment.
In Bohnet & Zeckhauser’s study (2004), betrayal aversion is measured by investors’ (first players) Minimum Acceptance Probability (MAP). This applied measurement is defined by the investor’s indication on how likely the “good” lottery outcome has to happen in order for this specific investor to decide to enter the risky lottery and not take the “sure” outcome.
Three different treatments, namely Decision Problem, Risky Dictator and Trust Game are performed. The main objective of the study is to compare the outcomes of the Decision Problem with the ones of the Trust Game to measure betrayal aversion as two different types of risks, namely a probabilistic one and one caused by a social interaction. This, however, can only be executed correctly with the help of the third treatment (Risky Dictator) as otherwise not only the type of risk encountered is alternated but also the number of parties affected by decision-making. Results show higher MAPs in the trust game in comparison to both the Minimum Acceptance Probability in the Risky Dictator and Decision Problem. Thus, this experiment provides solid evidence that risk and trusting are two different behavioural concepts. Moreover, a trusting situation incurs an additional costly element, namely betrayal aversion during the process of decision-making.
A neuroscientific study by Aimone et al. (2014) provides evidence that the anterior insula is involved in betrayal aversion or the perception of the risk of a future potential negative emotion triggered by being betrayed.
2.4.Oxytocin’s effects on trust
Oxytocin is primarily distributed during labour to initiate and strengthen contractions of the uterus. Once the infant is born, oxytocin triggers the start of lactation to enable breast-feeding by the biological mother (Nishimori et al., 1996). Animal research has shown that the neuropeptide oxytocin has a positive effect on prosocial behaviour and attachment, especially in non-human mammals (Choleris et al., 2013). The critical research review on oxytocin’s effect on trust by Nave et al. (2015) points out that as replications of most studies in this field fail studies’ external validity is highly questionable. Moreover, a solid method of measuring oxytocin in blood levels has not been found yet which introduces noise into the experiments and renders comparisons across different experimental studies highly instable. Finally, even in large-sample studies, researchers fail to find robust correlations between oxytocin and trust. Thus, in conclusion this critical research review assesses the current research status
insufficient to solidly assume any (causal) effect of oxytocin on trust.
Kosfeld et al. (2005) were able to distinguish the willingness to face risks from a readiness to enter a risky situation due to a social interactive component via their
experimental design. An increase in the hormone oxytocin exclusively affected decision-making when trust is an issue and did not render subjects more optimistic about the
this hormone could not facilitate prosocial behaviour per se as trustees’ giving did not rise significantly. This fact is also supported by animal research as oxytocin prohibits defensive mechanisms but not reciprocity. Thus, solely investors’ transfers experienced a robust increase in value.
Baumgartner et al. (2008) assume oxytocin’s positive effect on trusting to be robust and extend their research scope. Firstly, they encompass also the effects of the phenomenon “breach of trust” on the investor in their study and secondly, fMRI evidence is added to further understand trust’s underlying neural mechanisms. Oxytocin significantly prevents trust adaptation to having previously experienced a breach in trust which can be associated with a significant reduction in amygdala, midbrain regions and dorsal striatum activation. The first two brain areas mediate fear administering while the dorsal striatum handles adaptation to obtaining feedback. Moreover, the considerable reduction in neural stimulation could be sustained by significantly shorter response times of Oxytocin-users in the post-feedback phase. Thus, the interpretation of a decrease in the trust-suppressing force of betrayal aversion because of the reduced neural activity appears to be further supported.
Mikolajczak et al.’s (2010) results further investigate the effects of oxytocin on decision-makers’ trusting behaviour. The authors could only replicate Baumgartner et al.’s results of a decrease in betrayal aversion if the trustee was completely anonymous. However, if hints in form of cues pin-pointing towards the untrustworthiness of the social partner were given, trust decreased like wisely in participants of the placebo- and the oxytocin-group. This study concludes that humans become more trusting but not gullible via the administration of oxytocin.
Mikolajczak et al. (2010) inspect the concept of trusting without money being at stake but rather confidential information by an envelope task. They were able to extent the positive effects of oxytocin also on a significant decrease in betrayal aversion regarding private data. Lane et al. (2012) attempted a replication of the above described analysis and failed twice. Thus, the external validity of the envelope task remains strongly questionable.
Yao et al. (2014) focus their experimental study on trust repair methods and were able to identify apologies and financial compensation as the most effective methods which is closely in line with past research. Furthermore, oxytocin was administered after the
experience of trust betrayal and before the performance of trust repair mechanisms. Female oxytocin-consumers, especially naturally rather forgiving characters, were significantly less
effectively compensated for the previously suffered betrayal. This weakening in the effect of trust repair means could not be observed in males after an administration of oxytocin and appears to be therefore gender-specific.
3. Methodology 3.1. Participation criteria
The major exclusion criteria for this study are current usage of hormonal contraceptive measures as current as three months prior to the start of this experiment, current or past pregnancies and no current experience of a menstrual cycle. Hormonal contraceptive measures interfere with the normal female menstrual cycle and suppress the Gonadatropin-Releasing-hormone (GnRh) which is usually produced in the hypophysis (Kiene, H., 2014). The GnRh triggers the production of FSH and LH who themselves in turn initiate ovulation. Progesterone and oestrogen in turn affect the development of GnRh (Kiene, H., 2014). All potential participants provide confidential data on their menstrual cycle via a pdf-form. In detail the length and end date of the last and penultimate menstrual phase are stated as well as information on usage of hormonal contraceptive measures, experience of PMS and/or
physical pain during the menstrual phase (see appendix 8.2.). Fourteen participants had to be excluded because their provided data on their personal menstrual cycle was too volatile to allow a solid calculation of the different hormonal phases. In particular, the duration of their menstrual cycle and the length of their menstrual phase both fluctuated strongly between months. Moreover, two participants dropped out because they started taking hormonal contraceptive measures during the course of this experiment. Furthermore, one participant disclosed to have used emergency contraceptive measures (hormonal after pill) in two
occasions as recent as three months prior to the start of the experiment which has an effect on the participant’s hormonal status. The morning-after pill postpones the ovulation and can therefore alter the menstrual cycle in the short term (Princeton, 2017). One additional participant’s data was excluded from this analysis because of her thyroid disorder.
Irregularities in the menstrual cycle are common side effects of thyroid diseases; moreover, the disorder shows similar symptoms to the ones inherited by PMS such as fatigue or mood swings (Casper, 2017). Thus, disentangling the actual source of this participant’s emotional state would be highly difficult.
A non-obligatory but highly appreciated criterion towards a successful participation is a membership in any online application providing predictions on the user’s menstrual cycle. Two participants shared their clue data with the experimenter. Clue is an online health
application which predicts the menstrual and ovulatory phases of its users for up to three months. It continuously updates its calculations based on the information provided by its user. Advanced options even track the client’s mood, eating habits and physical pain (helloclue, 2017). Data provided by these participants can be assessed as significantly more solid. Buser (2012) for instance had to cope with classical measurement error caused by women’s false estimation of cycle length (Small et al., 2007) and general variation of the cycle length around the mean over time (Creinin et al., 2004). This random noise biased any of the estimated effects towards zero (Buser, 2012).
