Master Thesis David de Wilde 5835097 Supervisor: Aljaz Ule Universiteit van Amsterdam
Heterogeneous payoffs and
domination in the group
Table of content
• Introduction P. 3
• Literature review
o Ultimatum Game P. 6
o Group decision making versus individual decision making P. 8
o Heterogeneous payoffs in games P. 11
o Theories on group polarisation P. 13
• Experiment
o Goal P.15
o Design P. 15
o Procedures P. 16
o Predictions and hypotheses P. 22
• Results and conclusions P. 26
• Discussion P. 35
• Reference list P. 37
• Appendix P. 40
Introduction
Imagine an entrepreneur and his older brother who own a hotel together. Because the brother is older and works longer at the hotel, his income is determined by 70% of the total profits. Similar, the income of the entrepreneur is 30% of the total profits. The usual price for a room in their hotel is $50 a night. The two brothers decided to keep the prices fixed for the entire year. A few times a year, during holidays, there is an enormous excess demand for rooms. The entrepreneur realizes that he could easily fill the hotel during holidays at a price of $150 a night. For the entrepreneur this price adaption during holidays would raise his income by 30$ per hotel room per night. However, he is a bit uneasy about doing this. He is worried about being labelled a ‘’griper’’ and is afraid that his clients choose to search for another hotel. For the older brother, the price adaption would raise his income by 70$ per night. He probably has the same fear of losing his clients. However, perhaps he is more willing to raise the prices during the holidays since he will earn an extra income of 70$ per hotel room per night instead of only 30$. What also may influence their joint decision is that one of the two brothers thinks more egoistic and does care less of being labelled a ‘’griper’’ by his
customers. If there are mixed preferences, who will dominate this decision? While arguing over this problem, the brothers realize that they need more than economic theory to make a final decision. But what?
Inequality of wages within a working team may have influences on the group performance due to inequality aversion and a lack of fairness. Similar to the story of the brothers above, another real life problem is for example a board of directors which have to make a job offer to an applicant, but within the board each person earns a different wage. Imagine that in this board of directors one member has a higher wage than the other because he is more educated or has more experience in the company. This may lead to biases in the interest both members have when they make the decision to offer of a potential wage to the applicant. Next to that, we are interested to see which of these two directors dominates this decision. Is it the director with the higher wage? Or the director who has relatively more altruistic characteristics? A game which is in common with the problem of the two brothers or the board of directors is known as the Ultimatum Game. In this game two players have to interact to decide how to divide an endowed amount of money. The first player moves first by making an offer of the division, and the second player is able to accept or reject the offer. If the offer is accepted, the proposed division of money is paid out. If the offer is rejected, neither player earns any
money. As far as my knowledge goes there is no research done how to solve the problem in the example with the problem of the brothers who own a hotel. We may find interesting insights by determining the brothers (of the hotel example) as the proposing player, and their customers as the receiving player in an Ultimatum Game. If we model this situation, we see that both brothers’ income would rise with 300% if they adapt the price change. However, the nominal raise of income of the younger brother is lower compared to the older brother, and we are interested if this has influence on the group decision. Hence, this thesis will provide an addition to the research done on Ultimatum Games by extending the game with
heterogeneous payoffs within the groups. Besides that, we are interested which team member dominates the group decision in an Ultimatum Game when looking at the level of altruism. We model how the group decision is made based on the Social Comparison Theory and the Persuasive Argument Theory. The research questions are ‘What is the impact of
heterogeneity on group behaviour in the Ultimatum Game?’ and ‘Which player dominates the two people Ultimatum Game, the more or less altruistic player?’.
In a lab experiment with 32 subjects I run an experiment to test these hypotheses. In the experiment there were two treatments, one with heterogeneous payoffs and one with homogeneous payoffs. Based on the results we concluded that groups with heterogeneous payoffs make lower offers than groups with homogeneous payoffs. However, acceptance rate was similar in the two treatments. Another conclusion based on my results is that in an Ultimatum Game with teams consisting of two subjects, the subject who is relatively more altruistic dominates the team offer.
This thesis contains a literature review which will provide further insights on the Ultimatum Game. I will also discuss the research which has been done on economic group decision making and heterogeneous payoff within groups. To answer our research question we look at group decision making. Human decision-making in real world situations is typically
embedded in a social environment. Economic choices made by households and firms are commonly not done by individuals. For example, a government which has to determine some kind of policy is made by a group instead of an individual. This may be important for
economics. Next to that, I will provide an overview of the research which is done on games with heterogeneous payoffs and endowments.
One purpose of the experiment is to see how payoff heterogeneity within groups affects the choices made in the Ultimatum Game. We are interested if the decisions are influenced by
heterogeneous payoffs. We test if teams with heterogeneous payoffs make more selfish decisions than teams with homogeneous payoffs. The second purpose of this thesis is to see by which member the group decision was dominated by looking at their level of altruism. We test if the more altruistic member dominates the decision in teams with heterogeneous
payoffs. In this design I will define groups as teams. That is, does the decision of teams with heterogeneous payoffs differ compared to the homogeneous teams, and if so which of the two team member has the most influence on this decision?
Literature Review
Ultimatum Game
In the last two decades there has been a lot of experimental economics research and a key insight is that people typically do not behave as egoistic as traditional economics assume them to do (Oosterbeek, Sloof et al. June 2004). This behaviour appears in an experimental game which we know as the Ultimatum Game.
The one shot Ultimatum Game is a two player bargaining game in which two players, one proposer and one receiver, are endowed with a sum of money, which we denote y. The proposer has to offer a division of this sum y between himself and the receiver, which we denote, c. If the receiver accepts the offer, both players are paid the proposed division (so the proposer earns y-c, and the receiver earns c). If the receiver rejects the offer, both players are paid nothing. The game-theoretic equilibrium is for the proposer to offer the minimum amount of the money to the receiver. In this case the proposer maximizes his profits and the receiver will accept the offer since the minimum amount is better than nothing. Experimental evidence shows that in real life this equilibrium is rarely reached since people often reject low offers. This is often attributed to psychological effects as lack of fairness and inequality aversion (Fehr, Gächter 1998). Instead, the average proposal is typically about 30 to 40 percent of the total value of y, with a 50-50 split being the modus. Offers lower than 20 percent are commonly rejected (Camerer, Thaler 1995).
A common interpretation of the behaviour of the receiver is that they prefer to forgo some money instead of be treated unfair. The behaviour of the proposer is commonly explained by two motives; the feeling of fairness and the anticipation that an offer which is very small may be rejected (Oosterbeek, Sloof et al. June 2004). Further research on the Ultimatum Game was done by Cameron who conducted an experiment in which she raised the stakes of the money to be divided (Cameron 1999). Cameron implemented the experiment in Indonesia and raised the stakes to three times the monthly expenditure of the average participants. The results still did not approach the classical economic selfish outcomes. More specifically, the receivers were more willing to accept a given percentage offer at higher stakes, but the behaviour of proposers was uncorrelated to the raise of the stakes. Other results show that in a repeated Ultimatum Game, raising the stakes only have a small effect on the behaviour of
the inexperienced players (who play the game one time) compared to the experienced players (who repeat the game a couple of times) (Slonim, Roth 1998).
