GENDER DIFFERENCES IN THE ULTIMATUM GAME.

SOLNICK, SARA J.

SARA J. SOLNICK [*]

I explore the behavior of men and women in the ultimatum game. In one treatment, players remain mutually anonymous. In the second treatment, players' gender is common knowledge. Average offers made do not differ based on the gender of player 1. Offers are affected by the gender of player 2, with men attracting higher offers, particularly from female players 1. Players 2 of both genders choose a higher minimum acceptable offer when facing a female player 1. These patterns led to substantial differences in earnings. Such striking differences in expectations and decisions could impact salary negotiations and other real-world transactions. (JEL C78, C92, J16)

1. INTRODUCTION

The gender gap in wages has been a persistent feature of the labor market (Goldin, 1990). Women consistently earn less than men, even after controlling for a variety of human capital factors. Socialization before encountering the labor market may affect the divergent labor market outcomes of women and men (Corcoran and Courant, 1987). One contributing factor to women's lower wages that has not been explored may be different expectations and outcomes in bargaining. For many jobs, the market does not completely specify the wage. There is a "zone of indeterminacy," allowing the wage setter room to negotiate (Rees, 1993). In general, women may end up with a smaller share of the portion of wages that is up for grabs. Gerhart and Rynes (1991) found that male and female MBA students were equally likely to negotiate about their starting salaries. On average, men obtained increases of 4.3% over the initial offer, while women raised their salaries by only 2.7%. The differential negotiation outcomes accounted for 16% o f the male advantage in starting salary.

Different abilities and expectations in bargaining can also affect the prices men and women pay as consumers when haggling is possible. In an experiment on discrimination in consumer-goods markets, testers were trained to bargain for new cars (Ayres, 1991, 1995; Ayres and Siegelman, 1995). Males received significantly lower initial offers and final prices after negotiating in a prescribed manner. Ayres attributed these results partly to factors specific to the car market, such as a lack of awareness by some groups that haggling over the price of a new car is expected. An alternative possibility is a widespread attitude among both women and men, perhaps based on decades of women's worse labor market experience, that women will be satisfied with less. Such an attitude could affect the wages offered to women whenever salary negotiation takes place.

I search for differences in bargaining by men and women that may affect wages and other economic outcomes by exploring behavior in a stylized setting: the ultimatum game. The ultimatum game has been the basis for many experimental investigations (reviewed in Thaler [1988] and Roth [1995]). In the simplest form of the ultimatum game, one player proposes an allocation of a fixed sum of money. The second player may either accept the proposal, in which case the funds are divided accordingly, or reject it, in which case both receive nothing. [1] Outcomes rarely match what is expected from standard economic theory for the one-shot game, which indicates a token offer being made and accepted.

The experiment reported in this paper involves two treatments of the ultimatum game. In each case I recorded the gender of the players. In the first treatment, players remain mutually anonymous. In the second treatment, the gender of the players is common knowledge. I examine how behavior is affected by the gender of the players under these conditions.

I find that men and women both make lower offers to women and both men and women chose higher minimum acceptable offers when player 1 is a woman. Players 1 seem to believe that women will accept a smaller amount than men will. As a consequence of these patterns, men in the experiment earn more than women, with men paired with women gaining the most. The results are consistent with the evidence that women are asked to pay more for cars and that women gain smaller increases in salary when they choose to bargain.

II. LITERATURE REVIEW

Gender Differences in Bargaining Experiments

Various laboratory experiments have examined the effect of gender in bargaining and strategic behavior, with mixed results (Ball and Cech, 1996). Some experiments require subjects to represent firms that are buying or selling. In one study, men and women negotiated with the same degree of contentiousness and achieved similar results (Pruitt et al., 1986). In another study, however, men negotiated more effectively than women, particularly as sellers (King and Hinson, 1994).

A study that required business students to prepare for a hypothetical job interview compared expected pay and planned negotiation strategies between men and women (Kaman and Hartel, 1994). The opening bid, the highest offer that the person planned to refuse, and the salary the person intended to settle on were higher for men than for women. These tactics would presumably lead to their achieving higher salaries. In another study of MBA students, subjects bargained over salary with a trained confederate of the experimenter, who rewarded them for specific behaviors (Stevens et al., 1993). Women set lower goals for themselves and negotiated lower salaries.