3.2. Experiment’s timing
Participants receive an email notification to perform the online survey via Qualtrics three times a month for a complete duration of two months (see appendix 8.1.). Therefore, six data points can be collected per participants. The first date is during participants’ menstrual phase (Q1a and Q1b), thus within day one and three of their menstrual cycle. Both
progesterone and oestrogen are at their lowest levels during the entire menstrual cycle then. The second point in time (Q2a and Q2b) is during the follicular phase (between day nine and ten) when progesterone is still at its lowest level but oestrogen amounts to its medium level. The last point in time (Q3a and Q3b) is during day 19 and 22, the luteal phase, when
progesterone peaks and oestrogen is at the same level as during the follicular phase. LH and FSH are at stable levels during all three selected timing points.
The timing was calculated case-specific and based on the information provided by participants via the initial pdf form. Exemplary, the timing for participant X, having a menstrual cycle length of 31 days and a menstrual phase of seven days is calculated the following way. Furthermore the end of her last menstrual bleeding was on the 18th of April 2017. This woman’s menstrual phase lasts two days longer than that of an average woman. Because cycle length and in particular the follicular phase can vary across women, (Hampson & Young, 2008), the timing of each woman’s menstrual cycle was calculated individually for each participant based on the information provided by participants via the initial pdf form (see Table 5). To give an example, one participant had a menstrual cycle length of 31 days and a menstrual phase of seven days. This woman’s menstrual phase therefore lasts two days longer than that of an average woman. Thus, this subject’s follicular phase is estimated with eight days; one day longer than on average.
Based on all this information, the calculation of the timing for Q1a is the following: (𝑙𝑎𝑠𝑡 𝑑𝑎𝑦 𝑜𝑓 𝑚𝑒𝑛𝑠𝑡𝑟𝑢𝑎𝑙 𝑏𝑙𝑒𝑒𝑑𝑖𝑛𝑔 𝑖𝑛 𝐴𝑝𝑟𝑖𝑙) + (𝑑𝑢𝑟𝑎𝑡𝑖𝑜𝑛 𝑜𝑓 𝑚𝑒𝑛𝑠𝑡𝑟𝑢𝑎𝑙 𝑐𝑦𝑐𝑙𝑒 − 𝑑𝑢𝑟𝑎𝑡𝑖𝑜𝑛 𝑜𝑓 𝑚𝑒𝑛𝑠𝑡𝑟𝑢𝑎𝑙 𝑝ℎ𝑎𝑠𝑒) + 1
18𝑡ℎ 𝐴𝑝𝑟𝑖𝑙 + 24 𝑑𝑎𝑦𝑠 = 10𝑡ℎ 𝑜𝑓 𝑀𝑎𝑦; This day is the last day of this participant’s cycle. On the 11th of May, her new cycle and therefore her menstrual phase commences and Q1a has to be complied during the 11th of May until the 13th of May. The calculation for Q1b is
identical but the last day of the menstrual bleeding in May has to be inserted.
Q2a is computed as follows:
(𝐿𝑎𝑠𝑡 𝑑𝑎𝑦 𝑜𝑓 𝑚𝑒𝑛𝑠𝑡𝑟𝑢𝑎𝑙 𝑏𝑙𝑒𝑒𝑑𝑖𝑛𝑔 𝑖𝑛 𝑀𝑎𝑦) + 4 + 1; four days are added as the fourth day of the follicular phase shall be estimated. In addition, one day is augmented as the follicular phase is predicted slightly longer.
17th of May + 4 + 1 = 22st of May; Thus, on either the 22nd and 23rd of May, this participant is requested to fill in the online survey. The above dates should coincide with her 9th and 10th day of her menstrual cycle. The calculation for Q2b is identical but the last day of the menstrual bleeding in June has to be inserted.
Q3a is determined by using this formula:
(𝐹𝑖𝑟𝑠𝑡 𝑑𝑎𝑦 𝑜𝑓 𝑚𝑒𝑛𝑠𝑡𝑟𝑢𝑎𝑙 𝑏𝑙𝑒𝑒𝑑𝑖𝑛𝑔 𝑖𝑛 𝐽𝑢𝑛𝑒) – 9; thereby the 19th day of the menstrual cycle is intended. In this exemplary case, Q3a should be processed between the 1st of June and the 3rd of June. The calculation for Q3b is alike but the last day of the menstrual bleeding
in July has to be used.
3.3. Experimental design
As betrayal aversion is the research subject, an implementation of a simple Trust game (Berg et al., 1995), observing the first players’ decisions, would be obvious. However, as the sample size of 34 participants is rather small, one would lose half of the participants and their potential data as first decision-makers by having them act as trustees. On the other hand, simply using trustees’ responses of an already existing data set (Engelmann, April 2011, University of Zurich) would exclude the option of paying out all involved parties. Such a case would measure betrayal aversion successfully but not fully capture social preferences. Thus, a high risk of framing and deception would be in place.
The experimental set-up of this experiment relates in most aspects very closely to the one implemented by Bohnet and Zeckhauser (2004) in their study which was elaborated on in the literature review (see 2.3). The entire sample takes decisions in the role of the investor and if a second player (trustee) is involved, the data set by Engelmann (2011) provides the
respective trustee data points.
The experiment is conducted online via the software Qualtrics; at all times participants are forced to respond and cannot continue otherwise. Participants complete all six times the same survey which consists of the following parts: Introduction, Part 1, Part 2, Part 3 and final questionnaire. The introductory part provides participants with the entire experiment’s
structure into namely, six sessions with three parts and five rounds each; and in addition a final questionnaire. Furthermore, the payment modality is disclosed, specifically that the payouts depend on personal choices and the decisions taken by others. Moreover, after the completion of each session one participant is randomly selected for payment based on her final payoff of one randomly chosen round. The six winners were paid out on the 23rd of June 2017 via a bank transfer and shortly informed about this study’s results. Finally, participants were informed about the confidential and anonymous treatment of their provided data and decisions at all times.
Part 1 of this experiment is a simple binary-choice problem, called Decision problem. Individuals are informed that their decisions only affect their personal payoff during this entire part. The decision-maker is required to select between a certain “Sure” outcome
(option A) and a lottery (option B) whose outcome could either be “Good” or “Bad” and is determined by chance (Bohnet & Zeckhauser, 2004).
The concrete decision problem asked for the decision-maker’s Minimum Acceptance Probability (MAP) and is phrased as follows, “how large would P have to be for you to pick option B over option A?”.
The probabilities assigned to any of the two lottery outcomes are unknown to the decision maker. The payoff-calculation of every taken choice during each round is performed as follows: Participants are informed that prior to the performance of this experiment a P*, the probability of the “good” lottery outcome to happen, has been calculated. If the previously indicated P is higher than P*, earnings are 6 Euros. On the other hand, if the previously indicated P is smaller than or equal to P*, the lottery (option B) is played with probability P*. In this case, a computer generates the final payoff based on a randomization mechanism. However, this entire method of computation is not disclosed to participants at any time.