When the endowed money for bargaining is earned, for example by a knowledge quiz, people are less willing to make a fair offer (Hoffman, McCabe et al. 1994). In the same article Hoffman showed that it is more difficult to be a selfish bargainer when you have to make the offer not anonymously. In a double blind Ultimatum Game experiment, where the actions of the proposer are anonymous to the receiver as well as the experimenter, results showed less social constraints on rational self-interest. Roth suggests that face-to-face bargaining may trigger social norms that have influence on your underlying preferences (Roth 1995). As a reaction to this finding Shogren argues that it is not the face-to-face structure which is the reason for the less selfish offers, but rather the context-free environment of previous experiments (Shogren 1997). He shows that if you create an environment which rewards competition, such as a tournament where you have to earn money to win, bargaining will not necessarily lead to fair splits.
When you play the Ultimatum Game more than once you might learn during the experiment which may affect behaviour. Playing the game repeatedly makes subjects learn how to play the game. This was tested in an experiment done by Roth (Roth, Erev 1995). The subjects in this experiments repeated the Ultimatum Game against different unknown others. The article presents evidence showing that proposers give smaller offers to the receivers when they have gained experience. Hence, they conclude that repeating the Ultimatum Game will make the participants converge more to the general economic equilibrium. Later research on repeated Ultimatum Games with different stakes shows that the learning progress of the proposers is more observable when the stakes are high (Slonim, Roth 1998). Similar, the rate of rejection is frequently lower in the repeated game when stakes are high. Slonim suggests that the lower rejection frequency is the reason that the proposers learn to make lower offers when the stakes are high.
The subjects which were used in the existing research on Ultimatum Game experiments were recruited from different pools. Most of the experiments are done with a population consisting of students with an economic background. However, in some studies the population consisted of students with a sociologic or psychological background, or even no academic background at all. The question if the backgrounds of the subjects have a big influence on the behaviour gives mixed answers (Oosterbeek, Sloof et al. June 2004). Carter conducted an experiment in
which he compared ultimatum bargaining between economic and non-economic students. He concluded that economic students act more in accordance with the general economic theory, i.e. act more selfish and propose lower offers and reject fewer offers (Carter, Irons 1991). Contrary to these findings in a similar experiment with economic students and psychological students, Kagel et al. did not find any significance difference in the behaviour between the two subject pools (Kagel, Kim et al. 1996).
Group decision making versus individual decision making
Economic choices made by households and firms are commonly not done by individuals. For example, a government which has to determine some kind of policy is made by a group instead of an individual. By similar reasoning, negotiations are commonly not carried out by one person but by a group. In particular, recent research shows that groups behave more cognitively sophisticated when making economic choices compared to individuals (Charness, Sutter 2012). With regard to our experiment we will look at group decision making. First, I will give a short overview of the research which is done on group decision making and how this differs from individual decision making in economic situations.
Most group decision tasks are cooperative, in other words individuals within the group are rewarded for group performance. That is, in a cooperative group the success of one member and the success of the other members are positively correlated. However, in voluntary cooperation groups there is the possibility to free-ride by maximizing your own profit. In competitive groups, the success of one member implies a loss of the other member. In collaborative groups, the incentive of each group member is aligned, and there is no space to free-ride. For our research, we will focus on collaborative groups since the incentives in an Ultimatum Game are aligned within the group members. To see this, look at the example from the introduction. If the price is raised by 300%, each brother’s income will raise with 300%. This is the same in an Ultimatum game with groups. If an offer is accepted, each member within the groups would earn his part of the division of the tokens which was proposed. For the group members there is no option to free-ride, since the game requires no individual voluntary effort.
To analyse difference between group and individual decision making without the effects of social preferences like inequality aversion, fairness or reciprocity the beauty-contest game is a suitable game. The beauty-contest game (Keynes 1937) is a game in which N-decision makers simultaneously chose a number of the interval [0, 100]. The winner of the game is the player whose decision number is closest to x times the average chosen number, where x is less than 1. So the players have to anticipate on what the expected average number will be. However, since x < 1 the rational equilibrium will be to choose the number 0. If for example
x = 2/3 and you would expect the other players to choose their number randomly, you expect
the average to be 50 and your best choice will be 33,33. If however, you expect the other players to be rational and also use this best respond, your best choice will be 22,22. If you continue to reason like this the game-theoretic equilibrium is to choose the number 0. There is no loss or risk aversion and the game clearly shows the effects of rationality and learning. A controlled laboratory study by Kocher and Sutter provides this comparison between the behaviour of groups and individuals in the beauty-contest game (Kocher, Sutter 2005). The article shows that groups reason more deeply through the game and expect the other players to do as well. They conclude that groups anticipate one step ahead of individuals, which means they converge faster to the equilibrium number 0 when the game is repeated. In their results Kocher and Sutter showed that if groups and individuals compete against each other in the beauty-contest game, groups will have higher average payoffs. This result may be
explained by the conclusion that groups think more deeply through the situations, and also expect other groups to reason more deeply than individuals (Charness, Sutter 2012).
The finding that groups are less influenced by social considerations is supported by Cox in an experiment where the decisions of groups and individuals were analysed in an investment game (Cox 2002). An investment game (Berg, Dickhaut et al. 1995) is a two player game which consists of a trustor and a trustee. In this game both players are endowed with amount money of c. The trustor makes the first move by sending an amount of money x < c to the trustee. The amount x is multiplied by three and the trustee can send back any amount y < 3x. The final payoff for the trustor is c – x + y and the final payoff for the trustee is 3x – y + c. The game-theoretic equilibrium is for the trustee to send back zero money, so they maximize their own profits. The results show no significant difference between groups and individuals with the amount of money x sent, but groups return significantly lower amounts of money y back to the trustor. Again, the conclusion states that groups behave more rational by sending back a lower amount of money.
