Bachelor Thesis Economics & Finance
Gender difference of communication effect in Battle
of Sexes game - An experimental test
Abstract
This paper investigates the role gender plays in communication effect on coordination of Battle of Sexes (BoS) game. I hypothesize that communication will improve coordination in BoS and that there are gender differences in this communication effect. I test my hypothesis using controlled laboratory experiments which is conducted by Simin He, a PhD candidate at University of Amsterdam. I find that (i) communication could improve coordination;(ii) males prefer larger share than females do; (iii) when communication is possible, total earnings of a pair vary among different gender-interaction pairs where female playing with female pairs have the highest mean payoff.
Name: Jieqiong Jin
Student Number: 10630341 Date: 09/06/2016
Specialization: Economics and Finance Subject: Economics
Statement of Originality
This document is written by Student Jieqiong Jin who declares to take full responsibility for the contents of this document.
I declare that the text and the work presented in this document is 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.
1. Introduction
Coordination game is not rare in real life. For instance, imagine a situation when two people are driving towards each other in a very narrow lane, which only allows one car to pass through. Each driver has two options, either to swerve or to go straight. The outcome that one driver goes straight but the other swerves gives the straight going driver the maximum utility, while it gives a margin utility to the swerved driver. However, they dislike being involved in a car crash when both of them go straight as this will bring them loss. In addition, swerving together is also not a desired outcome since their time is wasted. This situation can be summarized in the following table: Table 1
Driver 2 Straight Swerve Driver 1 Straight -2, -2 3, l
Swerve l, 3 0,0
Note: Numbers in table 1 are just examples to illustrate the two drivers’ payoffs for different outcomes. There are three Nash equilibria in this game. Two pure strategies in which one plays swerve and the other plays straight. There also exists a mixed strategy where both of them assign a certain probability to straight and swerve. It is reasonable to assume that they will not randomize their choices since it is risky in this game, so the best result is either (straight, swerve) or (swerve, straight). However, as the other driver’s action is unpredictable, in order to achieve one of the equilibria, they need to coordinate.
Another similar example is when two firms are both considering to enter a new market but it has been found out that the market demand is smaller than the total supply of these two firms. Therefore, they need to coordinate to avoid both entering the market and earning negative profit, or avoid both failing to enter the market and earning zero profit. In this case, there are multiple ways to coordinate. For instance, they could just post an advertisement in the local newspaper announcing that they will enter the market. However, the disadvantage of this method is that the first firm who posts this advertisement will gain huge firs-mover advantage against the late one and therefore the second firm might suffer some loss including the costs of posting Ad and the risk of failing to enter the market.
to improve coordination is important to understand. It has been studied that costless communication can help achieve and improve coordination significantly (Farrel, 1987). In addition, by examining the Battle of Sexes game, Cooper and DeJong (1989) found that communication could significantly help to deal with opponent player’s unforeseeable actions and thus improve coordination. Moreover, they also indicated that the effect of communicating in multiple rounds was more significant than the effect of one-round chat. However, the role gender plays on the effect of communication remains uninvestigated. In most of the prevailing economic studies, researchers tend to treat all the decision-makers homogenously, however, we cannot deny that males and females are different, both physically and psychologically. As written by Tannen (1990), males and females have different communication styles and patterns. As he said, the language, for most women, is principally a method of building connections and bargaining relationships. Nonetheless, for most men it functions as a way to keep independence and maintain social hierarchy. Due to these difference in viewing talk, females and males might behave differently. Hence, I study whether gender plays a role in improving coordination with communication under a laboratory setting. There are at least two advantages of using laboratory experiment for this research question. First, selection bias is ruled out as all the subjects are randomly assigned to different treatments. In addition, ceteris paribus condition can easily be met in a lab. In summary, the research questions of this paper are: 1) Does pre-play two-way communication increase coordination in Battle of Sexes games? 2) Does communication effect in Battle of Sexes games differ across gender? In order to answer these two questions, several experimental tests will be done, using data from CREED laboratory at University of Amsterdam. The aim of this paper is to investigate the gender difference on effect of communication in Battle of Sexes games, which has seldom been paid attention to, so as to provide some additional insights on coordination. The results are as follows: 1) two-way communication improves coordination significantly; 2) when it is possible to communicate, males are more inclined to choose a higher share for themselves than females do; 3) total payoffs of pairs differ across gender only when communication is possible.
The remaining part of this paper is structured as follows. It will begin with section 2 that gives a brief introduction to Battle of Sexes game and presents discussions on the effect of communication and later gender effect in games.
Afterwards the experimental design will be provided and explained in section 3, followed by three hypotheses to the experiment in section 4. Later, in section 5 results of the experiment will be analyzed and lastly in section 6 conclusions will be drawn and the answers to research questions will be presented. In spite of this, section 6 will put forward some suggestions for future studies.
2. Literature Review
The literature review of this research consists of 3 sections. Section 2.1 will provide an introduction and some theoretical aspects of Battle of Sexes (BoS) game. Section 2.2 will illustrate studies of effect of introducing costless pre-play communication in several different coordination games. Section 2.3 will then focus on the discussion of gender-related behavioral difference in both coordination and non-coordination games.