P* is the fraction of which equals to 26% when
taking a subset of Engelmann’s data set (2011, University of Zurich). Only the first trial and decisions exclusively taken by trustee four were considered and lead to the above defined percentage of P*. Furthermore, a fair transfer is defined as a back-transfer of at least 18 CHR by a trustee given that the investor transferred 12 CHR, the entire initial endowment.
Engelmann’s experimental design (2011) was a binary choice requiring investors to transfer the entire initial endowment of 12 CHR in order to be able to reach the stage of playing the trust game. If any value below 12 CHR was passed onto the respective trustee the game ended already at this stage leaving both players with their initial endowment.
The payoffs were chosen with respect to Engelmann’s data set and are the following:
You choose
Type of choice
Probability Outcome Your earnings
A Certainty 1 “Sure” 6
B Lottery P “Good” 12
1-P “Bad” 0
The „good“ outcome’s payoff was determined by reducing the entire data set to the respective cases in which the investor actually sent 12 CHR to trustees number three and four. The mode of this subset is 12 which generates 39 decisions. The “bad” potential outcome is the mode of the subset of all investor-trustee-pairs that entered the trust-game-stage
successfully (investors sent no less than 12 CHR to trustee). 278 trustees make up this subset. Payoff of 6 for the “sure” outcome was determined in accordance with the other payoffs.
The general instructions for this part are followed by a control question which has to be answered correctly to allow the participant to continue. Let us assume that you set P equal to 43%. Assuming increments of 1%, what is the smallest possible value of P*that leads to (A) receiving the certain outcome; or (B) entering the lottery? 𝑃 ∗= 0% results in the
implementation of option A and 𝑃 ∗ = 43% leads to option B. The nature of this control questions checks whether participants have completely understood their payoff calculation. Furthermore, a warning message informs the participant to read and decide carefully during the upcoming five rounds and that their final payment could be selected among any of these answered decision problems.
Finally, Qualtrics measures the decision makers’ response times via controlling for timing of the first and last page click, the page submit and the entire click count.
The Decision problem acts as a necessary control for the investors’ risk attitudes in a one-stage risk decision problem, their other-regarding preferences and efficiency concerns (Bohnet & Zeckhauser, 2004).
Part 2 of this experiment is the so called Risky Dictator Game. Individuals are informed that their decisions affect their personal payoff and those of another party that remains passive during this entire part. Decision-Makers never face the same trustee twice. The risk to be faced by the decision-maker is alike to the one during the Decision problem but the number of parties affected is increased to two. Unfortunately, for this specific part, the experimenter could not rely on the pre-existing data set (Engelmann, 2011) and a subsequent payment of the respective trustees does not appear feasible. In order to avoid deception, part 2 of this experiment remains hypothetical and is not included in the final payment. Participants are explicitly and multiple times informed about this.
You choose
Type of choice
Probability Outcome Your earnings Earnings to person X A Certainty 1 “Sure” 6 6 B Lottery P “Good” 12 24 1-P “Bad” 0 36
Table 2: Risky Dictator
The „good“ outcome’s payoff comes about by limiting the entire data set to the incidences when the investor actually sent 12 CHR to trustees number three and four. The 12 CHR were tripled by the experimenters and therefore amounting to a total transfer of 36 CHR to the trustee. The mode of trustees’ decisions within this subset is 12 which generates 39 decisions; all 39 trustees receive a personal payoff of 24 CHR. The “bad” potential outcome (0) is the mode of trustees’ decisions within the subset of all investor-trustee-pairs that entered the trust-game-stage successfully in the trust game (investors sent no less than 12 CHR to trustee). 278 trustees form this subset and all respective individuals kept the entire 36 CHR transferred. Payoff of 6 for the “sure” outcome was determined in accordance with the other payoffs.
The probabilities assigned to any of the two lottery outcomes are again unknown to the decision maker. The payoff-calculation of every taken choice during each round is performed identically to the method applied in part 1. In this case as in the Decision Problem, a computer generates the final payoff based on a randomization mechanism. Again, this entire method of computation is not disclosed to participants at any time.
The general instructions for this part are followed by a control question which has to be answered correctly to allow the participant to continue. Let us assume that you set P equal to 35%. Assuming increments of 1%, what is the largest possible value of P*that leads to (A) receiving the certain outcome; or (B) entering the lottery? 𝑃 ∗ = 34% finalizes in the “sure” outcome and 𝑃 ∗ = 100% allows participants to play the lottery. Furthermore, a warning message informs the participant to read and decide carefully during the upcoming five rounds and that their final payment could be selected among any of these answered decision
problems.
Finally, Qualtrics measures the decision makers’ response times via controlling for timing of the first and last page click, the page submit and the entire click count.
The Risky Dictator treatment is implemented to enable a solid comparison between the first and third part of this experiment; thus individuals’ behaviour in situations with different kinds of risk (Bohnet & Zeckhauser, 2004).
Part 3 of this experiment is a binary-choice Trust Game. Individuals are informed that their own decisions and those of a second player affect both their personal payoffs. Decision-makers never face the same trustee twice. The number of parties involved is two as in the previous experiment’s part. The risk to be faced by the decision-maker, however, is caused by a social interaction. Participants are informed that all trustees’ decisions were pre-recorded during an experiment with students at the University of Zurich (Engelmann, 2011). This part is considered for the final payment and participants are explicitly and multiple times informed about this.
The concrete decision problem asked for the decision maker’s Minimum Acceptance Probability (MAP) and is phrased as follows, “how large would the probability of being paired with a Person Y who chose outcome "Good" have to be for you to pick B over A?”.
The payoffs are identical in their kind and method of computation to the ones used in the Risky Dictator treatment.
You choose
Type of choice
Probability Outcome Your earnings Earnings to person Y A Certainty 1 “Sure” 6 6 B Lottery P “Good” 12 24 1-P “Bad” 0 36
Table 3: Trust Game
The probabilities assigned to any of the two lottery outcomes are again unknown to the decision maker. The payoff-calculation of every taken choice during each round is performed identically to the method applied in part 1 and 2: If the previously indicated P is higher than P*, earnings are 6 Euros. On the other hand, if the previously indicated P is smaller than or equal to P*, the lottery (option B) is played with probability P*. Again, this entire method of computation is not disclosed to participants at any time. However, if the lottery stage of this experiment is entered, not a computer algorithm but the respective trustee (Engelmann, 2011) decides on whether the “Good” or “Bad” outcome is implemented.
The general instructions for this part are followed by a control question which has to be answered correctly to allow the participant to continue: “Your indicated P is lower than P*. Which method determines the outcome and which option (A or B) will be
implemented?”. The correct answer would require participants to realize that the trustee determines the outcome after the lottery (option B) was entered. The nature of this control question checks whether participants have correctly realized the trustee’s impact and the payoff modality. Furthermore, a warning message informs the participant to read and decide carefully during the upcoming five rounds and that their final payment could be selected among any of these answered decision problems.