This conventional wisdom has been challenged by laboratory data on altruism, however, which shows that group choices are more altruistic compared to the choices made by individuals (Cason, Mui 1997). In the individual dictator game there are two players, a dictator and a receiver. The dictator needs to make a division of the endowed sum of money between him and the receiver. This game differs from the Ultimatum Game in the rule that the receiver has only one option which is to accept the offer, no matter what the quantity of the offer was. Cason and Mui conducted an experiment in which they compared the
allocation of y dollars in an individual dictator game with the allocation of 2y dollars in a group (of 2 subjects) dictator game. Contrary to the findings of Cox, their results indicate that groups dictated more ‘fair’ divisions of the endowed money compared with the individuals. Applied to ultimatum bargaining, there has been done a lot of research to see if groups in contrast to individuals give more weight to the fair perspective instead of the rational
perspective when they have to make, accept or reject an offer. Given the discussed literature on group behaviour the prediction is straightforward: In an Ultimatum Game groups
behaviour it is more common to adopt a rational perspective and less common to adopt a fairness perspective compared to individuals (Robert, Carnevale 1997). Bornstein and Yaniv conducted an experiment in which they compared the standard ultimatum game played by individuals and the same game played by groups of three persons (Bornstein, Yaniv 1998). The proposal groups made their decision by having a brief face-to-face discussion before they made their offer to the receiver. Similar, the members of the receiver group held a small discussion on whether to accept or reject the offer. The results showed that the offers which were made by groups were significantly lower than the offers made by individuals. With the same reasoning, the rejection rate of groups was low in the experiment, which showed that groups were willing to accept less compared to individuals. More broadly, we may conclude that groups act more rational (in terms of the general economic theory) in games in which individuals are more likely to be influenced by social considerations as lack of fairness and inequality aversion (Charness, Sutter 2012).
There is an important role of social decision rules on group decisions, and it is useful to identify these rules (Manski 2002). Consider an Ultimatum Game experiment where groups of five people either accept or reject the offer made by one proposer. Messick (1997) hypothesized that proposers will find it hard to incorporate the implications of the group’s decision rule in their offers. This hypothesis is tested in an experiment where the proposers had to make offers to groups of 5 subjects with two different types of decision rules; the
disjunctive decision rule (if any of the five accepts the offer, the offer is accepted) and the conjunctive decision rule (if any of the five rejects the offer, the offer is rejected). Although you would expect proposers to make higher offers to groups with the disjunctive rule compared to groups with the conjunctive decision rule, results showed no significance difference in the offers between the two groups. That is, bargainers are insensitive to the implication of the decision rule and have problems with thinking accurately about the cognitions of others (Messick, Moore et al. 1997).
Robert and Carnevale conducted an ultimatum bargaining experiment to see how the beliefs of the proposal groups of which criterion the receiver groups will use in the decision to accept or reject the offer had influence on the offers. The results show that, when the other groups were expected to be ‘fair’’, this implies a need to show greater cooperation and to make more altruistic offers (Robert, Carnevale 1997).
Heterogeneous payoffs in games
Although homogeneity of payoffs in group tasks is an obvious abstraction from reality, there is little experimental evidence in how groups bargain where the members have heterogeneous rewards.
Consider a public good game, which is a game used to analyse the behaviour within the voluntary contribution mechanism. In the n-players basic version, subjects anonymously choose a certain amount of their endowed value to contribute to a public good. The total amount contributed to the public good in a round is multiplied by a factor which is higher than 1 and this in then divided in homogeneous shares across the group members. In addition they are rewarded with the rest of their endowed value which they did not contribute. The group’s total payoff is maximized when everyone contributes all of their endowed money to the public good. Contrary to the group optimal outcome, the Nash equilibrium in this game is simply to contribute zero regardless of whatever anyone else does. However, similar to behaviour in the Ultimatum Game, research shows that people make altruistic contributions. This is commonly explained by fairness and equality preferences (Fischbacher, Gächter et al. 2001).
In a public good game the participants in a group have the option to free-ride, which means they contribute zero the public good to maximize their own profits. In our experiment we analyse the problem of the two brothers in the example in the introduction). This is why we focus on the Ultimatum Game, since we have an collaborative group tasks where there is no option to free-ride. Nevertheless we can get some useful insights to look at these social dilemma tasks with heterogeneous payoffs.
It has been shown that group-members with a higher income contribute less to the public good compared to the group-members with a lower income (Chan, Mestelman et al. 1996). Based on these results we may conclude that in a public game people with a higher
endowment of money are more selfish than people with a lower endowment of money, which is an interesting finding with regard to our own research question. Other research done on heterogeneity endowments in public good groups shows that contributions to the public good were significantly lower when groups had heterogeneous rather than homogenous
endowments (Cherry, Kroll et al. 2005). Hence, we may conclude that groups in which the endowments are heterogeneous act more selfish in a public good game.
Applied to the Ultimatum Game, it is important to notice that the economical game theoretic Nash equilibrium does not change when the payoffs between the players are heterogeneous. For example, imagine you give the participants 100 chips with different two monetary values for the proposer and the receiver of the chips (a higher and a lower value of $0,30 and $0,10 per chip). Assuming the bargainers maximize their own payoffs, the sub game perfect equilibrium is unaffected by the monetary value the player’s chips is determined by the experimenter. In particular, for both values of the chips the equilibrium is for the proposer to give the smallest amount of chips possible, and the receiver will accept this offer. The Nash equilibrium in the Ultimatum Game depends on the strategy of the receiver, which can be anything. If you have 10 tokens to divide, and the receiver has a strategy to reject anything less than X, the Nash equilibrium of the proposer is to make an offer of X. However, when players were fully informed about each other’s chip value, the players will develop
conflicting fairness norms (an ‘equal chip norm’ for the player with the higher chip value, and an ‘equal money norm’ for the player with the lower chip value). When the proposer obtains the higher chip value, these conflicting norms will results in unusually high rejection rates (Kagel, Kim et al. 1996).
In the same experiment Kagel conducted two treatments; treatment 1 where the proposer was fully informed of the two payoffs and the receiver was not, treatment 2 visa versa. In
treatment 1, when the proposers were fully informed and had the higher chip value, they offered roughly equal chip splits. When the proposers were fully informed and had the lower chip value the offers were unequal in the amount of chips, which resulted in roughly equal money splits. Kagel stated that this behaviour is consistent with the fact that proposers are motivated by self-serving notion of fairness (What if fair? Equal chips or equal payoffs?). At the same time proposers take strategic considerations into account, since a lower chip offer makes more chance to be rejected (Kagel, Kim et al. 1996). When looking at the behaviour of the receivers the results show higher rejection rates when they had the lower chip value and were fully informed about this, compared to when they had the lower chip value and were not informed about this. This inconsistency is explained by the fact that bargainers do not only bargain over absolute money, but also over relative money. In other words the players compare each other’s payoff which influences their behaviour (Bolton 1991).
Theories on group polarisation, who dominates who in group decisions?
Imagine the example of the two brothers from the introduction. In the previous section we discussed if the different level of earnings may lead to different incentives when the brothers will determine a new price. In this section we discuss how the psychological characteristics, as altruism or risk, of each member influence the final group decision. What if one of the brothers of the example thinks it is more important to treat his regular clients fair by not raising the price in the high season, while the other brother thinks the only important thing are his own earnings?
