The influence of gender and attractiveness on bargaining behaviour

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U

NIVERSITY OF

A

MSTERDAM

M

ASTER

T

HESIS

The Influence of Gender and

Attractiveness on Bargaining Behaviour

Author:

Shiv R

AMBARRAN

(11127716)

Supervisor:

Dr. Ailko

VAN DER

V

EEN

Second Reader:

Prof. Joep S

ONNEMANS

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Statement of Originality

This document is written by Shiv Rambarran 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.

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Abstract

This paper examines the influence of gender and physical attractiveness on bargaining behaviour through the proxy of ultimatum games. Two samples were recruited from Western Europe and North America, each comprising of 6 men and 6 women, all of whom were randomly matched with 6 players from the other sample and completed ultimatum game decisions. Players saw a photo of the other player and completed a strategy profile as both a proposer and responder, along with stating their expecta-tions about the other player’s expected offer and minimum acceptable offer. Players were then prompted to rate their matched players on perceived attractiveness, trust-worthiness, and friendliness. Summary statistics and regression analysis were used to understand the impact and predictive value of gender and attractiveness on ultimatum decisions and expectations. It is found that more attractive players received higher of-fers on average than less attractive players. Players were also willing to accept lower offers from more attractive players on average than from less attractive players. More attractive players were also expected to offer less and demand more than less attractive players. No significant difference was found in the amount men were offered on aver-age compared to women. Men were expected to offer less and have higher minimum offers on average than women however these results were not statistically significant. It is concluded that perceived attractiveness creates a significant bias in a simplified bargaining context whereas gender differences in behaviour were small in comparison to the differences in how genders were treated and expected to behave.

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Contents

1 Introduction

Over the course of the past decade, the rise of social media (Khamis, Ang, & Welling, 2017; Marwick, 2015) and the digital transformation of business (Ljubiša, 2017; Bush, 2016), have caused much of communication, as well as consumer decision making, to take place online (Newman, 2017). The most effective and profitable advertising mediums are now digital (Heinig, 2018). The market for social media influencers has grown exponentially in the past two years, being projected to reach 10 billion dollars by 2020 (Contestabile, 2018). In most contexts, the only information social media patrons and consumers have are pictures and very minimal text (Jendro, 2016). This begs the question: how does this new framing of information influence how we bargain? Given the dominance of sex appeal in the social media narrative (Yaa, 2018), what is the influence of physical attractiveness, as seen through digital images, on how we make decisions regarding those people?

This question overlaps into the topic of gender and job recruitment. It is widely ac-knowledged that the majority of HR professionals and recruiters are female (Sands, 2017; Petrone, 2015). It is also found that impressions made from a photographed face predict face-to-face impressions, post an actual impression, one month later (Gunaydin, Selcuk, & Zayas, 2017). This coupled with the rise of Linkedin (Beall, 2017; Peters, 2017) which pro-vides recruiters with a photograph of applicants (Morin, 2016), unlike traditional resumes, begs the question: what is the impact of a photographed face on recruiter perceptions? Does gender and perceived physical attractiveness provide a distinct edge in a recruitment and bargaining context?

This research seeks to better understand the impact of gender and physical attractiveness on bargaining behaviour, how any unconscious biases may lead to suboptimal or irrational decisions, and ultimately, what this means in the context of social media and wage negoti-ations.

This paper seeks to explicitly answer the research question:

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1. Introduction

Another primary objective of this research is to build on the existing body of literature surrounding this topic by addressing areas for improvement within the methodology of previous literature. What happens in a one shot, decision context that doesn’t allow for repeated play and learning from outcomes? How does someone’s perceived gender and physical attractiveness impact our expectations of them? How do our expectations of them influence our decisions? How does one measure a more accurate rating for attractiveness that accounts for players’ subjective preferences? These questions are addressed in the following research.

Summary of Findings

From this study, it is found that (1) women received higher offers than men on average however this difference turned out not to be statistically significant. (2) Attractive people received higher offers than less attractive people. (3) Subjects are willing to accept less from attractive people than from unattractive people. With regards to players’ expecta-tions of other participants, it is shown that (4) Men were expected to offer less on average than women (5) Attractive people were expected to offer less on average than unattractive people. (6) Men were expected to demand more/have higher minimum acceptable offers (hereby denoted MAOs) on average than women. Similarly, (7) attractive people were expected to have higher MAOs than less attractive people. However, results (4) - (7) per-taining to expectations were not statistically significant therefore they cannot be claimed. (8) Players tended to award a “premium”, i.e. more than their expectation of Player 2’s ex-pected MAO, to attractive players. Lastly, it is found that (9) the higher a player’s personal MAO was, the less they were likely to offer another player. We attributed this to an omitted variable of competitiveness.

The subsequent thesis first sheds light on the existing body of literature surrounding the study of gender and attractiveness in the context of ultimatum games. The methodology, findings, and points for improvement are identified from all relevant papers and used to guide the methodology and added value of this paper. After the literature review, is the methodology, which explains why the experiment was structured as it is, the limitations of this method, and the hypotheses that guide it.