These studies did not include controls, such as for human capital. Subjects were all business students, but even among such a homogenous group, there can be important gender differences in achievement and specialization that can lead to different labor market outcomes (Wood et al., 1993; Fuller and Schoenberger, 1991). Women's lower opening bids and final negotiated salaries may have been caused by their legitimate belief that they were less qualified for the position or men's legitimate belief that they would work hard and justify the high salary.

In addition, the subjects may set their goals based on their knowledge of the typical salary earned in their industry, comparing themselves primarily to workers of the same gender. If so, these findings would merely reflect (rather than explain), the gender gap in the real world. The abstract nature of the ultimatum game allows us to examine gender differences in an environment where subjects have little experience and few assumptions.

Ultimatum Findings

The ultimatum game is both simple and abstract. Its simplicity gives subjects room for individual interpretation. Players can take different views over to what extent it is fair for player 1 to take advantage of the position of power. Numerous renditions of the ultimatum game, with a variety of conditions, have established that substantial offers are often made and sometimes rejected (Camerer and Thaler, 1995). [2] Offers average 30%-40% of the total with even splits generally the mode. Offers of less than 20% are commonly rejected.

Interpretations of the game might differ systematically between the sexes. The game has the potential to reveal gender-based differences in attitudes and expectations that might affect real economic transactions, such as with employers, salespeople, real estate agents, and landlords. Only a handful of previous studies of the ultimatum game have drawn any distinctions among subjects and examined how individual differences affect ultimatum play.

Roth et al. (1991) conducted ultimatum experiments in four countries--Israel, Yugoslavia, the United States, and Japan--and discovered differences in offers and rejection rates that they attribute to cultural factors. Students in a psychology class appear both to behave differently from students in a commerce class and to treat opponents in another psychology class differently from opponents in a commerce class. When matched with psychology students, psychology students made higher offers, were more likely to offer an even split, and stated higher minimum acceptable offers than commerce students (Kahneman et al., 1986a). Carter and Irons (1991) found that economics majors conformed more closely to the theoretical predictions than nonmajors. However, other investigators have not found differences by field of study (Kagel et al., 1996).

A few ultimatum studies include findings on subjects' gender, although it is not the main variable of interest. In an investigation of ultimatum play by children, girls from kindergarten to ninth grade tended to make more generous offers than boys (Murnighan and Saxon, 1998). In a high-stakes ultimatum game played in Slovakia, men were less likely to reject offers (Slonim and Roth, 1995). Other gender differences in these studies were not reported. In neither experiment did players know the gender of their partner.

Eckel and Grossman (2001) conducted the first ultimatum experiment designed explicitly to test for gender effects. Although the gender of player 1 did not affect the size of the offer, the gender of player 2 did, with men receiving higher offers. Men were more likely to reject offers. Both men and women were more likely to accept offers from women, which the authors label "chivalry" in the case of men and "solidarity" in the case of women. They conclude that women have different social norms about fairness than men.

An unusual feature of the experimental method may have affected these results. Eckel and Grossman put the parties face to face, in groups of four. For example, four women might be seated across from four men. None of the women would know which man was her partner, but each would know that she was paired with a man. In another case, four women might be seated across from a group consisting of two men and two women. The four women in this case would not know whether they were paired with a man or a woman.

In most bargaining experiments, players are not placed face to face, even in groups that serve to shield the precise identity of the partner, because the situation is charged and uncontrolled (Guth et al., 1982). Manners may play a more important role in this setting (Camerer and Thaler, 1995), leading to higher offers and fewer rejections. Women might feel the pressure of manners more strongly, increasing the gender difference in the probability of accepting an offer.

In addition, Eckel and Grossman used the game method. Although there do not appear to be any studies directly comparing the two methods, let alone how they affect men versus women, it is possible that the use of the game method also magnified gender differences. In the game method, player 2 knows precisely how his or her choice will affect the outcome. A rejection leads directly to both parties leaving the table empty-handed. In the strategy method, the outcome depends on player 1's offer, which is not known. Women, wishing to avoid conflict (Brown and Gilligan, 1992), may try to ensure that the bargainers both gain something, even at a cost to themselves of accepting a low offer. This desire for conflict reduction or avoidance may have been intensified by the face-to-face nature of the encounter.