Finally, Qualtrics measures the decision makers’ response times via controlling for timing of the first and last page click, the page submit and the entire click count.
The Trust Game measures individuals’ decisions in a risky setting caused by a social interaction (Bohnet & Zeckhauser, 2004).
Following the end of part 3, a control question measures the intensity of participants’ conviction of having interacted with real human beings. The to-be-obtained outcomes will provide an indication of the degree of external validity of this experimental design.
The questionnaire part of the experiment commences with a control for the emotional state of the participants in the categories alertness versus tiredness (AT), calmness versus restlessness (CN) and valence (GB) (good versus bad mood). For this purpose the
Multidimensional Mood State Questionnaire (Steyer et al., 1997) is used which requires participants to state the intensity (“Definitely not – Not – Not really – A little – Very much – Extremely”) of 30 different emotional adjectives belonging to the above specified three categories (AT, GB, CN) with respect to their current mood state. Participants are provided with the original instructions (see appendix 8.3). In the following, demographic information, namely nationality and age via birth month and year are inquired. Participants disclose data on their educational background and knowledge specific to the field of Economics as necessary controls for the interpretation of the obtained experimental results. In a next step, participants answer four medical questions, a necessary legitimization of the un-biasness of the retrieved data points. Participants are encouraged to truthfully indicate whether they have been using any hormonal medication in the last three months via a multiple choice question. Hormonal contraceptive measures, thyroid hormones, the after pill, hormonal diabetes medication and an option to specify any other medication case-specifically are given as
alternatives to be ticked. In a next step, participants are asked to state the intensity of their suffrage from the premenstrual syndrome (PMS) on a 7-Likert-Scale [“Not at all (1) – Very severly (7)”] to control for the effect of other physical and emotional changes on behaviour as the third and sixth timing point (Q3a and Q3b) coincide with the potential occurrence of PMS during the female cycle. Moreover, participants are encourage to disclose the usual
occurrence of physical pain, specified as cramps, headaches or an open field “Other” during their menstrual phase which is again information necessary to control for other confounding effects on behaviour apart from changes in participants’ hormonal levels. Finally, the date (day and month) of the respective participant’s last menstrual bleeding are inquired which can firstly provide a control for the correct calculation of the menstrual phases and secondly a control on the degree of natural variation in the participant’s menstrual cycle. In a last step, the participant is asked to provide her bank account detail (IBAN and BIC) which are crucial for the successful payment at the end of the experiment.
3.4. Hypotheses
In line with the result obtained by Bohnet & Zeckhauser (2004) the general hypothesis of this experimental study is the following:
3.4.1. General hypothesis
(1) 𝑀𝐴𝑃 > 𝑀𝐴𝑃 = 𝑀𝐴𝑃
Individuals incur an additional costly element when engaging in a risky situation whose outcome is determined by a second individual’s decisions and therefore the Minimum
Acceptance Probability (MAP) of the favourable outcome to happen during the lottery has to be relatively higher than the MAP in a situation of mere probabilistic risk, thus during the Risky Dictator treatment or the Decision Problem.
The upcoming reasoning will be done for the case of the Decision Problem exemplarily but can be equally applied to the two other treatments. If we consider an
individual with Neumann-Morgenstern preferences who is given the Decision Problem, these are the payoffs and utilities she assigns to the single outcomes. Furthermore we define
Outcome Utility Payoff Probability Option A – “Sure Outcome” Sure 𝑈 6 1 Outcome B – “Lottery” Good 𝑈 12 P Outcome B – “Lottery” Bad 𝑈 0 1-P
Table 4: Payoffs for Decision Problem
This individual’s MAP satisfies the following equation:
(3) 𝑈 = 𝑀𝐴𝑃 (𝑈 ) + (1 − 𝑀𝐴𝑃)𝑈 Following this, solving for MAP we get this equation:
(4) M𝐴𝑃 =
In the circumstance of receiving the “bad” outcome in the trust game, this individual actually has to face an additional element, the betrayal cost which leads to concluding on this inequality (taking both payoffs as equal and 𝑈 = 𝑈 ).
(5)𝑈 ( ) < 𝑈 ( )
In the initial case of the Decision Problem, MAP was determined as equation (4) given that equation (5) implies an additional decrease in the utility of the “bad outcome” in the context of the trust game, 𝑈 decreases in (4) and the Minimum Acceptance Probability, necessary for the decision-maker to remain indifferent between taking the “sure” outcome or the “good” outcome, increases.
Hence we have arrived at the first part of the general hypothesis, namely that (6) 𝑀𝐴𝑃 > 𝑀𝐴𝑃
Furthermore, in line with the results retrieved by Bohnet & Zeckhauser (2004), namely that other-regarding preferences equal to efficiency preferences, we assume that
(7) 𝑀𝐴𝑃 = 𝑀𝐴𝑃 .
(1) 𝑀𝐴𝑃 > 𝑀𝐴𝑃 = 𝑀𝐴𝑃 (Bohnet & Zeckhauser, 2004).
3.4.2. Hormonal hypotheses
The following hypotheses all take the general hypothesis into consideration and additionally predict behavioural patterns specific to the effect of changes in the level of progesterone throughout the menstrual cycle.
First hypothesis: Women’s 𝑀𝐴𝑃 is higher during the luteal phase when progesterone is high.
Second hypothesis: 𝑀𝐴𝑃 = 𝑀𝐴𝑃 during all menstrual
phases.
These two hypotheses assume that changes in progesterone levels only affect women’s betrayal aversion and leave their risk preferences unchanged. This is line with Buser’s
experimental findings (2012) and the body of research stating that risk preferences and betrayal aversion are two distinct concepts (e.g.: Bohnet & Zeckhauser, 2004).
4. Results 4.1. Sample’s idiosyncrasies
Participants were recruited within the experimenter’s close and not so close circles of friends and acquaintances. The answers of 19 individuals are considered in the statistical analysis. Participants’ age range lies between 18 and 31 years with an average age of 24. The average menstrual cycle duration is 30 days; the maximum length is 38 days and the
minimum duration equals to 26 days. The mode of this sample’s menstrual cycle length is 28 days. The average length of participants’ menstrual phase is five days with a range of three until seven and a mode of five days. 18% of this sample can be classified as women with an average menstrual cycle with a 28-days-menstrual cycle and a five-days-long menstrual phase (Richardson, 1992).
Average Maximum Minimum Mode
Length of menstrual cycle
30 days 38 days 26 days 28 days
Length of menstrual phase
Table 5: Summary Statistics on participant’s menstrual cycle
4.2. Statistical Analysis
4.2.1. General Analysis
The dataset at hand includes 660 observations of 27 variables from 19 subjects with Minimum Acceptance Probability (MAP) being defined as the dependent variable. The most crucial independent variables for this analysis are Participant ID, Period, TreatmentType, PMS, AT, CN and GB. All participating subjects received their identifying Participant ID, a positive integer number between 1 and 34 via an email to complete the first survey. This identification code had to be indicated during the questionnaire part of every survey.