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2. Literature Review

The experimental results are exhibited alongside an analysis and interpretation of them. This format serves to provide a more coherent and intuitive read by putting data within the context of the greater discussion. Finally, this paper assesses the validity of the hypothe-ses, limitations within the analysis, overall conclusions, and recommendations for further research.

2 Literature Review

While there have been numerous studies examining gender effects in bargaining, histori-cally, results have been inconsistent (Dawes et al. 1977, Stockard et al. 1988; Ball & Cech, 1993; Orbell et al. 1994). On the other hand, while there have been relatively few stud-ies that examine the effect of facial attractiveness on decision making through an economic lens, findings tend to consistently confirm that attractiveness influences application success, wage levels, promotion rates, and multiple other areas (Bardack & McAndrew, 1985; Raza & Carpenter, 1987; Marlowe, Schneider, & Nelson,1996; Todorov, 2008; Maurer-Fazio & Lei, 2015). Indeed, recent studies even show that judgements of attractiveness, based on people’s college yearbook photos, can reliably predict their financial earnings and career success (Rule & Ambady, 2011; Scholz & Sicinski, 2015).

Solnick & Schweitzer (1999) were among the first to investigate the effects of both gender and physical attractiveness on bargaining behaviour, using ultimatum games1_{. In the first}

stage of their experiment, 70 subjects completed strategy profiles2 _{in the role of proposer}

and responder against a hypothetical player 2. Participants photos were then taken which a panel of external judges rated and ranked based on attractiveness. Photos of the most and least attractive men and women were selected and placed randomly in a photo book. Finally, a second group of 108 subjects viewed the photographs and made ultimatum game

1_{An ultimatum game comprises of two players: a proper and responder. A proper decides how to split a}

certain amount between himself/herself and the responder. The responder then accepts or rejects the offer. If the responder accepts, both sides keep the proposed split; if he/she rejects, both players get zero. The game theoretical Nash Equilibrium is that the proposer offers the smallest possible amount and the responder accepts because it is more than zero.

2_{A strategy profile is a set of strategies for all players that outlines all actions in a game. In an ultimatum}

game, this includes stating how much player 1 would offer to, and the minimum they would accept from, a given player 2.

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decisions.

Their results found no significant difference in the offers or demands attractive and unattrac-tive participants made. However, there was a difference in how subjects were treated that correlated with their gender and level of attractiveness. Subjects offered more on average to more attractive participants and demanded more on average from them as well. Men were also offered more on average than women and less was demanded from men than from women (Solnick & Schweitzer, 1999).

As the authors defend, the use of photographs over face-to-face interactions unrealistically simplifies a bargaining context however this enabled them to control and present stimuli consistently across participants (Solnick & Schweitzer, 1999). A clearer point of concern though is that subjects in Phase 1 made ultimatum strategy decisions without seeing or be-ing matched with another participant. This means that players were in essence, playbe-ing no one, and does not account for potentially different strategy profiles per matched candidate.

Secondly, the ratings for attractiveness of participants were done by external judges. This does not account for the subjective judgments of the actual participants. It is very con-ceivable that the judges’ perceptions differ from that of participants in the context of the experiment and is therefore potentially misrepresentative. This rationale guided the deci-sion to use participants’ individual and subjective perceptions of attractiveness, in place of external scores, in this paper’s methodology.

Thirdly, all participants in the final stage received outcome feedback after each round thereby causing potential bias for subsequent rounds. In theory, a Player A who saw a high offer in the previous round may more likely reject a lower offer in the present round than Player B who saw a relatively lower offer in the previous round and saw the same offer as Player A in the present round. This final critique guides the decision to not allow learning between rounds in the following paper so as to gage the true initial impression and potential bias of players. The two next papers that built upon this previous work and contribute to the current dialogue are Solnick (2001) and Eckel & Grossman (2001). Sol-nick conducted a one-shot ultimatum game with two treatments; in one treatment players were mutually anonymous and in the other, gender-revealed first names were made known.

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Consistent with Solnick’s previous work, the subjects used the gender-revealing strategy method.

Eckel and Grossman (2001) also used ultimatum game experiments to test for gender dif-ferences but varied the context and enabled repeated play. Placing 4 participants on one side, facing 4 participants of another gender group on the other side, subjects record pro-posals on a paper, which is given to the responder, filled in, and given back to the proposer. Players do not know who their partner is, only the gender group they belong to. I.e. in a given round, if 3 men are the proposers and 3 women are the responders, the proposers will know that their partner is a woman across from them but do not know who specifically. Also, subjects play 8 rounds, each against a different participant, with the authors intention to see the effects on learning. Findings reveal that women tend to propose slightly more on average than men, regardless of partner gender, and that women are more likely than men to accept a proposal of a certain amount. It is also found that an offer is more likely to be accepted by both genders if it came from a woman than a man (Eckel & Grossman 2001). Comparing the findings of Eckel & Grossman (2001) with Solnick (2001), we see that both studies find no significant difference in the average offers made by men and women3. However both studies found significant differences in how genders are treated. Both papers conclude that women receive lower offers than men on average, from both male and female proposers4_.