In some ways, this experimental design lends itself to comparisons with real-world interactions. Many negotiations do take place face to face. However, the experiment also has drawbacks, making it less comparable to natural bargaining situations. In particular, the setting, with four people of the same gender across from four of the opposite gender, for example, may have alerted subjects that gender was a critical variable. The sense that they were representing their gender may have led subjects to behave uncharacteristically. [3]

I prevented players from seeing their partners. In one treatment I collected data on behavior by men and women when players were labeled by number and thus did not know each other's gender. In the other treatment, first names, rather than visual inspection, conveyed gender information to the players. I hoped that using first names to label the players would appear natural and that subjects would not realize or guess that gender was a variable of interest. By introducing gender information in an unobtrusive way, I attempted to isolate the differences in bargaining from the effects of social interaction.

III. METHODS

The ultimatum game was played one time, for $10. Subjects were recruited at the University of Pennsylvania by class announcements, flyers posted and handed out around campus, and advertisements on local Internet bulletin boards and in the campus newspaper. They were paid a $2 show-up fee and their winnings from the game, if any. They came in groups to the experiment room. The room was divided nearly in two by a divider, which separated players 1 from players 2. Players on both sides could see the experimenter and the blackboard, but they could not see the players on the other side. As subjects arrived, they were assigned to one or the other side of the room arbitrarily in an effort to keep equal numbers on the two sides.

Each subject had a folder at his or her place, containing instructions, the decision page, and a brief questionnaire regarding the decision, attitudes about fairness, and demographics (materials available from author). The decision page for players 1 allowed them to record their proposed division of the money (the offer to player 2 is analyzed here). The decision page for players 2 allowed them to record their minimum acceptable offer. The bottom of both decision pages provided room for the experimenter to record the outcome of the interaction. After decisions were made, subjects completed a questionnaire describing the factors that entered into the decision, what the player imagined the other player would do and what the player would do if the roles were reversed. Subjects also answered five questions on fairness (drawn from Kahneman et al. [1986b]) and demographic questions including the player's sex, age, year in school, major, coursework in mathematics and economics, and race.

The experimenter read the instructions aloud, displayed on the blackboard how subjects would be matched, [4] and answered questions. The subjects made their decisions simultaneously, using the strategy method. The experimenter and assistant collected the decision pages, matched them in the pairs that had been announced, recorded the outcome on both pages, and prepared the payments. Meanwhile, the subjects answered the questionnaire. When subjects had completed the questions, they were shown the outcome of the interaction, given their payment in an envelope, and released. Each session lasted approximately half an hour.

Two treatments of the experiment were conducted. In the "number" condition, subjects were given numbers ranging from 101 to 115 for players 1 and 201 to 215 for players 2. Pairs of numbers were displayed on the blackboard. Since I collected the data on players' gender but did not reveal it to the players, this version of the game allowed examination of the effect of gender on play when the players do not know each other's gender.

In the "name" condition, the first names of the subjects were used to identify the pairs. An effort was made to allow only subjects with gender-identifying first names to attend the name sessions. [5] However, it was at times impossible to prevent subjects with unrevealing first names from participating while concealing the nature of the experiment. In some cases subjects with unrevealing first names did play, but data from these pairs was discarded, since the experiment is based on common knowledge of the other player's gender.

t-tests and Wilcoxon tests are used to compare average offer and minimum acceptable offers among the different groups. t-tests compare distributions by comparing mean values, and the Wilcoxon test compares medians. While the t-test assumes that the data follow a normal distribution, the Wilcoxon test does not make any assumptions about the distribution of the sample and is not affected by the magnitude of any outliers. The Wilcoxon test is commonly used in analyzing results for ultimatum games because the data are often far from normally distributed and perhaps not even unimodal. In this experiment, the data were unimodal but not normal (in a Kolmogorov-Smirnov test). However, since the t-test is robust to deviations from normality, it is an appropriate measure of the significance of differences. z-tests of proportion are used to compare percentages of equal offers and rejections in the different groups.