2.1 Battle of Sexes game
Suppose a woman and her partner are heading to their date place, but they both could not recall whether they have agreed on going to the cinema or watching a soccer match. The woman prefers to see a movie while her partner prefers to watch the soccer game. Moreover, both of them definitely prefer to go to the same place together rather than to go to their own desired place alone. Without any coordination mechanism, this scenario resembles the BoS game which is commonly seen in real life situations. A formal example of BoS game used in study by Copper and DeJong (1989, pp. 569- 570) is shown in table 2 below, where x>y>0.
Table 2: Battle of Sexes game
This game has two pure-strategy Nash equilibria, (R2, C1) and (R1, C2), and a symmetric mixed-strategy equilibrium where strategy 1 is played with probability
Column Player C1 C2 Row Player R1 R2 (0, 0) (y, x) (x, y) (0, 0)
!" =%&$$ while strategy 2 is played with probability !' = %&$% . Moreover, the expected payoff for both players using mixed-strategy is %$
(%&$)* . Without communication, the symmetric mixed-strategy equilibrium is naturally the outcome of this game. Nevertheless, the possibility of reaching disequilibria, which are outcomes (R1, C1) and (R2, C2) where both players earn zero payoff, is %*&$*
(%&$)* that is not negligible and will become larger if the conflict is very extensive (that is, the difference between x and y is pretty significant). Take an extreme example that x equals positive infinity while y equals zero, the disequilibria probability is 1. In normal cases when conflict is not that immense, communication before making decisions might help to avoid this coordination failure.
2.2 Communication in coordination games
Camerer (2003, pp.336) points out that games with multiple equilibria, like the example given above, entail coordination between players and therefore are called coordination games. However, if different players have distinct preferences of conventions, or if different self-enforcing conventions exist, it is not easy to reach an agreement on how to behave, even though players have a shared motivation to conform to a convention or universally appreciated paradigm of behavior (Camerer 2003, pp.336). The uncertainty of the opponent player’s behavior could well lead to coordination failure. For instance, in the BoS game above, if the row player expects the column player to choose strategy 1, he/she would choose strategy 2. However, this expectation is not guaranteed as column player may instead choose strategy 2 or even just randomize his/her actions. Hence, searching for a method to solve this coordination problem is of researches’ interest. Meanwhile, the studies done so far on the influence of communication on coordination games are often seen. For instance, in the laboratory, introducing pre-play communication to coordination games, including prisoner’s dilemmas (Dawes, MacTavish, & Shaklee, 1977), battle of the sexes (Cooper, DeJong, Forsythe, & Ross, 1989), as well as the games with pareto-ranked equilibria (Blume & Ortmann, 2007) have shown that communications could promote coordination to a great extent.
A paper written by Dawes, MacTavish and Shaklee (1977) studies the influence of communication in prisoner’s dilemma. In their findings, compared to situations
when players are not allowed to communicate, being able to send messages significantly increases the chance to unravel the dilemma. They also point out that transmitting information relevant to the dilemma, other than simply introducing oneself to his/her opponent player, could indeed produce cooperative behavior (Dawes et al., 1977 p.6). Underlying explanation behind this result is that group members are more convinced to cooperate when they see the relevant information arising from the conversation (Dawes et al., 1977 p.3). Therefore, communication is added in the experiment done by CREED.
Likewise, Cooper and DeJong (1989, p.569) focus on the part communication plays in the battle of sex game as they thought cheap talk might facilitate as a substantial tool to deal with opponents’ unpredictable actions. Here cheap talk means costless communication which is nonbinding. They uncover that player’s behaviors are revised notably when communication is present, even if the method of communication is merely non-obligatory pronouncements between unidentified players. In addition, Cooper and DeJong (1989, p. 580) find that having compound rounds in two-way communication is proved to be more efficient than having single round.
What worth noting is that the dramatic effect of communication in coordination seems robust even in games with more than one player. In a study of Minimum and Median games which has Pareto-ranked equilibria, Blume and Ortmann (2007, p.288) conclude that historical coordination failure could be overcome by cheap talks. Besides, they observe that only with repeated interactions can communication be benefited to the most, where messages are interpreted as negotiation announcements (Blume & Ortmann, 2007, p.289). This additional finding is in line with what Cooper and DeJong find and could be served to justify the unstructured and unlimited two-way communication employed in the experiment done by CREED which will be explained in next section.
In these studies, variant parameters are used to measure coordination. Dawes et al. (1977) ,and Blume and Ortmann (2007) made use of payoffs or earnings while Cooper and DeJong (1989) employed coordination rate. However, in this paper, total payoff of a pair is a proxy of coordination.
There are many gender difference studies on behavioral economic topics. However, the significance of gender as an economic determinant in individual behaviors is quite controversial.