Eckel et al (2008) build further on this previous research by examining various studies on gender differences in dictator games and ultimatum games to uncover regularities in the re-sults. They find that women tend to be more generous than men, asking for less and expect-ing less. However, they contend that these differences are small relative to the differences in expectations about how men and women will behave in these games i.e. stereotypes. Their findings of no significant difference in how genders behave are consistent with sim-ilar experiments where gender was not highlighted in the experimental design (Bolton and Katok 1995; Solnick & Schweitzer 1999; Carpenter, Burks, and Verhoogen 2004; Whitt

3_{In Solnick (2001), men offer 46.7% and women offer 46.8%. In Eckel & Grossman (2001) men offer}

36.5% while women offer 38.5%

4_{Solnick reports an average of 43.7% offered to women vs. 48.9% offered to men. Eckel & Grossman}

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and Wilson 2007).

The authors however further claim that the higher offers are consistent with higher levels of risk aversion in women. This claim is tested and refuted by Garcia Gallego et al. (2012) which is elaborated upon subsequently.

Overall, Eckel et al (2008) is the first paper to address gender expectations and claim them as more significant than actual differences in gender behaviour. The pattern of findings between this paper, Solnick (2001), and Eckel and Grossman (2001) guided a critical deci-sion for this paper’s hypotheses and methodology to focus on differences in how genders are treated, over the differences in how genders behave.

Garcia-Gallego et al (2012) investigate whether gender differences are due to gender-associated risk attitudes. In this experiment, an ultimatum game is framed as a negotiation between employer (the proposer) and employee (the responder) over salary. Risk attitudes of participants are measured though a risk elicitation task and compared with gender effects from the ultimatum games. They find that women are more risk averse than men. Addi-tionally, that women make lower offers and reject more in an ultimatum game. However, it is concluded that while gender and risk-related effects do exist in ultimatum game deci-sions, differences in risk attitudes do not explain the gender effects present in ultimatum bargaining.

A strength and limitation of this paper is the use of roles, employer and employee, in the ultimatum game as well as an actual task for those who accepted. As the authors defend, this is in response to the concern of a lack of realism within the U.G. context. However, as they acknowledge, players may be bringing in their own beliefs and experiences of being an employer or employee into their role, thus biasing the game. Additionally, the mundane nature of the task, writing letters on an envelope, could also act as an asymmetric disin-centive for subjects. However, their clear finding that risk attitudes do not explain gender effects in ultimatum games, guide us to seek alternative explanations in this research. One of the most recent papers that challenges our hypothesis on the influence of physical attractiveness on ultimatum games, is Bhogal, Galbraith, and Manktelow (2016). The au-thors examine whether physical attractiveness has an influence on how people share and

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cooperate in a game theoretical framework through a face-to-face ultimatum game. A sample of 138 participants played a 2-round ultimatum game with chocolate coins as the monetary units. Participants completed questionnaires before and after playing the game, self-reporting how attractive they found the other player on a 7-point scale, and whether they would consider going on a date with them. Matched participants took a turn in the role of proposer and responder. After the first response was made, the chocolate coins were allocated, rebalanced, and the second round was commenced.

The researchers found males reported significantly greater co-operation and generosity to-ward attractive females in the context of images but that physical attractiveness exerted no influence on generosity and co-operation when participants played the UG face-to-face. The authors acknowledge that the result was not consistent with the bulk of previous re-search however, they contend that this result shows a difference in how attractiveness affects cooperation in person vs through digital images. This paper concludes that attractiveness may have an effect through digital images however they become insignificant in face-to-face bargaining situations and that players are instead driven by fairness considerations. A strength of this study is that face-to-face interactions are utilized to better replicate a real-life bargaining context. However, there are several areas of concern towards the in-ternal and exin-ternal validity of this methodology. Firstly, participants were strongly primed to consider the other player romantically through the questionnaires. While this should seemingly bias the players to give more weight to attractiveness, it signals to every partici-pant what the researchers are looking for and causes them to irregularly focus on their own potential bias. This arguably causes participants to act more fairly. Secondly, the allowing for outcomes to be observed and learned from between rounds will cause biases for the second round. Thirdly, the use of chocolate coins is not a uniform measure of value for all participants as it is quite plausible some participants like chocolate more than others. More so, chocolate coins are a reminder that the interaction is a game of little consequence or reward in place of actual or stated real currency.

However, even if we accept the hypothesis and conclusion that attractiveness bears no in-fluence in a face-to-face ultimatum game, it is more so worth investigating whether uncon-scious biases show up especially in a digital context containing images.

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Yujia Wu et al (2018) provide the final contribution to the existing body of literature sur-rounding unconscious bias in bargaining contexts due to gender and perceived facial at-tributes. The authors investigate the influence of proposers’ gender and facial trustworthi-ness on responders’ willingtrustworthi-ness to accept an offer in ultimatum games. Using a gallery of pictures of 212 Chinese undergraduate students, 4 subjects with the highest and lowest rat-ings for facial trustworthiness were chosen and set as proposers. These proposers “played” against 79 responders. Authors found that: I) responders were more willing to accept offers from proposers who looked more trustworthy, II) responders were more likely to accept of-fers from females, and III) female responders were more likely to accept unfair ofof-fers from females than from males.