IV. RESULTS AND DISCUSSION

Data were collected for 89 pairs of subjects (Table 1). Twenty-four pairs were in the number condition. Sixty-five pairs were in the name condition, in which players knew one another's gender. The first row of Table 1 shows that 48 men participated as player 1. Thirty-six of the male players 2 were in the name treatment, where 22 were paired with a man and 14 were paired with a woman. The remaining 12 male players 1 took part in the number treatment and did not know player 2's gender. The second row of Table 1 shows that there were 16 pairs of female player 1 and male player 2, 13 female-female pairs in the name condition, and 12 female players 1 in the number condition. The third row of Table 1 shows that the 24 players 2 in the number condition were comprised of 14 men and 10 women. The vast majority of subjects were undergraduates, but some graduate students and other associates of the university also participated.

Average offers made do not differ based on the gender of player 1 or whether the game is played in the name or the number condition (Table 2). Overall, the average offer made by male players 1 was $4.67 and by female players 1 was $4.68. In each treatment, the average offer was $4.68. There is a strong tendency to offer an even split of the money, with 71% of players 1 offering $5 or more (Table 3).

Offers do appear to be affected by the gender of player 2, with men attracting more generous offers, particularly from female players 1 (Table 2). Men offered $4.73 to male players 2 and only $4.43 to female players 2 (see row 1). The average offer to men from female players 1 exceeded $5 (average = $5.13). One female player 1 matched with a male player 2 consciously gave away the entire $10 (in answer to the question about her decision, she wrote, "I want at least one of us to get something"). All other female players 1 facing male players 2 offered either $4 or $5; the average of these offers is $4.80. By contrast, the average offer in the female-female pairs was $4.31 (see row 2).

Overall, offers to men averaged $4.89, while offers to women averaged $4.37 (see row 3) (p = .08 in t-test and Wilcoxon test for the difference between men and women). [6] Men received offers of $5 or more 82% of the time, while women received equal or favorable splits in only 59% of cases (p = .05 in z-test of proportions) (Table 3, bottom row).

The lower offers to women could mean that players 1 expect female players 2 to demand less by recording a lower minimum acceptable offer. When players 1 were asked what they imagined player 2's minimum acceptable offer to be, they predicted $3.90 for male players 2 and $3.71 for female players 2. However, not only are these expected minimum acceptable offers not significantly different, female players 1 actually predicted a higher minimum for female players 2 than for male players 2.

On the demand side, minimum acceptable offers were very similar when players knew each other's gender (average = $3.10) and when they did not (average = $2.96) (Table 4). Female players 2 may make higher minimum acceptable offers than male players 2 (average $3.42 versus average $2.81, bottom row, p = .10 in t-test and p = .14 in Wilcoxon test for the difference between men and women). Women's minimum acceptable offers are higher than men's for each type of player 1: male, female, and unknown gender (comparing columns 1 and 2).

Although some previous research has found that women were more likely than men to reject ultimatum offers (Slonim and Roth, 1995), the study that focused specifically on the effect of gender on ultimatum game found that women were more likely to accept at any given level of offer (Eckel and Grossman, 2001). I have found women to have equal or perhaps greater minimum acceptable offers, implying that they are more likely to reject.

This discrepancy might be due to the differences in experiment design. Perhaps when their decision has a direct effect on the outcome and the other player is visible, as in the method used by Eckel and Grossman, female players 2 are reluctant to reject and cause both players to receive nothing. However, when the impact of their decision is less obvious, as in the strategy method employed in this article, female players 2 consider primarily their wish to receive a fair portion of the pie. In future research, to test the effect of method, it would be necessary to replicate the Eckel and Grossman finding using their method and then conduct treatments in which players were separated but used the game method, or in which players were face to face but used the strategy method, or both.