Consider a study designed to see how different individual risk preferences make a group decisions (Hoyt, Stoner 1968). In his experiment Stoner asked the subjects first to make, individually, recommendations for several choice dilemma problems. After the individual decisions were made, again the subjects were asked to give the same recommendations but now in groups. Each group made their decision by having a discussion. The results showed that group recommendations were riskier than the mean of the individual decisions of group
members. Stoner proposed the group polarisation hypothesis, which states that the discussions which are made in groups drive the collective decision to extreme points. As a reaction to this ‘risky-shift’ phenomenon in group decisions, there emerged two dominant explanations. These are the Persuasive Argument Theory (PAT) and the Social Comparison Theory (SCT). The Persuasive Argument Theory (Burnstein, Vinokur 1977) indicates that individuals are influenced by the persuasiveness of the arguments that they remember during a discussion when making a decision. In other words, when a group is in a discussion each individual collects all the pro’s en con’s arguments and uses them to form a preference towards a group decision. If subjects in a group act in such a persuasive argument process, the choices of this group are likely to shift in favour of the initial pre-discussion tendency.
An alternative perspective is the Social Comparison Theory (Sanders, Baron et al. 1978). The SCT states that individuals have the need to perceive and present themselves in a social desirable way. All individuals want to present themselves in a ‘nicer’ way than what they perceive as the average social norm in the group they are dealing with. To do this, an individual observes how the group behaves and presents himself in a socially more
approvable way. If subjects in group towards pro social behaviour as in the social comparison process, the choices of the group will shift towards a more social decision because more pro social attitudes within the group.
Cason and Mui did an interesting finding in their experiments on the Dictator Game. They showed that when teams consisted of two persons who both had played the individual dictator game in the first treatment with different choices (one selfish, one altruistic), the group
decision was dominated by the more altruistic member (Cason, Mui 1997). Based on the theory of group polarisation, these results provide strong evidence against the Persuasive Argument Theory since the teams with solely selfish players did not polarise towards a more selfish offer. Instead, these selfish teams polarise towards a more altruistic offer, which is more consistent with the Social Comparison Theory. That is, PAT predicted that following group discussion, teams who consists of solely selfish individuals will make team offers that are more self-regarding. Contrary, SCT predicted that both selfish as altruistic teams would have made higher offers than the mean of the individuals offers. In heterogeneous teams, with one selfish and one altruistic player, the results showed that the team decision polarise
towards the individual decision of the more altruistic team member. 14
Experimental Design
Goal
The purpose of the experiment is to see how payoff heterogeneity within groups affects the choices made in the Ultimatum Game. We are interested if the decisions are influenced by heterogeneous payoffs. We test if teams with heterogeneous payoffs make more selfish decisions than teams with homogeneous payoffs. Furthermore, we want to see by which member the group decision is dominated. We determine a level of altruism from each subjects. We test if the more altruistic member within a team dominates the decision in an Ultimatum Game. In this design I will define groups as teams. That is, does the decision of teams with heterogeneous payoffs differ compared to the homogeneous teams? And does the team member who is more altruistic dominate this decision?
Design
The design of this experiment is an Ultimatum Game with groups and heterogeneous payoffs. We have done 4 experiment times with 8 participants each. There are two treatments, a treatment with heterogeneous payoffs and a treatment with homogeneous payoffs. In each experiment the subjects will make individual and group decisions. The subjects will be paired in groups of two. The subjects are going to bargain over their endowed tokens in a Dictator game and in an Ultimatum game.
Each subject makes four decisions – two individual decisions and two team decisions. The decisions were made sequentially. The experiment consists of 3 parts. In part 1 we have an individual decision stage, where we are asking the strategy method of each subject in a dictator game. That is, all the participants were given a table to fill in with all the possible amount of tokens you can offer when you have the role of ‘dictator’. This is to measure the level of altruism. In this part of the experiment each individual subject is matched with another single subject. I will inform the participants that their decision has influence on their payoff in this part of the experiment.
In part 2 we pair the subjects in teams of two. These teams will be randomly matched to each other and play an Ultimatum Game. Again, the group decision they make in has influence on their earnings in this part of the experiment. In part 3, the same teams who were matched to each other in part 2 will play another Ultimatum Game, only now the roles of proposer and receiver are switched. As in the other parts, their group decision has influence on their
earnings in this part of the experiment. To see who dominates the decision in the team decision stage, each individual team member also decides what (s)he would have chosen in the Ultimatum Game in the role of proposer if (s)he had to make the decision individually. This decision is purely hypothetical and has no influence on his or her earnings in the experiment. Between all the parts the participants will not get any feedback on their
decisions. At the end of the experiment I will randomly chose one part and one subject who will receive his or her final payoff. I will give the subjects feedback of the part which is chosen for the final pay out.
To form two different treatments, we have done two experiments in treatment 1 and two experiments in treatment 2. That is, there are four different experiments conducted with each 8 subjects participating. The individual decision stage is similar in each treatment. The team decision stage differs in the payoffs of the subjects. In treatment one, the payoffs within the teams are heterogeneous. On the other hand, in treatment two the payoffs within the teams are homogeneous.
Procedures
In each experiment, 8 participants enter the laboratory. The laboratory consists of two separate rooms. When a subject enters the lab he or she will receive a randomly chosen seat number. The numbers 1,2,3 and 4 will enter the left room and the numbers 5,6,7 and 8 will enter the right room. When seated, the subjects are handed out the main instructions of the experiment. After they have read it I will hand out the instructions of part 1. As stated before, these instruction are similar in both treatments. After reading these instructions out loud the decision forms of part 1 are handed out. Each subject fills in their strategy method of a Dictator Game. They are informed that for this part they are matched with a randomly chosen subject in the other room and their decision is fully anonymous. The subjects get 5 minutes to fill in these forms. The forms of part 1 are collected. After that the instructions of part 2 are handed out. Now each subjects is paired in teams of two with the person who sits next to him or her. They are informed that they are matched with a randomly chosen team in the other room during this part and their decision is fully anonymous. These instructions are different in each room. The teams (team A and B) in the left room receive the instruction for the proposing teams, and the teams (team C and D) in the right room receive the instructions for the receiving teams. After reading these instruction out loud each subject in the left room is handed out the individual decision form of what they would offer if he or she had to make the
decision as ‘proposer’ individually. Then I will collect these forms and hand out the team decision forms in the left room. In the right room I will only hand out the team decision form (right after the instructions), since there is no hypothetical individual decision for the
receiving teams. Each team gets 7 minutes to fill in these forms. After each team has made their decision I collect the decision forms of part 2 and hand out the instruction forms of part 3. The instructions of part 3 are similar to part 2 only now the groups have the opposing role in the Ultimatum Game. Again, they are informed that they are matched with a randomly chosen team in the other room during this part and their decision is fully anonymous. Similar to part 2, after reading these instruction out loud each subject in the right room is handed out the individual decision form of what they would offer if he or she had to make the decision as ‘proposer’. Also similar, the teams in the left room only receive a team decision form. Then I will collect these forms and hand out the team decision forms in both rooms. I will collect the decision forms of part three and randomly chose one part and one player who actually receive a pay-out of their earned chips. After that the subjects can leave the room and the experiment is over. See the picture below for an overview of how the subjects are seated in the laboratory and how the teams are determined.