Manson, Phillips and Redington (1991) examine the role gender enacts in decision-making behaviors in a two-player non-cooperative repeated game, which bears a resemblance to a duopoly competition with homogeneous traders. The results indicate that gender-related behavioral differences appear at the early stage of the game but gradually vanish over time. In spite of that, it is enthralling to notice that markets with two females are incontrovertibly more stable than those with two males (Manson et al., 1991, p. 227). In addition, a study done by Boton and Katok (1995) that investigate the dictator game under a player-player anonymity context supports this view, as no significant difference of choice behavior across gender is evident.
Nevertheless, there are also some experiments that reveal gender differences. By using data earlier collected from the United States, China, Japan and Korea, Croson and Buchan (1999) study gender differences in trusting and reciprocating behaviors in trust games where they conclude that females present more reciprocity in the game than males (p. 386, 390). Moreover, a research of provision of public good (Nowell & Tinkler, 1994) asserts that gender difference exists. In this study, it is found that all-female groups are more cooperative than all-male groups and that this difference is robust in long run. Furthermore, after analyzing results from three independent experiments that involve more than 450 participants, Holm (2000, p. 306) reveals that information about the opponent player’s gender is likely to be seen as a coordination signal and influence decision-related behavior in a way that is towards the discrimination of females. What worth noting in Holm’s study is that, in Battle of Sexes game, when subjects know their opponent player is female, both males and females are more “hawkish”; they preferred to receive larger shares themselves (2000, p.302).
Another recent study provides some novel aspects. Wang and Houser (2015) focus on the importance of the content and form of communication and find that natural language is systematically better than intention signaling. When they are analyzing gender difference in this study, they categorize four interaction pairs; female playing with female, female playing with male, male playing with female, and male playing with male (Wang& Houser, 2015, p.27). As this paper also puts
emphasis on gender differences during communication, it is reasonable to follow the way they classify pairs. However, in Wang and Houser’s experiment (2015), they reveal opponent player’s gender whereas in the experiment of this paper this information is kept secret, therefore I assume that female-male matched players and male-female matched players would give similar results.
These controversial results arise from different lab settings; studies that stating no gender differences in coordination or non-coordination games are under a player-player anonymity context while those claiming they find gender differences reveal another player’s gender to participants. Though the experiment studied in this paper falls into the setting of the opposing studies, it is still interesting to investigate the differences across gender.
3. Experimental design
The experiment is conducted at the University of Amsterdam. After the public announcement on the CREED website, subjects voluntarily sign up for the experiments. Most of the participants are from Faculty of Business and Economics; the rest of them are from various faculties such as Law, Humanities and Science. In total 252 students participate in the experiment, of whom 96 are in sessions of Battle of Sexes game. What worth mention is that three models of games are actually run in this experiment; the first one is a Battle of Sexes game, which is analyzed in this paper, the second one is a Chicken game with a small alternative option, and the last one is a Chicken game similar to the second one but has a larger outside option. Besides, for the entire experiment there are 14 sessions in total, of which session 3, 9, 11 and 13 are BoS games, and each session lasts for around one hour and a half. At beginning of the game every subject receives an endowment capital of 300 points that equals to 7,5 euros as their show up fee; the exchange rate is 40 points equal to 1 euro. Their final payoff depends on their own choices as well as their opponent players’ choices. At the end of the experiment they will be informed of their earnings and be paid privately.
Before starting, lab regulations are read out loud, which includes rules like communicating during the experiment, either with other participating students or using their cell phones, is not allowed. Each session has 24 subjects and they are
randomly divided to two groups. Splitting up participants into two 12-people groups is meant to shorten the duration of the experiment and hence increase the efficiency. Instructions are displayed on the computer screen after subjects are all sited at a randomly assigned table. Afterwards control questions are asked to test their comprehension about procedure and key elements of the experiment. Subjects could raise their hands if they encounter any problem and solutions are given privately and quietly. The experiment only begins when every subject answers the questions correctly. Full English instruction will be provided in Appendix.
There are 20 rounds of one-shot BoS games in each session. Subjects would not play the BoS games with fixed opponents so that long-run factors like reputation and learning would not affect the outcomes as subjects may make different decisions if they know the games will be repeated. The BoS game conducted with corresponding payoffs in this experiment is shown in Table 3 below. This figure is slightly different from Table 2 as here H denotes for the strategy yielding high payoff while L denotes for the strategy yielding low payoff for both players. This is designed to simplify the game so that players don’t need to memorize payoffs of different strategies for row and column players, as it is symmetric after the modification. Payoffs 50 and 200 are particularly set to increase the conflict between players hence only a few of them, as predicted, would be willing to choose Low payoffs without communication, under the assumption that they are rational and want to maximize their own earnings.