Female players 1 elicit higher minimum acceptable offers than male players 1 (average $3.73 versus average $2.59 in first two rows of column 3, Table 4, p = .006 in t-test and p = .01 in Wilcoxon test for the difference between male and female players 1), regardless of the gender of player 2. Female players 2 demanded $4.15 on average from female players 1, but only $2.82 on average from male players 1 (column 2) (p = .05 in t-test and p = .06 in Wilcoxon test for the difference by type of player 1). Male players 2 demanded $3.39 on average from female players 1, but only $2.45 on average from male players 1 (column 1) (p = .07 in t-test and p = .09 in Wilcoxon test for the difference by type of player 1).

The finding that players 2 of both genders choose a higher minimum acceptable offer when facing a female player 1 indicates that people seem to expect or require a greater level of fairness or generosity from women than from men. When asked what they imagined player 1's offer to be, they predicted higher offers from women (average = $4.25) than from men (average = $4.15). But as with the minimum acceptable offers predicted by player 1, the difference by gender of player 1 is not significant, and female players 2 actually expected men to be more generous in the role of player 1 than women, on average.

On average, players 2 will accept $3 from a man, but will reject that amount from a woman. But men and women did not differ in their behavior as player 1. Both sexes made substantial offers and were somewhat more generous toward men than toward women. As these player 2 expectations were not fulfilled, it would be interesting to find whether the expectations persisted in the face of repeated play with different male and female players 1. On the other hand, it would also be useful to discover whether player 1 behavior would differ by own sex as well as other player's gender if the game were structured to induce more selfishness.

The patterns of offers and minimum acceptable offers among the different types of players led to striking differences in rejection rates (i.e., the minimum acceptable offer exceeded the offer and both players received nothing). Differences in rejection rates coupled with the differences in the offers led to substantial differences in earnings. For example, men made low offers to women and women chose low minimum acceptable offers when paired with men. As a result, there were no rejections for the combination of male player 1 and female player 2 (Table 5), and these men achieved the highest average earnings, $5.57 (Table 6). By contrast, when women were paired together, they made low offers as player 1 and recorded high minimum acceptable offers as player 2. This combination had the highest rejection rate (23.1%, in Table 5) and the lowest average earnings for player 1 ($4.23, in Table 6). When the player's genders were not known to each other, men did not outearn women. But when the player's genders were kno wn, among players 1, earnings were highest for men paired with women (average = $5.57) and then for men paired with men (average = $4.82). Women matched with women earned the least (average = $4.23). Overall, male players 1 earned 14% more than female players 1 ($5.00 for men and $4.37 for women, p = .09 in t-test and p = .44 in Wilcoxon test for the difference between men and women).

Among players 2 as well, earnings were highest for men paired with women (average = $4.88) and then for men paired with men (average = $4.73) (Table 7). [7] For female players 1 and male players 2, the pattern was high offers and low minimum acceptable offers, leading to few rejections and high earnings for the male player 2 ($4.88). Again, the lowest amount was earned in the female-female pairs (average = $3.46). Among players 2, men earned 18% more than women ($4.70 for men and $3.97 for women, p = .04 in t-test and p = .10 in Wilcoxon test for the difference between men and women). [8]

The pattern of earnings conditional on the offer not being rejected is largely similar, although differences are not significant (not shown). As with actual earnings, for both players 1 and players 2, the highest earnings were for men matched with women. When we exclude rejections, we are examining a zero-sum game in which players are dividing $10, and by definition the lowest earnings are for women matched with men.

I explored the possibility that the gender effects were due to differing abilities or attitudes about fairness. Subjects answered a brief quiz about the game, provided some demographic information, and completed a short questionnaire designed to reveal attitudes about fairness. None of these variables were significantly associated with ultimatum play. In particular, simple comparisons show that offers and minimum acceptable offers were similar by age, by year in school, by number of math classes and number of economics classes taken, by race, and comparing various measures of attitude about fairness.

Both introspection and previous research indicate that smaller social distance leads to increased generosity and fairness. In fact, anticipating the methodology of this experiment, Camerer and Thaler (1995) speculate that offers would be higher if player 1 knew player 2's first name. In this experiment, the average offer and average minimum acceptable offer do not differ between the name and number conditions (for offers, p [greater than] .90 in t-test and Wilcoxon test for the difference between the groups; for minimum acceptable offers, p = .73 in t-test and Wilcoxon test for the difference between the groups).