Part one – individual decision stage with Dictator Game
This stage in similar in both treatments. Each individual subject is randomly matched to one other subject and asked to fill in their strategy method of a Dictator Game. We use the Dictator Game this game gives a good indication of the level of altruism from the subjects (Eckel, Grossman 1996). We use the strategy method to elicit the participants’ choices. This method indicates that subjects specify a complete strategy, rather than only choosing an
action in realized information sets. In this stage the subjects are informed that there are no consequences to their choices for later rounds in the experiment. This information for the subjects is to prevent that their strategy will be biased because they might think that they will be punished in later rounds if they give a selfish strategy. On the other hand the subjects are informed that their decisions do have influence on their earnings in this part of the
experiment.
The subjects will be matched randomly with one of the other participants. This match will be only hold for this part of the experiment. The subjects will never know who their matches are, hence their decisions are fully anonymous. Each subject receives 10 tokens, and from this tokens the subject has to make an allocation between them self and their match. In this part of the experiment every token is worth 0,50 euro. Each subject’s payoff will be 10 tokens minus the tokens (s)he allocated to his or her match. On the other side, the payoff of a subject’s match will be the amount of tokens which is allocated to him/her. For the payoff it will be randomly chosen which of the two subjects who are matched to each other is the dictator and who is the receiver. With the information from this game we know how self-regarding each subject is, which is useful to see how these subjects act in stage 2 when they are formed in teams. The decision form in this part of the experiment is similar to the table below.
Allocation: Tokens to you Tokens to the other person Put a X at your allocation 10 0 9 1 8 2 7 3 6 4 5 5 4 6 3 7 2 8 1 9 0 10
Part two – team decision stage with Ultimatum game
Part two and three differ in both treatments. The difference in both treatments is the chip
value of the tokens the subjects are playing with. In treatment one, the subjects have heterogeneous chip values. In treatment two, the subjects have homogeneous chip values. Treatment one – teams with heterogeneous chip values
In treatment one, there will be a random allocation between the value of the tokens among the participants; for 4 participants one token will be converted into €1 (Player 1,3,5 and 7) and for the other 4 participants one token will be converted into €0,50 (Player 2,4,6 and 8). There is full information; all participants know which chip value each member has and receive the table below (or the other way around depending on which player you are).
Your payoff value (if player 1,3,5,8) 1 token = 1 euro
Your teammates payoff value (players 2,4,6,8)
1 token = 0,50 euro
To form teams, we simply pair the subjects who are sitting next to each other. Hence, player 1 and player 2 form team A, player 3 and player 4 form team B, and so on. In this part of the experiment, the teams in the left room (team A and B) have the role of proposers and will play against a randomly chosen team in the right room (team C or D) who have the role of receivers.
Left Room
After we handed out the instructions of this part, each player in the left room (player 1,2,3 and 4) have to make their decisions on what he or she would decide if the decision had to be made individually. This individual decision is purely hypothetical and has no influence on the subject’s payoff in the experiment or on the further course of the experiment. We are
interested in these hypothetical individual decisions because it may show us who of the two team members dominates the final team decision. After these individual decision forms are filled in the teams in the left room receive their team decision forms where they have to decide how much of the 10 tokens the want to offer to the team they are matched to in the other room. They are informed that the teams they are matched to in the right rooms have the following two options:
1) To accept the allocation. In this case the proposing will earn 10 tokens minus what the amount of tokens they have proposed to the receiving team in this part of the
experiment. The receiving team will earn the amount of tokens which were allocated to them.
2) To reject the allocation. In this case the proposing team and the receiving team which were matched to each other will earn nothing in this part of the experiment.
The teams in the left room are asked to indicate which allocation they choose to offer by putting a cross in the blank next to the option of their allocation in a decision table similar to the left below.
Right Room
When the players in the left room receive their individual decision forms the players in the right room already receive their team decision forms. The receiving team’s task is to decide whether to accept or reject the allocation made by the proposing team they are matched with. This is done by a strategy method where the receivers have to fill in at any possible allocation if they would accept or reject the offer. The team decision form of the receiver is similar to the right table below.
Proposing team’s decision table: Receiving team’s decision table:
Allocation: Allocation: Tokens to the other team Tokens to your team Your team decision? Put one X at your allocation 10 0 9 1 8 2 7 3 6 4 5 5 4 6 3 7 2 8 1 9 0 10 Tokens to the other team Tokens to your team Does your team accept this allocation? Put a X Does your team reject this allocation? Put a X 10 0 9 1 8 2 7 3 6 4 5 5 4 6 3 7 2 8 1 9 0 10 20
In each treatment the participants were randomly divided into two-person teams. This is determined based on how they are seated. That is, subjects who sit next to each other are a team. All of the proposer teams were told that they have up to 5 minutes to reach a joint decision as how to allocate the 10 tokens between their team and the receiver team in the other room. They are asked to do this privately, because they have to be discrete so the proposing teams in the room will not know each other decision. Each proposing team is informed they are playing against one of the receiving teams in the other room and that the receiving team would have a similar discussion to decide whether to accept or reject the proposal. Both teams were informed that, should an offer be accepted, each group member would earn the tokens which are allocated (that is, if an offer of 5 tokens is accepted, both member of the proposer/receiver team would earn 5 tokens instead of each 2,5). On the other side, if the offer is rejected none of the proposer and receiver team will earn any tokens, i.e. the payoff is zero for all players.
Treatment two – teams with homogeneous chip values.
In the experiments with treatment two, there is no heterogeneity in the chip value. Each subject will be informed that one token will be converted into €0,50 at the end of the experiment. Apart from the homogeneous chip value the discussed procedures of this experiment are similar to treatment one.
Part three – team decision stage with Ultimatum Game with switched roles
Part three is similar to part two, only now the teams who had the role of proposer in part two now have the role of receiver. Similar, the teams who had the role of receiver in part two now have the role of proposer.
Treatment two – teams with homogeneous chip values
Similar to part two, part three only differs in the value of the tokens of the subjects. Again, treatment one determines heterogeneous chip values while treatment two determines homogeneous chip values.
Pay out and feedback
At the end of the experiment there is one part and one player randomly chosen by drawing a random card. First a random subject draws a card (options 1,2 and 3) to determine which part is paid out. After that a random subject draws a card (options 1 till 8) to determine which subject will be paid out. If part 1 is drawn to be paid out, it has to be determined if the subject is the ‘dictator’ or the ‘receiver’ of the pair of subjects which is matched to each other. Again,
this is done by drawing a single card from a deck with two options (receiver, dictator). If part 2 (or 3) is drawn to be paid out, the subject will receive the amount of tokens (s)he earned in with the team decision. The subjects are given feedback of the results from the game which is chosen to be paid out.