A strength of this paper is that the authors mitigate biases caused by interacting race and culture on perceived facial trustworthiness by keeping the sample consistent to one race of individuals. However, the ethnic homogeneity of the sample may be a concern of external validity due to inherent and unique cultural attitudes of the Chinese.

The first apparent weakness of the experiment is that the responders do not play against the actual proposers; rather, proposers’ photos and amounts are predetermined by the re-searchers. If responders correctly speculated that the subjects represented in pictures had not actually chosen the amounts, nor would the observed proposers be impacted by the responders’ choices, this could alter their behaviour, arguably a desire towards more con-sistency in their responses. A counter argument for predetermined proposals is that they provide multiple data points for the same proposer, allowing greater analysis.

A second point of concern with this paper is that researchers only used pictures for two men and two women for the proposers thereby drastically limiting the choice context for responders. On the other hand, these four subjects were chosen from a rated pool of 212 students, helping to ensure greater differences between selected proposers. Another coun-terargument for their smaller sample, is that having fewer proposers logistically enables the authors to have more matches per proposer and therefore more data.

A final critique of this paper, surrounding methodology, is that the results of each trial were displayed on the screen for 3 seconds for responders, allowing for learning between games (Yujia Wu 2018, p. 507). This opens the door to ordering effects as previous outcomes

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may plausibly affect responders’ perception of future proposals. While this approach of allowing for outcome feedback is consistent to the literature, it is a systematic concern that we seek to address in the subsequent thesis.

Lastly yet importantly for this research, Yujia Wu et al. acknowledge a correlation between perceived facial trustworthiness and attractiveness (Yujia Wu et al p. 510). An independent sample of students played the UG as responders and then rated the four proposers on at-tractiveness and trustworthiness. The authors find a significant correlation (r=.52, p < .001) between attractiveness and trustworthiness but argue that attractiveness did not correlate with the “just receivable amount”, that is, the minimum acceptable amount of responders on average.

Based on the varying results from previous literature, we arrived at the following seven hypotheses to be tested:

Hypothesis 1: Men will be offered more than women.

Hypothesis 2: Attractive people will receive higher offers on average than less attractive people.

Hypothesis 3: The more attractive someone is, the less we are willing to accept from them.

Hypothesis 4: The more attractive someone is, the less we expect them to offer.

Hypothesis 5: The more attractive someone is, the higher we expect their minimum to be. Hypothesis 6: The more attractive someone is, the higher the premium we will offer them (above their expected MAO).

Hypothesis 7: Men are generally expected to have a higher Minimum Acceptable Offer than women.

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3. Methodology

3 Methodology

Experimental Design: Participants were split into two samples: “Amsterdam” and “Abroad”. Each sample comprised of six males and six females, of various races and nationalities, all university educated, within the range of 22-27 years old.

Before taking the survey, participants were asked to send in a photograph of passport-like dimensions: a directly facing, neutral expression against a plain, light background, encom-passing the shoulders to the top of the head. These photographs were then put into one of the two surveys. The Amsterdam sample then received a link that matched them with participants from the Abroad sample while the Abroad sample received a link that matched them with participants from the Amsterdam sample. This was to ensure that participants faced players they did not know to avoid personal biases.

The online survey was programmed to randomly match participants with three (3) males and (3) females from their respective sample pool of 6 males and 6 females. Participants were firstly prompted with an explanation of the survey, examples of survey questions and responses, and were asked for their official consent before beginning.

Participants then saw a picture of one participant at a time and were asked to make decisions in an ultimatum game5, in the role of both proposer and responder. Notably, participants did not receive game outcome feedback between rounds. This was intentionally done to eliminate the effect of learning and mitigate the effect of pair ordering on decisions. Ad-ditionally, responses were written in such a way, that if a participant choose an amount for themselves, it showed what amount the other participant would receive. This made it impossible for participants to mistakenly choose amounts that did not mathematically add up to ten, the total amount to be allocated.

After participants finished making all ultimatum decisions, they were prompted again with the photographs of the participants they matched with and were asked to rate them on a four-point scale, for perceived trustworthiness, attractiveness, and friendliness. This was

5_{In the role of proposer, players decided how to allocate $10 between themselves and the photographed}

player. In the role of responder, players decided the minimum amount they would accept, rejecting all offers below and accepting all offers above.

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3. Methodology

done after ultimatum decisions had been entered so that these descriptors would not prime participants to overly focus on them. A critical objective for the use of subjects’ ratings of attractiveness for their opponents was to address a shortcoming in previous literature; the use of attractiveness ratings by external judges vs participants’ subjective ratings to evalu-ate the relationship between attractiveness and ultimatum decisions.

The descriptive variables, trustworthiness and friendliness were primarily included to make it unclear to participants what the experimenter was interested in – and thereby mitigate the chance that that information could be shared to other participants before they had com-pleted the survey. A second reason those descriptors were used is because previous research claims that trustworthiness correlates with attractiveness while friendliness was more an in-tuitive variable that one would expect to have an effect in a bargaining context (Yujia Wu et al 2018).