V. CONCLUSION

This experiment was intended to reveal differences between the sexes in bargaining behavior that might impact wage negotiations. Systematic differences in the expectations and decisions of men and women exist even in this spare negotiating environment, leading to substantial differences in outcomes.

The evidence did not show that women are content with less. On the contrary, female players 2 choose higher minimum acceptable amounts than male players 2. But players seem to expect that women would be satisfied with a smaller share. Both men and women make lower offers to women than to men, seeming to expect women to accept less. Both men and women who were paired with a woman set their minimum acceptable amount higher than those who were paired with a man, seeming to expect women to give them more and keep less. Consequently, among players 1, men earned 14% more than women, and among players 2, men earned 18% more than women. For players 1 and players 2, the highest earnings went to men who were paired with women. These differences could not be explained by other demographic variables, such as amount of coursework in math or economics.

The results are consistent with the evidence that women are quoted higher prices for cars and that women gain smaller increases in salary when they choose to bargain. Thus, it is possible that part of the pay gap between men and women is due to bargaining differences.

(*.) I am grateful to the Russell Sage Foundation for a small grant in Behavioral Economics, which funded this project. I would like to thank Nancy Buchan, Rachel Croson, Chris Hanes, David Hemenway, and David Neumark for help and advice.

Solnick: Assistant Professor, Department of Economics, University of Vermont, 229 Old Mill, Burlington, VT 05405. Phone 1-802-656-0183, Fax 1-802-656-8405, E-mail ssolnick@zoo.uvm.edu.

(1.) The ultimatum game can be played according to the "game method" or the "strategy method." In the game method, player 1 moves first, proposing a division of the money. Player 2 then sees player 1's offer and decides whether to accept or reject. If player 2 rejects, both players get nothing. In the strategy method, at the same time that player 1 decides the offer, player 2 records a minimum acceptable offer. If player 1's offer equals or exceeds player 2's minimum acceptable offer, the offer is accepted and the money is divided according to player 1's proposal. Otherwise the offer is rejected and both players get nothing.

(2.) These experiments are based on one-shot games. In some cases, individuals may play numerous rounds of the game, but each time with a different partner, making each interaction effectively a one-shot game.

(3.) Ayres took care to avoid this problem in a follow-up to the experiment with car dealerships by not informing the testers that the study concerned race and gender effects (Ayres, 1995).

(4.) For three sessions on a single day, the blackboard was not available, Subject pairings were read aloud by the experimenter. Results did not differ appreciably, and the data is pooled.

(5.) It should be noted that unrevealing names were not necessarily foreign or vice versa. Some apparent foreigners had English first names, and some participants had first names that did not reveal gender (e.g., Jordan, Casey).

(6.) Excluding thc offer of $10, the average offer to men falls to $4.75 (p = .12 in t-test and p = .11 in Wilcoxon test, compared to average offers to women.)

(7.) Excluding the offer of $10, the average earnings of male players 2 matched with female player 1 falls to $4.53 (p = .12 in t-test and p = .12 in Wilcoxon test, compared to average earnings of female players 2 matched with female players 1).

(8.) Excluding the offer of $10, the average earnings of all male players 2 falls to $4.59 (p = .06 in t-test and p = .13 in Wilcoxon test, compared to average earnings of all female players 2).