Moreover, participants were reminded of their specific ID in all six email notifications. The variable Period refers to time points 𝑄 ( ), 𝑄 ( )𝑎𝑛𝑑 𝑄 ( ) or more specifically it
relates to day one until three (menstrual period), day nine or ten (follicular phase) and day 19 until 22 (luteal phase) of participants. Please consult section 3.2. for the implications of these selected periods on hormonal variations. TreatmentType can assume the three different treatments type used in this study, namely Decision Problem, Risky Dictator and Trust Game (see section 3.3. for more information). The variable PMS ranges between all positive integer values of one and six and describes the ascending intensity of suffrage from the premenstrual syndrome; consult section 2.2. for more insights on PMS and its implications. The last three variables relate to the collected responses of the Multidimensional Mood State Questionnaire categorized by level of alertness versus tiredness (AT), calmness versus restlessness (CN) and valence: good versus bad mood (GB).
Each participant of this experimental study provided multiple answers to the survey at different time points, thereby the gathered data points per participant cannot be considered to be independent. In order to avoid a violation of the Independence Assumption of linear models, a random effect per participant, (1|ParticipantID), is included into this model. Thus, every participant is predicated to have a different baseline-MAP and different random intercepts are generated per individual. The implemented random intercept model accounts for idiosyncratic variation of each participant (Winter, 2014). The statistical analysis is performed in the R Project for Statistical Computing using the packages lme4 and lmerTest.
At first, categorical variables are generated for period which appears in three different levels. In two different steps, period one (𝑝𝑒𝑟𝑖𝑜𝑑 ) or three (𝑝𝑒𝑟𝑖𝑜𝑑 ) is taken as the baseline or default level and two dichotomous variables are generated. Thus the categorical variables
depict, if period one is defined as the reference level, period two and period three respectively contrasted with period one.
The underlying general hypothesis aims at replicating the results retrieved by Bohnet & Zeckhauser (2004) and predicts different levels for the Minimum Acceptance Probability dependent on the applied treatment type, namely higher levels during Trust Treatments and smaller during the Risky Dictator Treatment.
Decision Problem Risky Dictator Trust Game
Mean 56% 52% 55%
Mode 57% 51% 55%
Median 57% 52% 56%
Table 6: Statistical comparison of MAPs across treatments
However, Table 6 shows that Minimum Acceptance Probabilities across treatments do not vary strongly in Mean, Median and Mode. A non-parametric rank test, the Mann-Whitney U test , however rejects the Null-Hypothesis (z = 213) as the obtained z-value is bigger than the absolute value of the critical z-value of 1.96. The Null-Hypothesis is defined as assuming that that there is no difference between means of groups (see appendix 8.4.). As the sample size is larger than 20 which indicates that the value of U approaches a normal distribution, a Z-test was performed (Billiet, 2003). Therefore, the average Minimum Acceptance
Probabilities of Risky Dictator and Trust treatments are significantly different from each. It can thus be concluded that the first result of the study by Bohnet & Zeckhauser (2004) could be replicated:
Result 1 𝑩𝒆𝒕𝒓𝒂𝒚𝒂𝒍 𝑪𝒐𝒔𝒕 𝑴𝑨𝑷𝑻𝒓𝒖𝒔𝒕 > 𝑴𝑨𝑷𝑹𝒊𝒔𝒌 𝑫𝒊𝒄𝒕𝒂𝒕𝒐𝒓
Individuals seem to incur an additional betrayal cost which they consider beyond any potential monetary losses and which is generated by the risk of the social interaction.
Figure 2: Cumulative distributions of MAPs
With respect to a potential effects of other-regarding and efficiency preferences on the decision whether to enter a lottery which is beneficial for another person, the result of Bohnet & Zeckhauser (2004) could not be replicated. A non-parametric rank test, Mann-Whitney U test rejects the Null-Hypothesis (z = 168) as the obtained value is bigger than the critical z-value of 1.96. Thus, it can be concluded that there is a significant difference between means of both groups (see appendix 8.4.).
Result 2 𝑴𝑨𝑷𝑹𝒊𝒔𝒌 𝑫𝒊𝒄𝒕𝒂𝒕𝒐𝒓 < 𝑴𝑨𝑷𝑫𝒆𝒄𝒊𝒔𝒊𝒐𝒏 𝑷𝒓𝒐𝒃𝒍𝒆𝒎
Thus, individuals’ other-regarding preferences dominated their efficiency preferences as participants were willing to enter the lottery at a lower probability of occurrence of the “good” outcome.
4.2.2. Analysis - Hypothesis one and two
The first and second hypotheses require analysing the effect of different treatment types in different periods on decision-making measured as the dependent variable MAP. Therefore, the interaction term TreatmentType*𝑃𝑒𝑟𝑖𝑜𝑑 is included into the first simple regression with period one as the baseline for the categorical variables of period:
(1) 𝑀𝐴𝑃 ~ 𝑇𝑟𝑒𝑎𝑡𝑚𝑒𝑛𝑡𝑇𝑦𝑝𝑒 ∗ 𝑃𝑒𝑟𝑖𝑜𝑑 (see appendix 8.5.) (2) 𝑀𝐴𝑃 ~ 𝑇𝑟𝑒𝑎𝑡𝑚𝑒𝑛𝑡𝑇𝑦𝑝𝑒 ∗ 𝑃𝑒𝑟𝑖𝑜𝑑 (see appendix 8.6.) 0,00% 10,00% 20,00% 30,00% 40,00% 50,00% 60,00% 70,00% 80,00% 90,00% 100,00% MAP Cumulative frequencies DP Cumulative frequencies RD Cumulative frequencies TG
The regression models (1) and (2) test for potential positive or negative effects of playing the three different treatments during two timing points when contrasted with either period one or three as the baseline.
Menstrual phase (period) has differential effects on decision-making across the three choice contexts. Specifically, in the risky dictator game subjects decreased their MAP significantly between phase two compared to phase one (Mean MAP= 53%; p = 0.168) and phase two contrasted with phase three (Mean MAP= 53%; p = 0.0384). Similarly, in the trust game individuals required marginally-significantly lower MAPs to enter the lottery between phase two compared to phase one (Mean MAP= 54.7%; p= 0.7150) or phase two
discriminated with phase three (Mean MAP=54.7%; p= 0.1560).
Result 3 𝑴𝑨𝑷𝑹𝒊𝒔𝒌 𝑫𝒊𝒄𝒕𝒂𝒕𝒐𝒓 (𝒂𝒏𝒅 𝑴𝑨𝑷𝑻𝒓𝒖𝒔𝒕 ) decline during phase two of their
menstrual cycle when progesterone levels are low.
