Inter-gender interaction and communication in ultimatum games

ABSTRACT In this article, we focus on bargaining within male–female pairs, the most pervasive partnership in humankind. We analyse data from an ultimatum game played by Greek participants. Parallel to this, we introduce a one-way communication protocol according to which the responders can send short messages to the receivers, after making their decisions. The analysis shows that gender and message effects exist and males are more effective bargainers.


I. Introduction
When focusing on partnerships of different genders, it is usually assumed that men are in charge while women have to bargain to receive their share (Meisenbach 2010). In this article, we study the bargaining ability and the role of each gender on both the responder and the proposer positions in inter-gender pairs playing ultimatum games in the lab.
Concerning the role of gender in the ultimatum game, women appear to be indifferent on the gender of the other player and are more generous (Eckel and Grossman 2001). In the one-shot ultimatum game experiment conducted by Solnick (2001), the offers made to female players by both sexes were lower and the responders of both sexes intended to accept lower offers when facing female proposers. Moreover, in the literature, there is evidence (Sutter et al. 2009) that in pairs of the same gender there was much more competition and retaliation and thus lower efficiency than in mixed-gender pairs. Concerning the influence of gender pairing, women give significantly less to women than to men and to persons of unknown gender (Ben-Ner, Kong, and Putterman 2002). Furthermore, women paired with women almost never fail to reach an agreement, which is interpreted as solidarity (Eckel and Grossman, 2008;2001). In our experiment, we try to observe the behaviour of Greek participants on the aforementioned topics.
In this article, we focused on an ultimatum game between different genders, giving the responders the possibility to send a short opentype message to the proposers expressing their feelings about the offer they received after submitting their decision. Although there was no limitation at the length of each message, the participants were instructed at the beginning of each session to keep them short and compendious. We chose to insert virtual communication into our experiment because we wanted to compare the changes, if any, it produces in the participants' behaviour between the pre-and the post-message stages. As Winter and Zamir (2005) state, the proposers adapt their offers to the responders' rejection and the responders adapt their rejections to the proposers' behaviour.
The innovation of the current study is that there were used only pairs of different genders aiming to observe potential gender differences emerging when players are faced with the opposite gender. Furthermore, the introduction of communication between players in combination with the above structure makes this design unique, given the fact that very few bargaining experiments have been conducted under this scenario.

II. Experimental design
The results reported here were obtained from fourteen 60-period sessions of an ultimatum game played by 104 undergraduate students. In each session, the participants were assigned the role either of the proposer or of the responder according to their gender. Yet, participants of the same gender had the same role throughout each session. Every participant was provided with written instructions. The experiment was designed and executed using the z-Tree software (Fischbacher 2007).
In each period, the proposer's task was to place an offer of €X, which could be any amount between €0 and €20, in steps of €0.1. Random proposer-responder pairs were formed within fixed, stable and independent matching groups. The participants were located in the same room but were unaware of the participant with whom they were to bargain. A responder who was randomly selected to be matched with a proposer received an offer and was called to accept or reject it. In the case of acceptance, the responder gained €X and the proposer €20-Χ. Otherwise, they both earned nothing. In order to prevent cumulative wealth effects, participants were paid according to their earnings in one period randomly specified at the end of the session. Furthermore, due to limitation of funding, only 80% of the participants, randomly chosen in each session, were paid according to this rule and this was announced to them beforehand.
Every session included four stages depending on the role of each gender in the game as well as the presence or absence of communication and had the structure presented in Table 1. All the female participants were entering in the experiment with the role of proposer for 30 rounds (15 with and 15 without communication) with the male participants having the role of responder. For the rest 30 rounds, these roles were reverse. We followed this pattern of role changing in order to prevent any potential learning behaviour. The female participants had always the role of proposer at the beginning of the experiment and after the completion of the first 30 rounds they never returned to this role. As a consequence, they never had the opportunity to make biased offers based on their former experience on both roles. The same applies to male participants who were always had the role of responder at beginning of the experiment.
In the stages with communication, the proposers were not allowed to respond to the message sent by the responders. We adopted this kind of experimental design in order to search for potential effects that the messages would have on the participants' behaviour in the subsections with communication while at the same time searching for an impact of the message in the subsections without communication when the latter were conducted after the message subsections. Because participants' behaviour could be affected by the short time between sub-sessions, we made sure to have alternations in the sequence of the sections with and without communication in order to minimize this effect.

III. Results and discussion
Tables 2 and 3 present the mean values of the proposed amounts of money; the earnings were calculated on the basis of successful transactions and the percentage of accepted offers by participant role and gender. As Table 2 shows, there is an increase of €1.49 in offers in the message-based sub-sessions and a decrease of €0.43 in the amounts offered in   the message-based sub-sessions in rounds with male proposers (Wilcoxon test, p = 0.007).