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 Numbers of Pairs by Type of Pair
 Player 2
 Sex Unknown
 Male Female to Player 1 Total
Player 1
 Male 22 14 12 48
 Female 16 13 12 41
 Sex unknown
 to player 2 14 10 -- --
Total 52 37 -- 89
 Offers by Type of Pair Average
 and Standard Error
 Player 2
 Sex Unknown
 Male Female to Player 1 Average
Player 1
 Male $4.73 $4.43 $4.85 $4.67
 (0.25) (0.31) (0.20) (0.15)
 Female $5.13 $4.31 $4.50 $4.68
 (0.34) (0.26) (0.36) (0.19)
Average $4.89 $4.37 $4.68 $4.68
 (0.20) (0.20) (0.20) (0.12)
 Statistical tests on offers
 Wilcoxon
 t-Test Test
Comparing columns
 Male offers to males ($4.73) versus male N.S. N.S.
 offers to females ($4.43)
 Female offers to males ($5.13) versus female p=.08 p=.12
 offers to females ($4.31)
 Offers to males ($4.89) versus offers to p=.08 p=.08
 females ($4.37)
 Offers to known sex ($4.68) versus offers N.S. N.S.
 to unknown sex ($4.68)
Comparing rows
 Male offers to males ($4.73) versus female N.S. N.S.
 offers to males ($5.13)
 Male offers to females ($4.43) versus female N.S. N.S.
 offers to females ($4.31)
 Male offers to unknown ($4.85) versus female N.S. N.S.
 offers to unknown ($4.50)
 Offers by males ($4.67) versus offers by N.S. N.S.
 females ($4.68)
 Percentages of Even or Greater Offers
 by Type of Pair (n in parentheses)
 Player 2
 Sex Unknown
 Male Female to Player 1 Total
Player 1
 Male 82%(18/22) 64%(9/14) 67%(8/12) 73%(35/48)
 Female 81%(13/16) 54%(7/13) 67%(8/12) 68%(28/41)
Total 82%(31/38) 59%(16/27) 67%(16/24) 71%(63/89)
 Statistical tests on percentage even
 or greater offers
 z-Test
Comparing columns
 Male offers to males (82%) versus male N.S.
offers to females (64%)
 Female offers to males (81%) versus N.S
female offers to females (54%)
 Offers to males (82%) versus offers to p=.05
females (59%)
 Offers to known sex (72%) versus offers N.S.
to unknown sex (67%)
Comparing rows
 Male offers to males (82%) versus N.S.
female offers to males (81%)
 Male offers to females (64%) versus N.S.
female offers to females (54%)
 Male offers to unknown (67%) versus N.S.
female offers to unknown (67%)
 Offers by males (73%) versus offers by N.S.
females (68%)
 Minimum Acceptable Offers by Type
 of Pair Average and Standard Error
 Player 2
 Male Female Average
Player 1
 Male $2.45 $2.82 $2.59
 (0.36) (0.44) (0.28)
 Female $3.39 $4.15 $3.73
 (0.32) (0.46) (0.28)
 Sex unknown
 to player 2 $2.71 $3.30 $2.96
 (0.48) (0.58) (0.37)
Average $2.81 $3.42 $3.08
 (0.23) (0.29) (0.18)
 Statistical tests on minimum acceptable offer
 t-Test
Comparing columns
 By males to males ($2.45) versus by females N.S.
 to males ($2.82)
 By males to females ($3.39) versus by females N.S.
 to females ($4.15)
 By males to unknown ($2.71) versus by N.S.
 females to unknown ($3.30)
 By males ($2.81) versus by females ($3.42) p = .10
Comparing rows
 By males to males ($2.45) versus by males to p = .07
 females ($3.39)
 By females to males ($2.82) versus by females p = .05
 to females ($4.15)
 To males ($2.59) versus to females ($3.73) p = .006
 To known sex ($3.10) versus to unknown sex ($2.96) N.S.
 Wilcoxon
 Test
Comparing columns
 By males to males ($2.45) versus by females N.S.
 to males ($2.82)
 By males to females ($3.39) versus by females N.S.
 to females ($4.15)
 By males to unknown ($2.71) versus by N.S.
 females to unknown ($3.30)