At this point, the simple regression can be extended by other explaining variables. The potential independent variables Age, Nationality, Education, EconomicsBackground, Cramps, Headache and TenderBreast could not add any additional explanatory value to this model (see appendix 8.7. and 8.8.). Education indicates the highest obtained academic degree; the
variables EconomicsBackground, Cramps, Headache and TenderBreasts are binary. The last three refer to potentially-occurring pain during the menstrual period. The variables Age, Education and EconomicsBackground hardly vary in the sample of participants who were included in the data analysis which provides a solid explanation for the unobserved effect on the Minimum Acceptance Probabilities. However, adding PMS and the variables related to the Multidimensional Mood State Survey add strong supplementary explanation.
(3) 𝑀𝐴𝑃 ~ 𝑇𝑟𝑒𝑎𝑡𝑚𝑒𝑛𝑡𝑇𝑦𝑝𝑒 ∗ 𝑃𝑒𝑟𝑖𝑜𝑑 + 𝑃𝑀𝑆 + 𝐴𝑇 + 𝐶𝑁 + 𝐺𝐵 (see appendix 8.9.)
(4) 𝑀𝐴𝑃 ~ 𝑇𝑟𝑒𝑎𝑡𝑚𝑒𝑛𝑡𝑇𝑦𝑝𝑒 ∗ 𝑃𝑒𝑟𝑖𝑜𝑑 + 𝑃𝑀𝑆 + 𝐴𝑇 + 𝐶𝑁 + 𝐺𝐵 (see Regression Table 5)
The regression models (3) and (4) investigate the effect of playing the three different treatments during different timing points contrasted with either period one or three as the baseline while adding the covariates PMS, AT, CN and GB which had previously [regression models (1) and (2)] been captured within the error term.
The addition of the selected covariates increases the significance of the effect of the period point on decision-making across treatments. Specifically, in the trust game, disclosed MAPs decreased significantly between phase two compared to phase three (Mean MAP=
54.7%; p = 0.010039). Similarly as before but stronger in significance, in the risky dictator treatment, Period has a negative effect on decision-making when contrasting phase two with phase three (Mean MAP=53%; p= 0.001264).
Result 4 𝑴𝑨𝑷𝑻𝒓𝒖𝒔𝒕 𝒂𝒏𝒅 𝑴𝑨𝑷𝑹𝒊𝒔𝒌 𝑫𝒊𝒄𝒕𝒂𝒕𝒐𝒓 decline during phase two of their menstrual cycle when progesterone levels are low.
The singular effects of all newly included covariates selected MAP are significant, more specifically the degree of valence has a significantly negative effect (90%; p = 0.010576), whereas Alertness (90%; p = 0.032457) and especially the level of Calmness (99%; p = 0.000312) have a significantly positive effect, meaning that if the positive intensity of the three emotions’ categories rises also the Minimum Acceptance Probabilities increase. The variable PMS is only marginally significant (p = 0.052579) (see Regression Table 5).
Result 5 Levels of AT and CN are positively correlated with
𝑴𝑨𝑷𝑻𝒓𝒖𝒔𝒕 𝒂𝒏𝒅 𝑴𝑨𝑷𝑹𝒊𝒔𝒌 𝑫𝒊𝒄𝒕𝒂𝒕𝒐𝒓 during period two contrasted with the menstrual and luteal phase.
Fixed effects:
Estimate Std. Error df t value Pr(>|t|) (Intercept) 0.256441 0.085723 173.800000 2.992 0.00318 ** Risky Dictator 0.000400 0.036051 570.800000 0.011 0.99115 Trust Game 0.047400 0.036051 570.800000 1.315 0.18910 𝑝𝑒𝑟𝑖𝑜𝑑 versus 𝑝𝑒𝑟𝑖𝑜𝑑 0.098148 0.036485 582.000000 2.690 0.00735 ** 𝑝𝑒𝑟𝑖𝑜𝑑 versus 𝑝𝑒𝑟𝑖𝑜𝑑 -0.024290 0.038787 570.000000 -0.626 0.53141 PMS 0.040975 0.013616 72.000000 3.009 0.00361 ** AT 0.004610 0.002158 563.300000 2.136 0.03308 * CN 0.012825 0.003445 348.400000 3.722 0.00023 *** GB -0.015772 0.006805 330.900000 -2.318 0.02108 * Risky Dictator (𝑝𝑒𝑟𝑖𝑜𝑑 versu
s 𝑝𝑒𝑟𝑖𝑜𝑑
-0.154400 0.047202 570.800000 -3.271 0.00114 **
Trust Game (𝑝𝑒𝑟𝑖𝑜𝑑 versus 𝑝𝑒𝑟𝑖𝑜𝑑
-0.126086 0.047203 570.900000 -2.671 0.00778 **
Risky Dictator (𝑝𝑒𝑟𝑖𝑜𝑑 versu s 𝑝𝑒𝑟𝑖𝑜𝑑
-0.008650 0.045956 570.800000 -0.188 0.85077
Trust Game (𝑝𝑒𝑟𝑖𝑜𝑑 versus 𝑝𝑒𝑟𝑖𝑜𝑑
-0.065900 0.045956 570.800000 -1.434 0.15213
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Regression Table 5: Simple model with explanatory covariates (𝑃𝑒𝑟𝑖𝑜𝑑 )
Results four and five provide solid ground for the assumption that controlling for mood in the regression model increases the significance level of the previously detected effects (Result 3). However, it remains unclear whether the mood effects influence the dependent variable during specific menstrual cycle periods (period) and/or if they are also moderators of the influence on choice (TreatmentType). The precise influence remains uncertain as both independent variables form the interaction terms T𝑟𝑒𝑎𝑡𝑚𝑒𝑛𝑡𝑇𝑦𝑝𝑒 ∗ 𝑃𝑒𝑟𝑖𝑜𝑑 𝑎𝑛𝑑 𝑇𝑟𝑒𝑎𝑡𝑚𝑒𝑛𝑡𝑇𝑦𝑝𝑒 ∗ 𝑃𝑒𝑟𝑖𝑜𝑑 . In order to investigate the reference of the added covariates’ effects further, three-way-interactions are included into the Regression model.