Predictions and hypotheses
We conducted two different treatments because we want to investigate if groups make
different choices when the payoffs are heterogeneous within the proposer and receiver teams. Standard economic theory states that it is ‘rational’ for a proposer team to offer the lowest possible amount of tokens. For the receiver team it is payoff-optimal to accept every positive amount offered by the proposer team, since every offer is (at least) better than a payoff of zero. However, previous research shows us that these economical rational choices are far from reality in an Ultimatum Game because subjects seem to make decisions based on the perceived fairness of the game.
In the example from the introduction, we see that both brothers’ income will rise with 300% if they adapt the price change. However, the nominal rise of income of the younger brother is much lower compared to the older brother, and we are interested if this has influence on the group decision. If we model this situation the two brothers have two options, to raise the price or to leave it like it was. If they raise the price, each brother receives 3 times more profits per booked hotel night. That is, the younger brother receives 30$ more per booked night, and the older brother receives 70$ more per booked night. On the other hand, they might risk the chance that the hotel guest will perceive the two brothers as ‘’gripers’’ which can lead to a loss of future customers. Let’s denote the chance of being perceived as a ‘’griper’’ as chance 𝑷. The personal objectives of the two brothers are summarized in the following table, where Brother A is the younger brother:
Raise the price Do not raise the price
Brother A Income of 45$ per night – cost of 𝑷 Income of 15$ per night Brother B Income of 105$ per night – cost of 𝑷 Income of 35$ per night
We are interested to see if the heterogeneous in income has influence on the decision how, or even if the two brothers raise the price. Based on the nominal payoffs in the table I expect that the older brother is more willing to raise the price since his gain will be 70$ per night
minus the cost of 𝑷 . The younger brother’s gain will be 30$ minus 𝑷. So if both brothers give the same value to 𝑷 we see that the older brother has a net gain of 40$ - 𝑷 per night more compared to his younger brother. But we should keep in mind that each brother may have a different value of 𝑷.
The discussed literature over public good games concluded that groups in which the
endowments are heterogeneous act more selfish in a public good game (Cherry, Kroll et al. 2005) and states that subjects with a higher endowment of money are more selfish than people with a lower endowment of money (Chan, Mestelman et al. 1996). In my experiment, the total possible earnings for teams in treatment one is €30 and for the teams in treatment two is €20. So the stakes are higher in treatment one, which may also lead to a more selfish choices from the heterogeneous teams. However, discussed literature only saw difference in the behaviour of the receivers when raising the stakes in an Ultimatum Game (Cameron 1999). Based on these findings I made the following hypothesis:
1) Teams with heterogeneous payoffs make more selfish offers and have a larger acceptance rate
To answer our second research question (Does the more altruistic player in a group
Ultimatum Game dominates the decision?) this hypothesis is not sufficient. We are interested
in how this decision is made. That is, which of the team member dominates the decision? What do the economic theories summarized in the literature review predict for the group Ultimatum Game studied here? The offers made in the Dictator Game of our experiment are classified as ‘less altruistic’ and ‘more altruistic’.
In part 1 of our experiment the decision the subjects have made in the Dictator Game shows how altruistic they are. How do we determine the level of altruism of each subject? That is, what is the neutral point in this altruism-selfishness continuum of dictating 10 tokens? It is possible to determine a neutral point of 5 tokens, since this offer gives an equal pay off between both players. On the other hand, when you play with an economist from who you know that he is a rational and selfish player, you might perceive an offer of 1 or even 0 tokens as the neutral point. Research shown that nearly all offers lie between the interval of the rational selfish offer (which is 1 or 0 token(s) in our game) and the other-regarding equal split offer (which is 5 tokens in our game) (Camerer, Thaler 1995). Another possibility is to define the neutral point 𝑦� as the overall mean of all the offers from the individual decision stage (Cason, Mui 1997). If a subject’s offer in the individual stage is higher than 𝑦�, this
person was classified as other-regarding. If a subject’s offer is lower than 𝑦�, this person was classified as self-regarding. But it is not fair to classify a person who offers slightly below 𝑦� as self-regarding while subjects who offer slightly above 𝑦� are classified other-regarding. Hence, to distinguish the composition in our two-person groups, we classify the person who offered more than his group member in the Dictator Game as ‘more altruistic’. Similar, the person who offered less than his group member is classified as ‘less altruistic’.
We have the following information over each subject; their strength of altruism (‘more altruistic’, ‘less altruistic’) and their chip value (high, low or neutral). According to the Persuasive Argument Theory (PAT) (Burnstein, Vinokur 1977) it is plausible that teams where each player has made a low offer in part 1 will make a group offer below the overall mean of all the offers in the team decision stage. According to the group polarisation theory (Hoyt, Stoner 1968) which we discussed in the literature review we may expect even more selfish offers from these groups compared to what each player would have made individually. Contrary, the Social Comparison Theory (SCT) (Sanders, Baron et al. 1978) predicts that the offer from these teams (where each player made a low offer in the Dictator Game) will be higher than the average which the players of the selfish group would have made individually. On the other side, both theories predict that teams where each player made a high offer in the Dictator Game will make an offer above the overall mean of offers.
We are interested in teams where there is a difference between the levels of altruism of the players. Because in these teams we can see if the ‘more altruistic’ or the ‘less altruistic’ player dominates the decision. In part 1 we discussed that when teams consisted of two persons who both had played an individual Dictator Game in the first treatment with different choices, the group decision in a Dictator Game was dominated by the ‘more altruistic’
member (Cason, Mui 1997). Cason and Mui stated that this was consistent with the SCT. Based on the Ultimatum Game, the SCT predicts that both players will observe each other and present themselves as more altruistic, which will lead to team offers which are higher than the average hypothetical offers of the two players within each team.
The PAT predicts for the Ultimatum Game that each player will collect all the arguments which are given and form a decision preference. In an Ultimatum Game, there are strong arguments for giving relatively high or low offers. The argument for making a high offer is for example the possible rejection from the receiving team when the offer is too low. On the other hand, the argument for making a low offer is that they are able to earn more money if
the other team would act rational and accept every offer they make. It is unknown which argument is more persuasive. We may expect that the ‘more altruistic’ player wants to make a higher offer, and the ‘less altruistic’ player wants to make a lower offer. We must also keep in mind that the strategies in an Ultimatum Game are not solely based on altruism as in the Dictator Game. In other words, making a low or a high offer in an Ultimatum Game is not exclusive due altruism. Hence, ‘less altruistic’ players may also make a higher offer due to the possible rejection of the other team and use this in their arguments. This means that there may exists situations where a ‘less altruistic’ player might due strategy reasons make a higher hypothetical individual offer in the Ultimatum Game than his ‘more altruistic’ team member. Hence, according to PAT it is unknown if the more altruistic or the less altruistic player would dominate the decision.