Gender effects
The emergence of possible gender effects in the offers and earnings of participants in sub-sessions with and without communication was checked with respect to either of the two roles. All the earnings were calculated exclusively on the basis of the successful transactions. The results are presented in Table 4.

Message effects
The existence of potential message effects was investigated in the amounts offered and in the participants' earnings in sub-sessions with and without communication for both roles. In order to do so, we read and analysed all the messages sent by the responders and categorized them based on the offered amount demanded by the responder, the amount that he was receiving and his reaction when he was not getting the desired amount of money. The results of this analysis are reported in Table 5.
From the analysis of the messages was found that when the responders were receiving the desired amount of money, they tended to encourage the proposer to continue offering them the same amount of money or they applauded the offer with expressions like 'well done', 'good offer', 'keep offering this amount', etc. On the contrary, when the offered amount was low and not acceptable, they reacted by threatening the proposer of a possible further rejection of their offers if they do not increase the offered amount. Expressions like 'I need more', 'this is a low offer', 'you have to offer more', etc. were used.
In order to ensure that differences in offers across pre-and post-message sub-sessions are not attributed to other factors, such as learning, we also examined and rejected the existence of learning behaviour across the experiment sub-sessions, by analysing the string of offers from each participant.
Moreover, in order to analyse the acceptance or rejection decision with respect to gender roles and the presence (or absence) of messages, we used the following Probit model, in which the Higher amounts offered by females (p < 0.044).
Finding 2: Gender effect on earnings in sub-sessions without communication 1. Female proposers tended to gain more (p < 0.001).
No significant difference in the earnings of both genders in the role of proposer and responder (p = 0.565 and p = 0.540, respectively).
p-Values referred to Mann-Whitney U test. When proposers: increase of offered amounts in message-based sub-sessions compared with those in message-free sub-sessions (p < 0.001).
When proposers: increase in offers in the messagebased sub-sessions (p < 0.001) and decrease in the amounts offered in the message-based subsessions (p = 0.007). Finding 4: Decrease in the proposer's earnings in message-based sub-sessions with female proposers.
When proposers: earnings decreased by 11.17% in the message-based sub-sessions (p < 0.001) and increase of acceptance.
When proposers: the decline of 0.5% in earnings presented in Table 3 is not statistically significant (p = 0.873). Finding 5: Positive impact of messages on the responders' average earnings with males in the role of the responder increasing their earnings.
When messages sent by females: no effect on their earnings (p = 0.858).
When messages sent by males: increase in their earnings (p < 0.001).
Finding 6: Female responders failed to convince male proposers to give them the amount of money they demanded.
Messages sent by the females implied that they had no strategy regarding their target of acceptable offers.
Male proposers managed to receive almost always the desired amount of money, when sending their message. p-Values referred to Wilcoxon test. dependent variable is the participants' decision and it takes the value 1 for acceptance and the value 0 for rejection. The results are displayed in Table 6.
The interpretation of findings in Table 6 produces the following conclusions: (1) An increase in offers will increase the probability of acceptance (p > |z|<0.001).
(3) The presence of post-decision messages increases the probability of accepting an offer (p > |z| = 0.007). (4) Being a female participant in the messagebased sub-sessions decreases the probability of accepting an offer (p > |z| = 0.043).

IV. Conclusion
It has been conjectured that women may be discouraged from making riskier choices, in male-female groups, because they are inhibited by culturally driven norms about the appropriate mode of female behaviour which is avoiding risk (Booth & Nolen, 2015). As the analysis of the results has shown, gender does play a role in the amount of money offered in both types of sub-sessions (i.e. message-based and message-free) as on the one hand, male participants opted to offer more in the sub-sessions without communication, whereas on the other hand, females were more generous in the subsessions with communication. Although we cannot reach a definite answer on gender effects in competitive environments, our findings differ from those of other studies in which it was found that female participants tend to reject offers more often and to make lower offers Jaramillo-Gutiérrez 2008, 2012). This generosity of the female participants can be explained as a riskavoiding behaviour given the fact that higher offers may reduce the level of rejection.
In addition, a message effect also occurs affecting the level of offers. Females appeared more prone to changing their attitude and increasing their offers, when being aware of the other player's intentions and wishes.
Hence, it is apparent that the female participants in our experiment have used negotiation in a less aggressive manner than the male ones, while at the same time insisting on their demands. However, there is no evidence that women negotiate better than men. To sum up, the overall effect of the presence of communication is positive for male participants, increasing their profits and their willingness to accept an offer.

Disclosure statement
No potential conflict of interest was reported by the authors. Offer: offered amount of money; Female: female = 1, male = 0; Message: 1 for the presence and 0 for the absence of messages; Female × Message: dummy product of gender and message. Significance: **1% and *5%.