The following regressions were run:
(5) 𝑀𝐴𝑃 ~ 𝑇𝑟𝑒𝑎𝑡𝑚𝑒𝑛𝑡𝑇𝑦𝑝𝑒 ∗ 𝑃𝑒𝑟𝑖𝑜𝑑 ∗ 𝐴𝑇 + 𝑃𝑀𝑆 + 𝐶𝑁 + 𝐺𝐵 (see appendix 8.11) (6) 𝑀𝐴𝑃 ~ 𝑇𝑟𝑒𝑎𝑡𝑚𝑒𝑛𝑡𝑇𝑦𝑝𝑒 ∗ 𝑃𝑒𝑟𝑖𝑜𝑑 ∗ 𝐴𝑇 + 𝑃𝑀𝑆 + 𝐶𝑁 + 𝐺𝐵 (see appendix 8.12) (7) 𝑀𝐴𝑃 ~ 𝑇𝑟𝑒𝑎𝑡𝑚𝑒𝑛𝑡𝑇𝑦𝑝𝑒 ∗ 𝑃𝑒𝑟𝑖𝑜𝑑 ∗ 𝐶𝑁 + 𝑃𝑀𝑆 + 𝐴𝑇 + 𝐺𝐵 (see appendix 8.13) (8) 𝑀𝐴𝑃 ~ 𝑇𝑟𝑒𝑎𝑡𝑚𝑒𝑛𝑡𝑇𝑦𝑝𝑒 ∗ 𝑃𝑒𝑟𝑖𝑜𝑑 ∗ 𝐶𝑁 + 𝑃𝑀𝑆 + 𝐴𝑇 + 𝐺𝐵 (see appendix 8.14) (9) 𝑀𝐴𝑃 ~ 𝑇𝑟𝑒𝑎𝑡𝑚𝑒𝑛𝑡𝑇𝑦𝑝𝑒 ∗ 𝑃𝑒𝑟𝑖𝑜𝑑 ∗ 𝐺𝐵 + 𝑃𝑀𝑆 + 𝐴𝑇 + 𝐶𝑁 (see appendix 8.15) (10) 𝑀𝐴𝑃 ~ 𝑇𝑟𝑒𝑎𝑡𝑚𝑒𝑛𝑡𝑇𝑦𝑝𝑒 ∗ 𝑃𝑒𝑟𝑖𝑜𝑑 ∗ 𝐺𝐵 + 𝑃𝑀𝑆 + 𝐴𝑇 + 𝐶𝑁 (see appendix 8.16)
The regressions (5) up until (10) investigate the effects of changes in three different mood categories (AT, GB, CN) across periods and treatment types on the size of MAPs while adding PMS as an explanatory covariate.
Regression models (5) and (6) give indications about the reference of AT’s effect within the interaction term. The level of alertness is positively correlated with period two contrasted with baseline three (p = 0.000321) rather than with TreatmentType.1
Result 6 The positive effect of an increase in AT on the dependent variable is directed towards the cycle period.
Figure four portrays the impact of a change in the level of alertness versus tiredness (y-axis) on MAP (x-axis) via implementing grouping by periods. Especially, when comparing period two to the baseline, an increase in AT positively influences the dependent variable.
1 Only significant results were reported. In the case of GB and CN no significant and thus clear direction of the influence could be determined.
However, the correlation described by the interaction term 𝑇𝑟𝑒𝑎𝑡𝑚𝑒𝑛𝑡𝑇𝑦𝑝𝑒 ∗ 𝑃𝑒𝑟𝑖𝑜𝑑 ∗ 𝐴𝑇 is only significant during the Trust Game treatment (p-values=1.76e05) (see appendices 8.11).
Figure 4: Effect of degree of alertness (AT) on MAP (𝑃𝑒𝑟𝑖𝑜𝑑 )
Figure five depicts the effect of variations in the category calmness versus restlessness (y-axis) on MAP (x-axis) via classifying by periods. The pink line related to group “period two” is positively sloped and in combination with the regression output it can be deducted that when comparing period two to the baseline, an increase in CN yields a rise in the dependent variable during the Trust Game treatment. The interaction term 𝑇𝑟𝑒𝑎𝑡𝑚𝑒𝑛𝑡𝑇𝑦𝑝𝑒 ∗ 𝑃𝑒𝑟𝑖𝑜𝑑 ∗ 𝐶𝑁 is significant at a 99% level (p-values=5.31e-06) (see appendices 8.13).
Figure 5: Effect of degree of calmness (CN) on MAP (𝑃𝑒𝑟𝑖𝑜𝑑 )
Period one period two period three Period one period two period three Low AT High M AP M AP Low CN High
Figure six graphs the effect of fluctuations in the mental state, more in particular in good versus bad mood (y-axis) on MAP (x-axis) and sorting by periods. Via combining the regression output with the graphical representation, a positive correlation between CN and the dependent variable is observed when comparing period two to the baseline. The interaction term 𝑇𝑟𝑒𝑎𝑡𝑚𝑒𝑛𝑡𝑇𝑦𝑝𝑒 ∗ 𝑃𝑒𝑟𝑖𝑜𝑑 ∗ 𝐺𝐵 is significant at a 99% level (p-values=0.000302) (see appendices 8.15).
Figure 6: Effect of valence (GB) on MAP (𝑃𝑒𝑟𝑖𝑜𝑑 )
Result 7 Levels of AT, GB and CN are positively correlated with 𝑴𝑨𝑷𝑻𝒓𝒖𝒔𝒕 𝑮𝒂𝒎𝒆 during timing period two versus one (when progesterone levels plunge).
Regressions (3) and (4) could only finalize in a marginally significant added
explanatory value of PMS but also in this case three-way-interactions might provide further insights. Regressions (11) and (12) analyse the effect of an intensification of PMS across treatments and during menstrual cycle periods on decision-making while including mood effects.
(11) 𝑀𝐴𝑃 ~ 𝑇𝑟𝑒𝑎𝑡𝑚𝑒𝑛𝑡𝑇𝑦𝑝𝑒 ∗ 𝑃𝑒𝑟𝑖𝑜𝑑 ∗ 𝑃𝑀𝑆 + 𝐴𝑇 + 𝐶𝑁 + 𝐺𝐵 (see appendix 8.10) (12) 𝑀𝐴𝑃 ~ 𝑇𝑟𝑒𝑎𝑡𝑚𝑒𝑛𝑡𝑇𝑦𝑝𝑒 ∗ 𝑃𝑒𝑟𝑖𝑜𝑑 ∗ 𝑃𝑀𝑆 + 𝐴𝑇 + 𝐶𝑁 + 𝐺𝐵 (see Regression Table 8)
This regression model indicates that PMS is positively correlated with both period and TreatmentType. The two-way interaction-terms show that especially an increase in the
Period one period two period three Low GB High M AP
intensity of PMS during the Risky Dictator significantly increases MAPs (p = 6.48e-05). Moreover, an intensification of suffrage from PMS during period 2 versus period 3 leads to a significant rise in Minimum Acceptance Probabilities (p = 0.001750).
However, the three-way-interaction 𝑇𝑟𝑒𝑎𝑡𝑚𝑒𝑛𝑡𝑇𝑦𝑝𝑒 ∗ 𝑃𝑒𝑟𝑖𝑜𝑑 ∗ 𝑃𝑀𝑆 predicts a decrease in MAPs when the strength of PMS rises, regardless of which period and both during the Risky Dictator and the Trust Game (see Regression Table 9).