Table 3 Payoff matrix of BoS game
The other
H L
You H 0, 0 200, 50
L 50, 200 0, 0
There are two treatments in each session, namely the sequential communication treatment (S) during which communication is possible and the non-communication treatment (N) where standard BoS games without communication are played. The latter one is a control treatment which measures subjects’ preferences when it is not possible to communicate so that any increment of the results in sequential-communication treatment upon the results in control treatment indicates the effect of communication. In sequential communication treatment, a two-way
sequential communication is available. The intuition in using this scheme instead of two-way simultaneous communication or one-way communication, as are applied in previous researches, is that this method is employed more often in any real-word situation such as firm negotiations and therefore makes more sense. Besides, during the communication subjects are not allowed to identify themselves, neither information of the other player is revealed to them; the games are played under an anonymous context. In each round, participants are randomly paired with another player from the same group, but they would never meet the same player within one treatment, on that account, learning the other player’s behavior is not possible. Besides, in each round of sequential communication treatment, one subject is randomly chosen as the first sender in a pair, who has the option to start the conversation by sending the other player a message or just leave the chat at the very beginning. When the conversation has begun, subjects could send unstructured message (up to 150 characters) to each other and any of them could choose to quit the chat after reading the other player’s last message and subsequently make the decision. The format of message is designed in this way as it corresponds to the real word the best because constrain to content of the communication is seldom seen. However, the communication is not free as total communication cost is calculated based on the sum of messages sent by both players, where the price of each message is 2 points, as in firm negotiations communication do result in costs such as time cost and meeting cost. Below in Table 4 presents the difference between two treatments.
Table 4 Difference between two treatments
Treatment Duration Description
1 Control (N) 10 rounds Subjects make choices directly.
2 Two-way sequential communication (S)
10 rounds Subjects have a chance to communicate with each other sequentially with a cost of 2 points per message.
Since subjects will go through both treatments in one single session, the sequence of treatments should be taken into account as it might lead to different results if a subject begin with different treatments. Therefore, two types of sessions are used in the experiment. The first one begins with S treatment while the second one begins with N treatment. Table 5 summarizes both types. The reason for having two treatments in one particular session instead of using one session as a control treatment
where subjects only play 20 rounds one-shot BoS games without communication is to compare results within subjects so that personal factors like family backgrounds and personalities could be eliminated.
Table 5: Two types of sessions
At the end of each session, after all rounds are finished, a questionnaire regarding subject’s personal information like study, gender and age, and experiment feedback like their feeling towards the games and lying actions is filled by participant. The complete questionnaire will be provided in the appendix as well.
As in many experiments, monetary incentive is used to motivate subjects to play the game actively. In order to make them treat every round equally and seriously, only payoffs of 4 out of total 20 rounds are randomly chosen to be paid. This information is also provided in the instruction.
4. Hypotheses
The following theoretical hypotheses are all relevant to answer the research questions. Hypothesis 1 will focus on the effect of communication on coordination where as hypothesis 2 and 3 put emphasis on gender differences in BoS with and without communication where the former on individual choices while the latter on pairwise payoffs.
Hypothesis 1: Payoff is improved when communication is possible in BoS.
If participants hold selfish preferences, then This conjecture is in line with the finding in previous studies (Dawes, et al, 1977, Cooper, et al, 1989, and Blume & Ortmann, 2007). However, as the research question of this paper centers at the different communication effects across gender, it does not make sense to carry on the analysis if communication does not bring significant improvement to the game.
Hypothesis 2: The percentage of males choosing a higher share (choosing H) is Round 1-5 6-10 11-15 16-20
Type 1 S N S N
larger than the percentage of females when communication exists.
As Nowell and Tinkler (1994) put forward in their study, females are more cooperative than males, it is fair to predict that females will choose L more often than males. Despite this, Holm (2000) also points out that males are more hawkish than females so that they would take the risk of wining nothing to choose H in BoS. Therefore, the proportion of males choosing H might be higher than females.
Hypothesis 3: Pairwise payoffs differ across gender-interaction pairs only when
communicate is available in BoS.
Without communication, all the participants are assumed have the same behavioral pattern; they will randomly choose between High and Low as their opponent players’ actions are unpredictable, which replicates the standard model of BoS game. This is because in this research, it is assumed that when subjects’ preferences will not be affected if they cannot communicate.
Under cases when it is possible to communicate, the different communicating strategies and styles presented by females and males, which will inevitably lead to distinct outcomes, should be taken into account when analyzing the results. Therefore, theoretically speaking, the average payoff among female-female pairs, female-male pairs and male-male pairs should be different. Moreover, as presented in some studies that females are more cooperative, it is possible that female-female pairs would have the highest mean payoffs while male-male pairs would have the least. However, it is not necessary that the mean payoffs of all three gender-interaction pairs are different.
If final results are in line with these predictions, the answer of research questions could be provided by this experiment.
5. Analyses of Results
The analysis of the results of this research includes 95 of the 96 participants because one subject did not provide his/her gender in the questionnaire. This section will therefore discuss data gathered in the remaining 95 participants. Almost half of the subjects are female (45.26%) and their mean age is 21.93 (Std. Dev.=2.34). Since each participant played 20 rounds, in total there were 960 observations in treatment 1 and 940 observations in treatment 2. Observation consists of the decision and payoff
of one subject in a single round.