Based on these theories we test the following hypothesis:
2) When a team needs to make an offer in an Ultimatum Game, is the decision dominated by the more or less altruistic player?
Critical notes
In treatment A, we have the data from 8 Ultimatum Games with heterogeneous payoffs. Similar, in treatment B, we have the data from 8 Ultimatum Games with homogeneous payoffs. By comparing these data we can test if there is a significance difference in their decisions. Because this is a small data set the results may lead to biased conclusions. A proposal for further research is to do the same experiment with a larger subject pool. In the individual decision stage I make the use of a strategy method. The use of a strategy method is criticized by Roth in an article where he shows that subjects give different responses in the strategy and non-strategy method (Roth, Kagel 1995). Roth states that subjects might give different responses because they are asked to make simultaneously all potential choices at the same time. In complex games with many information sets, this may influence the strategic environment and so gives different responses. Because our Ultimatum Game is extremely simple, however, we may probably ignore this effect. This prediction is supported by Cason and Mui who compared the responses in a strategy method and a non-strategy method during a sequential dictator game. The results show that there is no
significance difference in the responses between the two methods, and the authors concluded that this is due the simplicity of the game (Cason, Mui 1998).
Results and conclusions
Do teams with heterogeneous payoffs make more selfish offers? Table 1 shows the offers made by the groups in treatment A and the groups in treatment B and the mean offer in each condition. As can be seen in the table, the groups in heterogeneous treatment offered an average of only 2,75 tokens, whereas the average offer in the homogeneous treatment was 4,5 tokens. In figure 1 and 2 you can see the distribution of offers in percentages of the groups in treatment A and B.
Treatment A 1 3 5 4 1 1 4 3 Mean: 2,75
Treatment B 4 5 5 4 3 5 5 5 Mean: 4,5
Table 1 – Offers proposing teams
Figure 1 – Distribution of offers made in percentages in treatment A
Figure 2 - Distribution of offers made in percentages in treatment B
In order to apply a non-parametric Mann-Whitney test, the raw data from treatment A and B were combined into a set of 16 elements, which are ranked from lowest to highest, including tied rank values where appropriate. These rankings are then re-sorted into the separate
samples. The difference between the two means is significant since UA = 53,5 (P=0,0136) in a
one-sided Mann-Whitney test with α = 0,025.
Conclusion 1: Based on these results we may reject the null hypothesis and conclude that
groups with heterogeneous payoffs make lower offers than groups with homogeneous payoffs.
Do teams with heterogeneous payoffs have a lower acceptance rate than teams with
homogeneous payoffs? Table 3 shows for each receiving group in both treatments the lowest possible offer from the proposing team which they would have accepted, and the mean minimum accepted offers in each condition. As can be seen in the table, the receiving groups in heterogeneous treatment accepted a minimum average offer of 2 tokens, whereas the minimum average accepted offer in the homogeneous treatment was 2,875 tokens.
Treatment A 1 5 0 3 0 0 3 4 Mean: 2
Treatment B 3 2 3 4 2 4 3 2 Mean: 2,875
Table 3 – Minimum accepted offers receiving teams
The difference between the two means is not significant since UA = 40 (P=0,4148) in a
one-sided non-parametric Mann-Whitney test with α = 0,05.
Conclusion 2: Based on these results we may not reject the null hypothesis and conclude that
groups with heterogeneous payoffs have a similar acceptance rate compared to groups with homogeneous payoffs.
For all 32 subjects, figure 3 presents the percentages of decisions made in the dictator game. Consistent with previous dictator game experiments, offers range widely between 0 and 5. The mean offer is 2,25.
Figure 3 – Dictated amounts made by all subjects
Recall that according the Social Comparison Theory team offers are higher than the average of what each player within each teams would have offered individually. The expectation which player would dominate according the Persuasive Argument Theory is indifferent since we do not know which arguments are more persuasive.
To see which player dominates the group decision, we asked in the experiment each subject prior to their group decision to make a decision what he would offer is he had to make the decision individually. By this, we are able to see in which direction the group-decision shifts. In other words, we are able to see towards which player’s individual choice the direction of the group decision shifts. The player towards whose individual offer the direction of the group offer shifts is the team-member who has dominated the group decision.
For example, imagine a team where the left player made an individual offer in the Ultimatum Game of 1, while the right player of this team made an individual offer of 5. After the
individual decisions, when they have to make the decision together, we see that this team made a group offer of 4. Since the offer of 4 is closer towards the individual choice of the right player (which was 5), we state that the right player has dominate the group decision. Which team member will dominate the decision, the more or less altruistic player?
Tables 4 and 5 below show the decisions of all subjects in the Dictator Game, the
hypothetical offer in the Ultimatum Game, the mean of these two individual offers per team and the team offer in the Ultimatum Game. If a subject is a ‘left’ or ‘right’ player is
determined on how they were seated. That is, in team A player 1 is the left player, player 2 the right player, etc. Recall that in treatment A the chip value was based on how the subjects were seated, which means that every ‘left’ player had a high chip value and every ‘right’ player had a low chip value. In treatment B every player had an equal chip value.
In the 2nd and the 3rd column we see the decisions in the Dictator Game. The decisions of the ‘more altruistic’ team-members in these columns, which are the higher offer in the Dictator Game within each team, are marked with the symbol *. The 4th and the 5th column show the decision each subject made if they had to play the Ultimatum Game individually. The individual decisions which dominate the final team offer are marked with the symbol º. The 6th column shows the average offer of the individual decisions of the group members. The 7th column shows the team offer in the Ultimatum Game.
The last column shows the player towards whose individual offer the direction of the group offer shifts is. In other words, it shows which player dominated the decision, the ‘more altruistic’ or the ‘less altruistic’ team member. The individual that dominates the decision is the player whose individual decision is closer to the team decision. These are the individual decision marked with the symbol º. Recall that the more altruistic decisions in the Dictator
Game are marked with the symbol *. We know see that if in a team a subject has the higher offer in the Dictator Game (marked *) and has the dominating decision in the individual part of the Ultimatum Game (marked º); the team decision is dominated by the ‘more altruistic’ player. On the other side, if the player who dominates the Ultimatum Game (marked º) but has the lower offer in the Dictator Game (no symbol), the team decision is dominated by the ‘less altruistic’ player.
There are two situations where we have no clear domination. The first situation is when there is no difference between the levels of altruism within the team. That is, if both team members have the same decision in the Dictator Game, there is no dominant player and the cell which team member dominates is left empty. The second situation is when there is no clear
domination. This happens if the individual decision of the Ultimatum Game from both team members is the same. Similar, in these situations I left the last column empty.