Another unique aspect of this methodology is the inclusion of questions that account for the expectations of participants of what their opponents would choose. This is to shed light on why differences may arise in proposals or MAOs. Men may be offered more than women for example, but without further information, it is not known if that is because men are expected to reject higher offers than women – or if participants feel a greater sense of generosity towards men. One reason, vs another, carries very different interpretations for gender dynamics and bargaining objectives.

Great care was also taken to avoid phrases such as “team”, “opponent”, “win”, or “score” that could elicit asymmetric feelings of comradery or competitiveness. Ratings were done on a 4-point scale to “force” participants from deferring to a middle number and to disasso-ciate from conventional 10-point scales for people, that may result in players “not wanting to score someone too low”. Survey instructions and format are provided in the Appendix. Basic summary statistics were calculated such as averages for each variable and group. Subsequently, multilinear regression analysis was done to further understand the relation-ship and predictive value between gender and perceived attractiveness on ultimatum game decisions and expectations.

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4. Results and Discussion

4 Results and Discussion

Upon gathering the data, the first hypothesis that the mean proposal to the photographed player would differ by gender of the photographed player was tested. The binary gender variable, ID Gender, took on a value of “0” if female and “1” if male. For combined genders, the average proposal was 4.09 which is consistent with previous empirical studies of ultimatum game behaviour. It deviates from the game theoretical equilibrium but falls within the range of 4-5 that is commonly observed (Camerer, 1995). The average proposal to females was 4.188 while the average proposal to men was 4.013. Females received, on average (.175) more than males in proposed offers. However, by testing this difference for statistical significance using a two-sample t-test, it is observed that the difference is not statistically significant with a P-value of 0.452. Therefore, it cannot be claimed that the proposed amount per gender is different. The H0 hypothesis that the proposed offer is equal for each gender cannot be rejected.

Table 1 below, provides a summary of the mean results, combining both samples: Table 1: Summary Statistics

Variable Mean Std. Dev. N proposedtoid 4.096 1.401 146 maofromthem 4.432 1.823 146 expectedofferfromid 4.493 1.335 146 expectedmaoofid 4.644 1.143 146 trustworthiness 2.459 0.762 146 attractiveness 2.678 0.87 146 friendliness 2.733 0.833 146 premiumoveroffer -0.548 1.797 146

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Table 2: Definitions

Variable Definition

ID Unique identifier for each photographed player Id Gender Dummy variable for gender of the photographed player Proposed to ID Amount a player proposed to a photographed player MAO from them Minimum acceptable offer of the player viewing the photograph Expected offer from ID What a player expected the photographed player would offer Expected MAO of ID Expected minimum a photographed player would accept Trustworthiness Perceived attribute based on image

Attractiveness Perceived attribute based on image Friendliness Perceived attribute based on image

Premium over Offer A player’s proposed offer minus their expectation of the photographed player’s minimum acceptable offer

Table 1 shows the mean scores for Trustworthiness, Attractiveness, and Friendliness fall within the desired range of average as averages above 3 or below 2 would imply the sample is biased in the direction of, for example, too attractive or too unattractive.

Interestingly, the premium over offer, which is the proposed amount minus expected MAO of photographed player, is negative. At face value, this suggests irrationality in decision making or a desire to null the game. However, more plausibly, it may be argued that each decision was made in isolation, rather than players seeking consistency across their answers. This in itself is a significant finding as it demonstrates players were not acting consistently in line with game theoretical solutions or behaviour (Camerer, 1995).

The minimum acceptable offer of subjects towards the photographs they observed averaged 4.432. This is notably higher than the average proposed amount, indicating self-interested behavior. However, the difference between these two variables turned out not be statisti-cally significant. By applying a t-test for equality of means, we find a p value of 0.1143. While this is close to significant at the 10%, it cannot be claimed that the average proposed amount is different from the MAO.

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subjects (proposedtoID) and players’ subjective ratings of attractiveness. We show various outcome variables regressed on Attractiveness. We include Trustworthiness and Friendli-ness as additional control variables in table 4 so as to mitigate any omitted variable bias. The regressions for Table 3 and 4 are as follows:

Outcome variablei = β0+ β1· Attractivenessi+ εi (1)

Outcome variablei = β0+ β1· Attractivenessi+ β2· Trustworthinessi+ β3· Friendlinessi+ εi

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Table 3: Regression table

(1) (2) (3) (4)

proposedtoid maofromthem expectedofferfromid premiumoveroffer attractiveness 0.624∗∗∗ -0.489∗∗ -0.0894 0.576∗∗∗ (5.04) (-2.88) (-0.70) (3.48) _cons 2.426∗∗∗ 5.741∗∗∗ 4.733∗∗∗ -2.090∗∗∗ (6.97) (12.02) (13.17) (-4.49) N 146 146 146 146 tstatistics in parentheses ∗_{p < 0.05,}∗∗_{p < 0.01,}∗∗∗_{p < 0.001}