Fixed effects:
Estimate Std. Error df t value Pr(>|t|) (Intercept) 0.501304 0.131795 193.100000 3.804 0.000191 *** Risky Dictator -0.406545 0.107089 562.900000 -3.796 0.000163 *** Trust Game -0.248136 0.107089 562.900000 -2.317 0.020855 * 𝑃𝑒𝑟𝑖𝑜𝑑 -0.199497 0.098639 578.900000 -2.022 0.043585 * 𝑃𝑒𝑟𝑖𝑜𝑑 -0.266608 0.104572 506.000000 -2.550 0.011081 * PMS -0.026666 0.026179 214.900000 -1.019 0.309534 AT 0.004545 0.002120 564.000000 2.144 0.032457 * CN 0.014717 0.004014 208.100000 3.666 0.000312 *** GB -0.018220 0.007080 288.600000 -2.573 0.010576 * Risky Dictator (𝑝𝑒𝑟𝑖𝑜𝑑 versus
𝑝𝑒𝑟𝑖𝑜𝑑
0.137081 0.132354 562.900000 1.036 0.300781
Trust Game (𝑝𝑒𝑟𝑖𝑜𝑑 versus 𝑝𝑒𝑟𝑖𝑜𝑑
0.312876 0.132239 562.900000 2.366 0.018320 *
Risky Dictator (𝑝𝑒𝑟𝑖𝑜𝑑 versus 𝑝𝑒𝑟𝑖𝑜𝑑
0.397426 0.124542 562.900000 3.191 0.001496 **
Trust Game (𝑝𝑒𝑟𝑖𝑜𝑑 versus 𝑝𝑒𝑟𝑖𝑜𝑑
0.251263 0.124542 562.900000 2.018 0.044117 *
Risky Dictator * PMS 0.107091 0.026606 562.900000 4.025 6.48e-05 *** Trust Game * PMS 0.077773 0.026606 562.900000 2.923 0.003605 ** 𝑝𝑒𝑟𝑖𝑜𝑑 versus 𝑝𝑒𝑟𝑖𝑜𝑑 * PMS 0.080582 0.025628 579.000000 3.144 0.001750 ** 𝑝𝑒𝑟𝑖𝑜𝑑 versus 𝑝𝑒𝑟𝑖𝑜𝑑 * PMS 0.063729 0.027136 527.200000 2.349 0.019216 * Risky Dictator * 𝑝𝑒𝑟𝑖𝑜𝑑 versus
𝑝𝑒𝑟𝑖𝑜𝑑 * PMS
-0.072697 0.034142 562.900000 -2.129 0.033669 *
Trust Game * 𝑝𝑒𝑟𝑖𝑜𝑑 versus 𝑝𝑒𝑟𝑖𝑜𝑑 * PMS
-0.120751 0.034160 562.900000 -3.535 0.000441 ***
Risky Dictator * 𝑝𝑒𝑟𝑖𝑜𝑑 versus 𝑝𝑒𝑟𝑖𝑜𝑑 * PMS
-0.106795 0.032957 562.900000 -3.240 0.001264 **
Trust Game * 𝑝𝑒𝑟𝑖𝑜𝑑 versus 𝑝𝑒𝑟𝑖𝑜𝑑 * PMS
-0.085135 0.032957 562.900000 -2.583 0.010039 *
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Regression Table 8: Complex Regression with interaction term “PMS” (𝑃𝑒𝑟𝑖𝑜𝑑 )
Result 8 The degree of PMS is negatively correlated with
𝑴𝑨𝑷𝑻𝒓𝒖𝒔𝒕 𝒂𝒏𝒅 𝑴𝑨𝑷𝑹𝒊𝒔𝒌 𝑫𝒊𝒄𝒕𝒂𝒕𝒐𝒓 during periods one and two when progesterone levels are at minimum.
4.2.3. Interpretation of results
This study aims at exploring the effects of variations in the level of the hormone progesterone on risk aversion, foremost betrayal aversion. The study at hand was able to detect an additional betrayal cost and thereby replicates Bohnet and Zeckhauser’s result (2004) but using a sample of exclusively women. The sample of both men and women (Bohnet & Zeckhauser, 2004) showed no difference in efficiency contrasted with other-regarding preferences but in the sole pool of female participants, other-other-regarding preferences dominate the efficient choice (Results 1 and 2). It is obvious to assume that gender-specific idiosyncrasies cause this difference in results. Bohnet and Zeckhauser (2004) do not disclose whether or not they tested for gender-specific disparities in their results.
The initially stated hypotheses could not be proven significant per se but the obtained results call for a more nuanced case processing. This experimental analysis produces
statistical evidence that women act less risk averse towards both risk types during period two contrasted with period one and three of their menstrual cycle (Results 3 and 4). Changes in progesterone appear to have an effect on the perception of risk in general. Both, the first and second hypothesis cannot be accepted.
Women’s 𝑀𝐴𝑃 𝑎𝑛𝑑 𝑀𝐴𝑃 are lower during days nine and ten of the
female menstrual cycle compared to the menstrual and luteal phase.
Women are generally less risk-averse during days nine and ten of the female menstrual cycle compared to the menstrual and luteal phase.
The more complex regressions run during the statistical analysis of this study reveal that the stronger the degrees of PMS women suffer from, the less averse they are towards both risk types during period one and two of their menstrual cycle, when progesterone levels are
minimal. Thus, the initial hypotheses were correctly assuming that a difference in risk
aversion is at place when comparing the luteal phase to the other two timing points. However, firstly not the level of progesterone causes the effect but the intensity of suffrage from PMS does and the syndrome affects the perception of both risk types (Result 8).
Women’s 𝑀𝐴𝑃 𝑎𝑛𝑑 𝑀𝐴𝑃 decrease when progesterone plunges given that women’s intensity of suffrage from PMS increases.
Women’s risk aversion is negatively correlated with the intensity of PMS during times of low levels of progesterone.
The results retrieved by the multidimensional mood state survey also add explanatory value to this model even if the obtained results might seem unexpected when analysing them in light of the initial hypotheses.
An improvement of women’s mental state generally increases risk-aversion during the decision-making-process and more detailed, this causality can be observed during timing period two versus one with respect to a socially-risky environment. If women are not burdened with a weaker emotional state, risk is perceived more aversely by them which implicates that they are relatively more risk averse by nature and in the absence of other influencing factors.
Women’s 𝑀𝐴𝑃 rise during day nine and ten of their menstrual cycle if the mental state upgrades.
Women’s risk aversion is negatively correlated to their mental state during day nine and then of their menstrual cycle.
Moreover, the three-way-interaction term (appendix 8.12.) could prove that the effect of a positive change in the level of alertness affects decision-making depending on the specific cycle period and not treatment-specifically.
The outcome of the simple regressions displays a trend towards lower degrees of general risk aversion during day nine and ten of the menstrual cycle compared to the luteal and menstrual phase as partially assumed. Women are supposedly more emotional stable and free from any physical side effects caused by the menstrual phase or PMS during timing point two. However, more complex regressions distinguish female behaviour more carefully with respect to risk types. The analysis suggests that if women are in a positive emotional state and free from hormonal effects potentially caused by PMS or the menstrual phase, they are more cautious when interacting with fellow (female) individuals under risk compared to their behaviour during the menstrual and luteal phase. This finding can be supported evolutionarily as the selected timing point (day nine and ten) is shortly before the ovulatory phase during which women select a male partner with presumably maximum genetic quality. Moreover, sorting for the right man for reproduction entails risk triggered by a social interaction and thus the described scenarios relates to the applied trust game treatment. Thus, this motivating force