In section 5.1 the main results of this study, an overview of the observed decisions and payoffs will be presented and discussed. Section 5.2 will focus on the first research question, which is “Will pre-play two-way communication increase coordination in Battle of Sexes games?” Later in section 5.3 an analysis of results, regarding the second research question “Does communication effect in Battle of Sexes games differ across gender?” Lastly section 5.4 summarizes all the results.
5.1 Main Results
The descriptive statistics in Table 6 shows several differences between two treatments. First, the mean payoff in treatment 2 (97.97) is higher than that of treatment 1 (53.65). Besides, the proportion choosing strategy H in treatment 1 (70.21%) is higher than the proportion choosing it in treatment 2(58.83%). Correspondingly, the percentage of reaching equilibrium in treatment 2 (80.64%) is also higher than that of treatment 1(42.92%). The outcomes indicate that communication improves coordination in BoS. Table 6 Overview of game outcomes
Treatment Number of observations Mean individual payoff Proportion choosing H Percentages equilibrium 1.No communication 960 53.65 (79.05) 70.21% (0.46) 42.92% (49.52%) 2.Two-way sequential communication 940 97.97 (83.72) 58.83% (0.49) 80.64% (39.53%)
Apart from differences between treatments, gender differences also worth noting. Below in Table 7 shows the proportion females and males choosing strategy H in both treatments. Proportion of choosing H does not significantly differ between males (71.86%) and females (68.87%) in non-communication treatment while males have a higher chance to choose H (64.64%) than females (54%) when they both have the opportunity to communicate. Moreover, in sequential communication treatment, 14.87% less females chose strategy H while only 7.18% less males did so. This outcome indicates that males are tougher when there are conflicts of interests.
Table 7 Proportion choosing H summary
Treatment 1. Non-communication 2.Sequential communication Probability female choosing H 68.87%
(0.46)
54% (0.50)
Probability male choosing H 71.86% (0.45)
64.64% (0.48)
Probability choosing H total 70.21% (0.46)
58.83% (0.49)
However, with respect to the ratio of equilibrium play, gender seems has no effect. As shown in Table 8, the ratio of achieving equilibrium in BoS game is 0.429 in non-communication treatment and 0.806 in sequential communication treatment. Besides, there is no gender difference within each treatment concerning the ratio of equilibrium play.
Table 8 Equilibrium play ratio
Treatment Female-Female pair Female-Male pair Male-Male pair Total 1.Non-communication 0.429 (0.495) 0.430 (0.495) 0.428 (0.495) 0.429 (0.495) 2.Sequential communication 0.810 (0.393) 0.806 (0.395) 0.806 (0.396) 0.806 (0.395)
5.2 Analyses of communication in Battle of Sexes game
From the analysis of the main results of the experiment, it is obvious that there are noteworthy differences between two treatments. In this section, statistical tests will be performed to ensure whether these differences are significant. As the sample sizes of both treatments are larger than 30, we could assume that they are normally distributed, according to Central Limit Theorem. Because the BoS game played was one-shot and subjects would never meet the same opponent player again, our observations are completely independent. Therefore, t-test will be performed. Moreover, as gender-interaction pair is used to categorize the observations, it makes more sense to look at pairwise total payoffs instead of individual payoffs.
The first research question can be formulated into hypothesis as “Mean payoff is improved when communication is possible”. Below in Table 9 presents the mean total payoffs of both treatments.
Table 9: Mean total payoff of both treatments
Treatment Mean total payoff Observations 1.Non-communication 197.29 (123.87) 480 2.Sequential communication 195.94 (99.43) 470
By observing Table 10 we could reject the null hypothesis +,: !' = !", where 1 refers to non-communication treat while 2 refers to sequential communication treatment, at one-tailed significance 0.000. Thus we could conclude that with communication, the mean total payoff increased significantly.
Table 10: Test statistics for t-test - Hypothesis 1
Test statistics
Non-communication- Sequential communication
t 12.1762
Pr(T>t) 0.0000
5.3 Analyses of gender difference
As briefly mentioned in main results, the probability of females and males choosing H in BoS is different when communication is present. This is the same as predicted in hypothesis 2. At significant level of 0.0010 we could well reject the null hypothesis that +,: !/,1 = !/,2. We could draw a conclusion that males tend to make a choice that will yield higher payoff for themselves more frequently.
Table 11: Test statistics for t-test - Hypothesis 2
Test statistics
Female- Male
t -3.329
Pr(T<t) 0.0005
From main results we could find some gender differences about subjects’ decisions but no obvious difference about the ratio of equilibrium play. However, in order to answer the second research question, mean payoff should be considered as the parameter to measure participants’ coordination performance. Therefore, the
question can be interpreted as Hypothesis 3: Pairwise payoff differs across gender-interaction pairs only when it is possible to communicate. However, directly perform a test against this hypothesis is too complicated. It could be broken into two sub-hypotheses, namely “sub-hypothesis 1: payoff does not differ across gender-interaction pairs with communication” and “sub-hypothesis 2: payoff differs across gender-interaction pairs with communication”. This is because if there are no gender differences without communication in mean payoff but if there are with communication, we could infer that there are gender difference in effect brought by communication.