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(1) (2) (3) (4)

proposedtoid maofromthem expectedofferfromid premiumoveroffer attractiveness 0.634∗∗∗ -0.473∗∗ -0.107 0.546∗∗ (4.96) (-2.70) (-0.82) (3.20) trustworthiness 0.0531 -0.216 -0.100 0.162 (0.30) (-0.89) (-0.55) (0.69) friendliness -0.110 0.131 0.197 -0.00236 (-0.69) (0.59) (1.19) (-0.01) _cons 2.568∗∗∗ 5.872∗∗∗ 4.488∗∗∗ -2.401∗∗∗ (5.35) (8.93) (9.10) (-3.75) N 146 146 146 146 tstatistics in parentheses ∗_{p < 0.05,}∗∗_{p < 0.01,}∗∗∗_{p < 0.001}

As a supplement to Tables 3 and 4, Table 5 shows the relationship between the same out-come variables and attractiveness of photographed subject, controlling this time for gender of photographed subject. Surprisingly, the coefficient for attractiveness, and therefore its influence on the dependent variables, stays relatively stable between regressions.

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(1) (2) (3) (4)

proposedtoid maofromthem expectedofferfromid premiumoveroffer attractiveness 0.630∗∗∗ -0.484∗∗ -0.0968 0.575∗∗∗ (4.97) (-2.78) (-0.74) (3.39) idgender 0.0533 0.0378 -0.0619 -0.00582 (0.24) (0.12) (-0.27) (-0.02) _cons 2.381∗∗∗ 5.709∗∗∗ 4.785∗∗∗ -2.085∗∗∗ (6.01) (10.50) (11.70) (-3.94) N 146 146 146 146 tstatistics in parentheses ∗_{p < 0.05,}∗∗_{p < 0.01,}∗∗∗_{p < 0.001}

It was checked to see if Attractiveness is correlated with ID Gender by regressing Attrac-tiveness on ID Gender:

Attractivenessi = β0+ β1· IDGenderi+ εi (3)

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Table 6: Regression table (1) attractiveness idgender -0.363∗ (-2.56) _cons 2.870∗∗∗ (27.90) N 146 tstatistics in parentheses ∗_{p < 0.05,}∗∗_{p < 0.01,}∗∗∗_{p < 0.001}

In Table 6, the T-stat of ID Gender is -2.56 with a P-value of 0.011. This implies ID Gen-der is statistically significant. Statistically, this presents an issue of multicollinearity as one predictor variable can be linearly predicted by another predictor variable with some degree of accuracy. From Tables 3 to 5 above, it can be observed that the coefficient of attractiveness remains relatively the same and statistically significant across left-hand side variables. Therefore, the decision was made to keep ID Gender in regressions as it does not significantly influence the attractiveness coefficient. This shall be further addressed in the limitations subsection.

Below provides an interpretation of each of the relationships between the dependent and independent variables, as seen in the above three tables:

Proposal on Attractiveness:By regressing proposedtoID (proposals made to photographed subjects) on attractiveness, we see that the relationship is positive and statistically signif-icant. That is to say, the more attractive a photographed subject was perceived to be, it is expected that they would be offered more. This confirms our second hypothesis: more attractive people will be offered more.

Additionally, as seen in the appendix, the constant of 2.43 shows that regardless of how attractive one was perceived, they were offered some share of the pie (some portion of the $10). Note that the low R-square of .15 means that most of the variation of “proposedtoID”

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remains to be explained. This is also why the constant is positive – it takes every factor that was not included or accounted for that is not correlated with attractiveness. Therefore, we regress “proposedtoID” on trustworthiness, attractiveness, and friendliness to find whether trust or friendliness are driving the results. As the above table 4 shows, the coefficient for attractiveness remains relatively the same and statistically significant while the R-square has not increased (see appendix) with the inclusion of trustworthiness and friendliness, both of which are not statistically significant.

MAO from them on Attractiveness: to investigate the relationship between MAO (Mini-mum Acceptable Offer based on photo) with attractiveness, we regress MAOfromthem on Attractiveness. The coefficient for attractiveness is (-.4889) and significant at the 5% level (T stat = -2.88). The negative coefficient means that the more attractive someone was rated, the lower you could expect the MAO to be from the responder. This is in line with our in-tuition, prevailing theory, and third stated hypothesis: we are willing to accept less from people who we deem more attractive.

Notably, the R-square is .05 meaning most of the variance is still to be explained. By regressing MAO on attractiveness and the other descriptive variables, we see that the co-efficient stays relatively stable (-.4728) and significant. Conversely, trustworthiness and friendliness are not statistically significant.

Expected Offer on attractiveness: Regressing expected offer of ID, i.e. how much you expect the photographed person would offer, on their rated attractiveness, a coefficient of -.0893 is obtained. Nevertheless, it turns out not to be statistically significant (t stat = -.7). The negative relationship still implies that the more attractive a photographed player was, the less a player expected them to give.

Controlling for trustworthiness and friendliness as well, the attractiveness coefficient is (-.1073). Although all coefficients are not statistically significant, the attractiveness coef-ficient continues to move in the intuitive and hypothesized direction; the more attractive one perceive someone, the less we expect from them. However, we fail to reject the null hypothesis that the coefficient is zero, i.e. It cannot be stated that more attractive players are expected to offer less nor more.