 By males ($2.81) versus by females ($3.42) p = .14
Comparing rows
 By males to males ($2.45) versus by males to p = .09
 females ($3.39)
 By females to males ($2.82) versus by females p = .06
 to females ($4.15)
 To males ($2.59) versus to females ($3.73) p = .01
 To known sex ($3.10) versus to unknown sex ($2.96) N.S.
 Rejection Rates by Type of Pair (n in parentheses)
 Player 2
 Sex Unknown
 Male Female to Player 1 Total
Player 1
 Male 4.5%(1/22) 0.0%(0/14) 8.3%(1/12) 4.2%(2/48)
 Female 6.3%(1/16) 23.1%(3/13) 16.7%(2/12) 14.6%(6/41)
 Sex unknown
 to player 2 7.1%(1/14) 20.0%(2/10) -- 12.5%(3/24)
Total 5.8%(3/52) 13.5%(5/37) 12.5%(3/24) 12.4%(11/89)
 Statistical tests on rejection rate
 z-Test
Comparing columns
 Male P1 and male P2 (4.5%) versus male P1 and N.S.
 female P2 (0.0%)
 Female P1 and male P2 (6.3%) versus female P1 and N.S
 female P2 (23.1%)
 Unknown P1 and male P2 (7.1%) versus unknown P1 and N.S.
 female P2 (20.0%)
 Male P2 (5.8%) versus female P2 (13.5%) N.S.
 In name condition (7.7%) versus in number N.S.
 condition (12.5%)
Comparing rows
 Male P1 and male P2 (4.5%) versus female P1 and N.S.
 male P2 (6.3%)
 Male P1 and female P2 (0.0%) versus female P1 and p = .06
 female P2 (23.1%)
 Male P1 and unknown P2 (8.3%) versus female P1 and N.S.
 unknown P2 (16.7%)
 Male P1 (4.2%) versus female P1 (14.6%) p = .08
 Actual Earnings for Player 1 by
 Type of Pair Average and Standard Error
 Player 2 Sex Unknown
 Male Female to Player 1 Average
Player 1
 Male $4.82 $5.57 $4.65 $5.00
 (0.25) (0.31) (0.46) (0.19)
 Female $4.50 $4.23 $4.33 $4.37
 (0.45) (0.71) (0.61) (0.33)
Average $4.68 $4.92 $4.49 $4.71
 (0.24) (0.39) (0.37) (0.18)
 Statistical tests on player 1 earnings
 Wilcoxon
 t-Test Test
Comparing columns
 Male P1 and male P2 ($4.82) versus male p = .07 p = .11
 P1 and female P2 ($5.57)
 Female P1 and male P2 ($4.50) versus N.S. N.S.
 female P1 and female P2 ($4.23)
 P1 and male P2 ($4.68) versus P1 and N.S. N.S.
 female P2 ($4.92)
 P1 and P2 of known sex ($4.78) versus N.S. N.S.
 P1 and P2 of unknown sex ($4.49)
Comparing rows
 Male P1 and male P2 ($4.82) versus N.S. N.S.
 female P1 and male P2 ($4.50)
 Male P1 and female P2 ($5.57) versus P = .09 P = .24
 female P1 and female P2 ($4.23)
 Male P1 and unknown P2 ($4.65) versus N.S. N.S.
 female P1 and unknown P2 ($4.33)
 Male P1 ($5.00) versus female P1 P = .09 P = .44
 ($4.37)
 Actual Earnings for Player 2 by Type of
 Pair Average and Standard Error
 Player 2
 Male Female Average
Player 1
 Male $4.73 $4.43 $4.61
 (0.25) (0.31) (0.19)
 Female $4.88 $3.46 $4.24
 (0.47) (0.59) (0.39)
Sex unknown
 to player 2 $4.44 $4.00 $4.26
 (0.39) (0.68) (0.36)
Average $4.70 $3.97 $4.40
 (0.20) (0.30) (0.18)
 Statistical tests on player 2 earnings
 Wilcoxon
 t-Test Test
Comparing columns
 Male P1 and male P2 ($4.73) versus male P1 and N.S. N.S.
 female P2 ($4.43)
 Female P1 and male P2 ($4.88) versus female P1 and p = .07 p = .07
 female P2 ($3.46)
 Unknown P1 and male P2 ($4.44) versus unknown N.S. N.S.
 P1 and female P2 ($4.00)
 Male P2 ($4.70) versus female P2 ($3.97) p = .04 p = .10
Comparing rows
 Male P1 and male P2 ($4.73) versus female P1 and N.S. N.S.
 male P2 ($4.88)
 Male P1 and female P2 ($4.43) versus female P1 and N.S. N.S.
 female P2 ($3.46)
 Male P1 and P2 ($4.61) versus female P1 N.S. N.S.
 and P2 ($4.24)
 P1 of known sex ($4.45) versus P1 N.S. N.S.
 of unknown sex ($4.26)