Table 12: Summary of pairwise payoffs
Treatment Gender-interaction pair Mean payoff Observations 1.Non-communication Female-Female 106.64 (124.08) 143 Male-Female 108.61 (124.18) 244 Male-Male 104.84 (124.03) 93 2.Sequential communication Female-Female 211.71 (85.30) 136 Male-Female 195.37 (100.00) 241 Male-Male 174.34 (113.12) 93 Sub-hypothesis 1: +,: !11," = !22,"= !21," +": 34 5634 786 !397:: ;< =;::6>684 :>7? 4ℎ6 74ℎ6>
First comes the two tests for sub-hypothesis 1. As rank-sum test is only able to compare the mean between two groups, a comparison between female-female pairs and male-male pairs, and a comparison between female-male pairs and male-male pairs will be made. The one-tailed significance for H,: !21,"= !11," is 0.8807, as shown in Table 13, which do not reject the null hypothesis. Therefore, we could infer that the mean payoff between female-female pairs is not significantly different from female-male pairs. Next, again from Table 13 we can observe that we are not able to reject null hypothesis +,: !22," = !21," at significance level of 0.9131. Therefore, it can be inferred that the mean payoff between female-male pairs and male-male pairs
are not significantly different. By combining the results of these two sub-hypotheses, we could conclude that there is no statistically significant evidence to infer that mean payoffs among different gender-interaction pairs are different when subjects had no chance to communicate.
Table 13: Test statistics for t-test – Sub-hypothesis 1 of Hypothesis 3
Test statistics FF,1-MF,1 MF,1-MM,1 t -0.1502 0.1092 Pr(|T|>|t|) 0.8807 0.9131 Sub-hypothesis 2: +,: !11,' = !22,'= !21,' +": 34 5634 786 !397:: ;< =;::6>684 :>7? 4ℎ6 74ℎ6>
Similar tests as in sub-hypothesis 1 are done here. We could reject the null hypothesis that H,: !11,' = !21,' at a significant level of 0.0473. Hence, a conclusion that mean payoffs of female-female pairs are significantly higher than the mean payoffs of female-male pairs can be drawn. In spite of that, at a significant level of 0.0038, the hull hypothesis H,: !11,' = !22,' could also be rejected. Moreover, a
comparable conclusion as above is drawn between female-male pairs and male-male pairs since the significant level is 0.0591 of null hypothesis H,: !21,'= !22,'. The test-statistic of this hypothesis is shown in Table 14. Looking at the results of sub-hypothesis 2, we could infer that there are gender-related differences with respect to mean payoffs when communication is possible. In addition, the mean total payoff of female-female pairs is significantly higher than the rest of two gender-interaction pairs. An overview of the test statistics of sub-hypothesis 2 can be found in Table 14.
Table 14: Test statistics for t-test – Sub-hypothesis 2 of Hypothesis 3
Test statistics
Hypothesis FF,2-MF,2 FF,2-MM,2 MF,2-MM,2
t 1.6762 2.7027 1.5711
Pr(T>t) 0.0473 0.0038 0.0591
In summary, males, compared to females, are more likely to choose H when communication exists. When communication is not possible, in each gender-interaction pairs, pairwise mean payoffs are not significantly different, however, when subjects could choose to communicate, mean payoffs vary across
gender-interaction pairs, from which we could conclude communication effect in BoS games differ across gender.
5.4 Summary of results
In general, the finding is similar to previous studies of communication effect in coordination games (Dawes, et al, 1977, Cooper, et al, 1989, and Blume & Ortmann, 2007) that it could improve coordination significantly. Unlike the cheap talk used in these studies, our experiment related a small amount of cost with the communication. The effect of communication, however, did not change with this modification. From significance level of 0.000 we could draw this conclusion. Nevertheless, the measurement of coordination deviated a bit from the studies by Dawes, et al (1977) and Cooper, et al (1989) as they measured coordination rates whereas payoffs were evaluated in this research.
In addition, which is also the main finding of this research, gender differences regarding pairwise total payoffs are evident in the experiment. Different from previous studies that also found gender difference in games (Croson & Buchan, 1999, Nowell & Tinkler, 1994, and Holm, 2000), this experiment was run anonymously (that is, opponent players’ personal information was not revealed to subjects). To be specific, it is found that males have higher chance to choose larger share(H) for themselves, which is to some degree in line with the finding of Holm (2000) and Nowell and Tinkler (1994). Besides, the pairwise mean payoffs of female-female matched players (211.71) were higher than rest of the two pairs. Moreover, no gender differences were found when communication is impossible.
6. Conclusion
In this research, effort has been made to answer the question whether communication will improve the coordination in the Battle of Sexes games. Moreover, we also find investigated whether female and males have different preferences in making their decisions. Apart from that, results from the experiment provide some insight on what role gender plays when a pre-play communication is added in the Battle of Sexes games. Overall this research presents some novel aspects of gender in Battle of Sexes games even under a player-player anonymous context. In section 6.1 answers of the
research questions will be provided. In section 6.2 are some suggestions for further researches.