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we get the attractiveness coefficient of (.0479) implying that the more attractive one is per-ceived, the higher we expect their minimum offer is. This could partially explain why more attractive people were proposed more on average; because it is assumed they would reject higher than average offers. Notably, while the direction of the coefficient is in line with our hypothesis, it is not statistically significant therefore we cannot reject the hypothesis that its effect is zero. This coefficient does double (0.0882) when we control for trust and friendliness, however with a low R-square, there is still much variation to explain.

Premium over offer on Attractiveness: By regressing Premiumoveroffer on Attractiveness, we see that the coefficient for attractiveness is positive and statistically significant. This means that attractiveness helps to explain the choice of players to allocate more money to the photographed player than necessary, as measured by expected MAO (of photographed player). In the same manner as previous, when we regress Premiumoveroffer on attrac-tiveness, friendliness and trustworthiness, the latter two are not statistically significant, reinforcing the conclusion that attractiveness drives premiums. This therefore confirms the sixth hypothesis: players tend to award more than the expected MAO to players who they deem more attractive.

To take a broader look, we regress “Proposed to ID” on every relevant variable, to see which have an influence or simply correlate with how much we propose. The regression is as follows:

ProposedtoID_i = β0+ β1· IDGenderi+ β2Personal MAOi+ β3 · ExpectedOfferfromIDi+

β4· ExpectedMAOofIDi+ β5 · Trustworthinessi+ β6· Attractivenessi+ β7· Friendlinessi+ εi

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Table 7: Regression table (1) proposedtoid idgender 0.0825 (0.38) maofromthem -0.190∗∗ (-2.86) expectedofferfromid 0.221∗ (2.40) expectedmaoofid 0.0488 (0.50) trustworthiness 0.0454 (0.26) attractiveness 0.573∗∗∗ (4.37) friendliness -0.129 (-0.81) _cons 2.377∗∗ (2.72) N 146 tstatistics in parentheses ∗_{p < 0.05,}∗∗_{p < 0.01,}∗∗∗_{p < 0.001}

We denote S.S for Statistical Significance. Based on Table 7, we observe:

ID Gender: Positive though not statistically significant men and women proposed more to photographed males on average. Note, the standard error (.217) was greater than the effect

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(.082) implying a tremendous amount of variance.

Mao from Them: Negative and S.S. The higher a player’s minimum offer was, the less he/she is likely to propose to the photographed player. This may be due to the omitted vari-able of competitiveness. Those who took the game more seriously or simply had a greater competitive drive, were willing to concede less and offer less. This omitted variable is a limitation of this design and something to be addressed in subsequent research.

Expected Offer: Positive and S.S. The amount a player offered correlated positively to how much they expected the photographed player would offer them. This alludes to the fairness consideration that is empirically found in ultimatum games (Miyaji et al, 2013).

Expected MAO of ID:Positive yet not statistically significant. The higher a player expected the photographed player’s MAO to be, the more they were offered. This implies some of the amount is due to the belief that they would reject a lower offer – vs. offering them more out of kindness.

Trustworthiness: Positive yet not statistically significant. The more trustworthy a pho-tographed player looked, the more they were offered. Trust is observed to correlate with attractiveness; we observe this by regressing Trustworthiness on Attractiveness and find-ing a statistically significant coefficient of .19. This is consistent with findfind-ings from Yujia Wu (2018). However, while facial attractiveness proves statistically significant in deter-mining the proposed amount –trustworthiness was not. Notably, the correlation between Attractiveness and Trustworthiness presents an issue of multicollinearity and therefore the possibility of misattributed weighting in the coefficients. However, from regressing the dependent variables separately on Attractiveness, and on Attractiveness, Trustworthiness, and Friendliness together, it is seen that the coefficient for Attractiveness, our variable of interest, does not significantly change. Therefore, to be consistent to the literature, we keep Trustworthiness in the regression.

Attractiveness: With a coefficient of .573 and S.S. this is shown to influence how much people offer. Attractiveness is notably the highest statistically significant variable – further validating the value of this research topic.

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Friendliness: Interestingly, this is both not statistically significant and negative. This im-plies that the friendlier someone looked, the less they were offered. This could be due to the thinking that a friendlier person is more likely to be accommodating, that is, they would accept a lower offer. Therefore, while friendliness does positively correlate with attractive-ness, in this case, it creates a counter effect in reducing someone’s bargaining power. It is further investigated whether Friendliness correlates with expected MAO by regressing Ex-pected MAO on Friendliness; we find that Friendliness has a negative coefficient of (-.15) but is not statistically significant (p value = .195).

Based on the previous findings, we may now evaluate our initial hypotheses: Hypothesis 1: Men will be offered more than women.

Women actually received more on average (.175) more than men however this difference was not statistically significant. Therefore, we reject the hypothesis that men are offered more than women.

Hypothesis 2: Attractive people will receive higher offers on average than less attrac-tive people.