TREATMENT A Dictator Game left player (high chip value) Dictator Game right player (low chip value) Ind. Offer Ult. Game left player Ind. Offer Ult. Game right player Mean Team Ind. Offers Ult. Game Team Offer Ult. Game Which team member dominates the team offer made in the Ultimatum Game?
Team 1 0 0 1 1 1 1 -
Team 2 5* 0 3º 0 1,5 3 More Altruistic
Team 3 4* 0 5º 1 3 5 More Altruistic
Team 4 2 2 4 4 4 4 -
Team 5 4* 0 3º 4 3,5 1 More Altruistic
Team 6 5* 4 1º 4 2,5 1 More Altruistic
Team 7 3* 2 4º 0 2 4 More Altruistic
Team 8 3* 0 3 3 3 3 -
Table 4
Treatment A: Dictator Game decisions, individual offers Ultimatum Game, Mean individual offers Ultimatum Game per team, team offers Ultimatum Game.
* = the ‘more altruistic’ dictator decision
º = the individual offer which dominates the team offer in the Ultimatum Game 30
TREATMENT B Dictator Game left player Dictator Game right player Ind. Offer Ult. Game left player Ind. Offer Ult. Game right player Mean Team Ind. Offers Ult. Game Team Offer Ult. Game Which team member dominates the team offer made in the Ultimatum Game?
Team 1 3 5* 4º 5 4,5 4 Less Altruistic
Team 2 0 5* 2 5º 3,5 5 More Altruistic
Team 3 0 4* 2 5º 3,5 5 More Altruistic
Team 4 0 0 3 4 3,5 4 -
Team 5 0 3* 1 3 2 2 -
Team 6 4* 0 5º 3 4 5 More Altruistic
Team 7 5* 4 5 5 5 5 -
Team 8 4* 1 5º 2 3,5 5 More Altruistic
Table 5
Treatment B: Dictator Game decisions, individual offers Ultimatum Game, Mean individual offers Ultimatum Game per team, team offers Ultimatum Game.
* = the ‘more altruistic’ dictator decision
º = the individual offer which dominates the team offer in the Ultimatum Game When a team needs to make an offer in an Ultimatum Game, is the decision dominated by the more or less altruistic player? To see this we have excluded the teams where the players have the same level of altruism. That is, the teams where the players have made the same offers in the Dictator Game (team 1 and 4 in treatment A, team 4 in treatment B). As we can see in the table below, of the thirteen ‘more altruistic’ players nine subjects dominated the decision, one subject was recessive and three subjects were neutral. Similar, of the thirteen ‘less altruistic’ players one subject dominated the decision, nine subjects were recessive and three subjects were neutral.
Dominant Recessive Neutral Total
More Altruistic 9 1 3 13
Less Altruistic 1 9 3 13
Total 10 10 6 26
Table 6 – Dominance in the group offer (excluded the players in teams with similar Dictator offers)
A 3x2 Fisher exact test gives probability Pa= 0,0006 and Pb = 0,0004. We may reject the null hypothesis that the relative proportions are independent. There is a significance difference in the dominance in a group Ultimatum Game of the subjects when we look at altruism.
Conclusion 3: Based on these results, we may conclude that the level of altruism of a subject
has influence if the player will be dominant, recessive or neutral when making a group offer in the Ultimatum Game.
The Fisher-Exact test only shows the dependency of the level of altruism on the dominance in the group offer in an Ultimatum Game, but not the magnitude. To analyze shift magnitudes, we run a regression with the team offer as dependent variable. The individual offer of the ‘more altruistic’ player and the individual offer of the ‘less altruistic’ player are the
independent variables. Consider the following team bargaining equation, where 𝑦𝑘𝑡 denotes the offer made by kth team, 𝑦𝑘1 denotes the offer of the ‘more altruistic’ player in team k and 𝑦𝑘2 denotes the offer of the ‘less altruistic’ player in team k:
𝑦𝑘𝑡 = ∝0+ ∝1 𝑦𝑘1+∝2 𝑦𝑘2+ 𝜖𝑘
where 𝜖𝑘 is the error term. The hypothesis that the ‘more altruistic’ player and the ‘less altruistic’ player have the same influence on the team decision implies ∝1 = ∝2. With the Fisher-Exact test we already concluded that 𝑦𝑘𝑡 is dependent from ∝1 and/or ∝2.
In treatment A we have another independent variable which is the ‘high’ or ‘low’ chip value. Unfortunately, of the 8 teams in treatment A there are 6 teams where the subject with the high chip is also the ‘more’ altruistic player, while the remaining 2 teams consisted of subjects with an equal level of altruism. This is why we are unable to test if the dominance in the group offer of the Ultimatum Game in this treatment is due the ‘high’ or ‘low’ chip value or because the subject was the ‘more’ or ‘less’ altruistic player. To solve this, we run above regression solely on treatment B to exclude the variables of the heterogeneous chip value. Again also, we excluded the team with equal offers in the Dictator Game (which is only one group (team 4) in treatment B).
As we see in table 8 we can reject the null hypothesis ∝1 = ∝2 with α = 0,01 and F=19,782. In table 9 you can see that ∝1>∝2. Notice that ∝2 is negative and is not significantly different from zero (t =-0,840 with p=0,448), which make us conclude that the ‘less altruistic’ player has no significant influence on the team offer. On the other hand, ∝2 is positive and
significance (t=5,676 with p=0,005), which make us conclude that the ‘more altruistic’ player has significant influence on the team offer. These findings indicate that when a team consist of two players who have made different individual offers in the Dictator Game, the team offer in the Ultimatum Game tends to be dominated by the ‘more altruistic’ team member.
Conclusion 4: In a group decision in the Ultimatum Game, team offers tend to shift in the
direction of the ‘more altruistic’ player.
Treatment B ANOVAa
Model Sum of Squares df Mean Square F
1
Regression 7,006 2 3,503 19,782
Residual ,708 4 ,177
Total 7,714 6
a. Dependent Variable: Team offer in the Ultimatum Game, 𝑦𝑘𝑡
Table 8 – ANOVA summary of the regression on team offers in the Ultimatum Game in Treatment B. We excluded team 4 with equal Dictator offers.
Treatment B Coefficientsa
Model Unstandardized Coefficients Standardized Coefficients
t Sig.
B Std. Error Beta
1
Intercept (∝0) -2,500 1,123 -2,226 ,090
Individual offer more
altruistic player (∝1) 1,542 ,272 1,028 5,676 ,005 Individual offer less altruistic
player (∝2) -,125 ,149 -,152 -,840 ,448
a. Dependent Variable: Team offer in the Ultimatum Game, 𝑦𝑘𝑡
Table 9 – Regression with the team offer in the Ultimatum Game as dependent variable and the individual offers as independent variables. All estimates exclude team 4 with equal
Dictator offers.