6.1 Conclusion of results
Not surprisingly, communication indeed can improve coordination in Battle of Sexes game as pairwise payoff is significantly higher in sequential-communication treatment. On top of that, males have a higher chance to choose H which is the larger share in equilibria, therefore we could conclude that maybe females are more cooperative than males when communication is available. As a consequence of this conscious, pairwise mean payoff of female-female matched payers is also the highest among all three gender-interaction pairs. Hence, we could conclude that gender plays a role when communication improves coordination, and from the result of this paper, it could be inferred that females tend to get more benefits in coordination than males. However, to what extent does effect of gender have is unknown and could not be explained by this experiment.
6.2 Recommendation for further research
It would be interesting to split the effect of gender with other factors like education backgrounds, family backgrounds, age, country of origin, etc. Nevertheless, all subjects were students at the University of Amsterdam, social-related factors were not that significant in our experiment, also age was quite small ranged, only from 18 to 28. Besides, most of the subjects were from the Faculty of Business and Economics so we could assume that they had some knowledge of game theory and probably some students played mixed-strategy regardless of the chance to communicate. Therefore, for further research it is advised to recruit a more diverse pool of subjects from all work.
Moreover, it is worth investigating why gender difference presents even when subjects do not know the gender of the other player. Are females naturally more cooperative or this is nurtured by the social environment. Perhaps a treatment with face to face communication or video communication could be added to this experiment to answer the question.
References
Blume, & Ortmann. (2007). The effects of costless pre-play communication: Experimental evidence from games with Pareto-ranked equilibria. Journal of
Economic Theory, 132(1), 274-290.
Brandts, J., & Cooper, D. (2007). It’s What You Say, Not What You Pay: An Experimental Study of Manager-employee Relationships in Overcoming Coordination Failure. Journal of the European Economic Association, 5(6), 1223-1268
Camerer, C. (2003). Behavioral game theory: Experiments in strategic interaction. New York, NY: Russell Sage Foundation.
Cooper, R., DeJong, D.V., Forsythe, R., & Ross, T.W. (1989). Communication in the Battle of the Sexes Games: Some Experimental Results. RAND Journal of
Economics, 20(4), 568-587
Croson, R., & Buchan, N. (1999). Gender and Culture: International Experimental Evidence from Trust Games. American Economic Review, 89(2),386-391. Dawes, R.M., McTavish, J., & Shaklee, H. (1977). Behavior Communication and
Assumptions about Other People’s Behavior in a Commons Dilemma Situation.
Personality and Social Psychology, 35(1), 1-11
Holm, H ̊akan J. (2000). Gender-Based Focal Points. Games and Economic Behavior, 32, 292-314
Mason, Charles F., Phillips, Owen R., & Redington, Douglas B. (1991). The role of gender in a noncooperative game. Journal of Economic Behavior &
Organization, 15(2), 215-235
Nowell, C., & Tinkler, S. (1994). The influence of gender on the provision of a public good. Journal of Economics Behavior and Organization, 25, 25-36
Houser, D., & Wang, S. (2009). Demanding or Deferring? The Economic Value of Communication with Attitude (Working Paper No.15-57). Retrieved from Social Science Research Network website http://dx.doi.org/10.2139/ssrn.2701558
Appendix: Instructions of the game
Welcome
Welcome to this experiment on decision-making. Please read the following instructions carefully.
During the experiment, do not communicate with other participants unless we explicitly ask you to do so. If you have any question at any time, please raise your hand, and an experimenter will come and assist you privately.
Your earnings depend on your own choices and the choices of other participants.
During the experiment, your earnings are denoted in points. At the start of the experiment you will receive a starting capital of 300 points. In addition you can earn points during the experiment. At the end of the experiment, your earnings will be converted to euros at the rate: 1 point = € 0.025. Hence, 40 points are equal to 1 euro. Your earnings will be paid to you privately.
Instructions 1
There are two pages of instructions. You can go back and forth by using the menu on top of the screen. A summary of these instructions will be distributed before the experiment starts.
You will be randomly matched with another person in the room. Each person will make a choice between H and L. If you and the other person both choose H, you will both receive nothing. If you choose H and the other person chooses L, then you receive 200 points and the other person receives 50 points. If you choose L and the other person chooses H, then you receive 50 points and the other person receives 200 points. If you and the other person both choose L, you will both receive 0 points.
The possible decisions and payoffs are also shown in the following matrix. In each cell of the matrix, the first number shows the amount of points for you (in red), and
the second number shows the amount of points for the other participant (in blue). The other H L You H 0, 0 200, 50 L 50, 200 0, 0
In total, there will be 20 rounds. In each round, you are randomly rematched to another participant.
At the end of each round, you will receive feedback about the decision of the other person and your payoffs.
Instructions 2
In some rounds, you and the other person will have the opportunity to communicate before deciding between H and L. This happens in rounds 6-10 and 16-20.