The coefficient for attractiveness is positive and statistically significant. Therefore, we fail to reject the hypothesis that more attractive people are offered more than less attractive people.

Hypothesis 3: The more attractive someone is, the less we are willing to accept from them.

When personal MAO was regressed on attractiveness, the coefficient for attractiveness was negative and statistically significant. From this we infer the more attractive a player is, the lower our minimum acceptance level is. We therefore fail to reject the hypothesis.

Hypothesis 4: The more attractive someone is, the less we expect them to offer. The Attractiveness coefficient was negative, implying the more attractive a player was per-ceived to be, the less an opponent expected them to offer, in line with our hypothesis. However, this was statistically insignificant at the 5% level. Therefore, we officially reject the hypothesis.

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to be.

The direction of the attractiveness coefficient is positive (.0479), in line with our hypoth-esis, however it is statistically insignificant. Therefore, we reject the hypothesis that the more attractive a player is, the higher their MAO is expected to be.

Hypothesis 6: The more attractive someone is, the higher the premium we will offer them (above their expected MAO).

The attractiveness coefficient is positive and statistically significant therefore we fail to re-ject this hypothesis.

Hypothesis 7. Men are generally expected to have a higher Minimum Acceptable Of-fer than women.

Regressing the expected MAO of a player on their gender, we get a positive coefficient for gender, implying that men were expected to have a higher MAO than women on average. However, this was statistically insignificant therefore we reject this hypothesis.

Limitations

The first limitation of this methodology is that while attractiveness can be accurately per-ceived from a photograph, trustworthiness and friendliness cannot. Fortunately, this re-search seeks only to study the impact of (perceived) attributes on bargaining behaviour. However, participants may have felt that they were making an uninformed judgement on trustworthiness and friendliness and therefore did not act in their truest nature. It is there-fore plausible that actual, observed and subjectively evaluated trustworthiness and friendli-ness may have a more pronounced impact on offers made, received and expectations. Another limitation of this methodology is that in an effort to be consistent with previous and relevant literature, as well as to ensure anonymity (and therefore honesty by participants), we used anonymous survey links. While honesty of participants and answers is a strength posited in this paper, anonymous links caused the authors to forego valuable information of identity, etc. in who was answering the questions. Other methods to ensure anonymity while collecting that data for a two-way analysis would be advised for the future.

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5. Conclusion

Thirdly, by inserting randomizing survey logic into the experimental survey, it is not guar-anteed that players will be matched with each other. Therefore, we forego some specific outcome data from each game.

Fourthly, due to the multitude of different races and cultures present in the samples, while all come from western backgrounds, it is possible there were confounding effects that could not be tracked given such a small sample from each culture. From Hessel Oosterbeek (2004), it is known that cultural differences can affect how ultimatum games are played as well as what are considered optimal outcomes.

Finally, the correlation between gender and attractiveness presents an issue of multicollinear-ity, leading to omitted variable bias. An approach such as an instrumental variable design would be recommended in future research to control for the variation in attractiveness per-ceptions caused by gender.

5 Conclusion

Based on these findings, one may reasonably infer that gender and physical attractiveness have an impact on bargaining behaviour. We offer more to attractive people and are willing to accept less from them. While the results surrounding the relationship between attrac-tiveness and expected offer and expect MAO are not statistically significant, the direction of the attractiveness coefficient implies that the more attractive a person is, the less we ex-pect they will offer and conversely, the higher we exex-pect their minimum acceptance level to be. It is also shown with statistical significance that higher premiums are awarded to more attractive players, that is, the more they are offered above their expected minimum acceptance.

Some limitations of this methodology to acknowledge are that firstly, “true” attractiveness, trustworthiness, and friendliness cannot be sufficiently evaluated from one digital image. Furthermore, players’ perceptions of these traits in someone else may be very different in person vs online as is anecdotally found. Therefore, these variables may have a different impact in different bargaining contexts. Secondly, the multicollinearity between gender

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5. Conclusion

and attractiveness ratings may lead to omitted variable bias and the need for an instrumen-tal variable to untangle effects. Thirdly, the use of anonymous survey links, enabled us to significantly increase the likelihood of honesty, in response to a proactive critique of this methodology, however it caused the authors to forgo individual data points – that may help to further distinguish the impact of different variables. Lastly, the relatively small sample size impacted the statistical significance of variables whose direction, are otherwise in line with our hypotheses but can therefore not be claimed. It is recommended to draw upon larger samples in future research.

While no decision context in real life is as simplified as the ultimatum game played in this experiment, the presence of biases for attractiveness and gender show how seemingly irrel-evant factors still affect our decision processes. The gender bias is particularly interesting given the growing awareness towards gender equality in the work environment and the per-ception of progress that is widely believed to be had from gender attitudes decades ago. The demonstrated attractiveness bias is consistent with previous research and of relevance, given the increasing role LinkedIn, where facial attributes are salient, plays in recruitment processes as well as the increasing marketability of social media celebrities. These results validate the timeliness of this study in our digitally transforming society and the need for further investigation on this topic.

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A. Survey

Appendix

A

Survey

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B. Code

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