The communication works as follows. You and the other person can send messages to each other. There are four important rules for the communication:
1) Only one person can send a message at a time. It will be randomly determined who can send the first message (you and the other person have an equal chance on being able to send the first message, independent of what happened in previous rounds). After that, you will take turns.
2) Each of you have to pay 2 points for every message that is sent, no matter who sent the message. These points will be subtracted from your earnings.
It is possible that your earnings in a round are negative. Any losses will be deducted from your starting capital.
3) If it is your turn to send a message, you can also decide not to send any messages (by clicking on the “Leave chat” button). This will end the communication without affecting any of your earnings, and you and the other person will not be able to send any more messages in that round.
4) You are not allowed to identify yourself in any way. If you identify yourself (for instance, by giving your name or describing what you look like or what you are wearing) you will be excluded from the experiment and lose all earnings including the starting capital.
In the rounds with communication, you will be paired with a different person in each round, so you will never chat with the same person twice. Likewise, in the rounds without communication, you will also be paired with a different person in each round, so you will never meet the same person twice in these rounds.
At the end of the experiment, 4 out of the 20 rounds will be randomly selected for payment. Your earnings equal the sum of the starting capital 300 points and your earnings in the 4 selected rounds. If your total earnings are negative, you will receive 0.
You have now reached the end of the instructions. If you have fully understood the instructions, please click “continue.”
Quiz Questions
Before the experiment starts, we will ask you some questions to check your understanding. You can go back to the instructions by clicking on the menu at the top of the screen.
The following statements deal with the rounds with communication; which one is true:
o I will always be matched with the same person o I might be matched with the same person twice
o I will never be matched with the same person more than once
Suppose you are in a round with communication, and you are assigned first sender in the first round. What will happen in the next round?
o I will still be a first sender
o I might be a first sender or a second sender
o I will be a second sender
Fill in the blanks:
This experiment consists of __ rounds, and __ rounds will be randomly selected for payment.
Suppose that you are in a round without communication. If you and the other person both choose L, what are your payoffs in points? __ points.
Suppose that you are in a round with communication. If you and the other person both choose H, and you and the other person have sent 3 messages in total, what are your payoffs in points? __ points.
Instructions summary
There are 20 rounds in this experiment. In each round, you will be randomly paired with another participant.
In each round, both of you will take a decision between H and L. The possible decisions and payoffs are shown in the following matrix.
The other
H L
You
H 0, 0 200, 50
L 50, 200 0, 0
In rounds 1-5 and 11-15, you will take a decision without communicating. Your payoffs only depend on your decision and the decision of the other person.
In rounds 6-10 and 16-20, you and the other person will have the opportunity to communicate before taking your decision. Your payoffs depend on your decision, the decision of the other person, and the total number of messages.
In a communication round, one of you will randomly be assigned to be the first sender. You can send messages in turn. Each message costs both you and the other person 5 points.
In the rounds that allow communication, you will NEVER be matched with the same person more than once. In the rounds that do not allow communication, you will also NEVER be matched with the same person more than once.
At the end of the experiment, 4 rounds will be randomly selected for payment. Your earnings equal the sum of the starting capital 300 points and your earnings in these 4 rounds.
Round 1
In this round you
cannot communicate
with the other participant.
Please take a decision.
The other H L You H 0, 0 120, 40 L 40, 120 60, 60 Your decision: H L
Results round 1:
Your decision was L, the decision of the other person was L
Your payoffs are 60 and the payoffs of the other person are 60
To the next round
Round 6
You are randomly selected as the second sender.
The other H L You H 0, 0 120, 40 L 40, 120 60, 60To the communication
Chat History and Decision
You left the chat. You can take a decision now.
Other H L You H 0, 0 120, 40 L 40, 120 60, 60 Your decision: H L OK
You and the other person have sent 2 messages in total. This table below shows you the chat history.
Number Sender The message
1 You hello
Appendix: Questionnaire
Questionnaire
Please fill in this short questionnaireAge: __ Gender:
o Male o Female
I study at: (choose from list)
How did you make your decisions when you could not communicate with the other? How did you make your decisions when you could communicate with the other? Have you ever reached agreement with the other during the communication?
o Yes o No
If so, how bad did you or would you feel if you deviated from the agreement? (1 is not bad at all, 7 is very bad)
1 2 3 4 5 6 7
Not bad at all
Very bad
If so, how bad did you or would you feel if the other deviated from the agreement? (1 is not bad at all, 7 is very bad)
1 2 3 4 5 6 7
Not bad at all
Very bad
If you mentioned that you would choose H but did not reach agreement, how bad did or would you feel if you would choose L?
Not bad at all
Very bad
Your earnings
The following 4 rounds are randomly selected for payment.
Round Your decision Decision Other Earnings
4 H L 120
8 H H -10
13 L H 40
19 L L 50
Total points: 200
Your earnings in euros are: (200+150)*0.05 = 17.50.
Thank you
Thank you for your participation in this experiment. Please remain seated until your table number is called.
If your table number is called, please bring your yellow card with the table number and you will receive your payment.
