DFG Research Group 2104 - Need-Based Justice and Distribution Procedures

DFG Research Group 2104
 Need-Based Justice and Distribution Procedures

 The Predicament of the Third Actor:
 Other-regarding Preferences in Unstructured
 Bargaining
 Manuel Schwaninger

 Working Paper Nr. 2019-01

 http://bedarfsgerechtigkeit.hsu-hh.de/dropbox/wp/2019-01.pdf

 Date: 2020-05

DFG Research Group 2104 at Helmut Schmidt University Hamburg
http://needs-based-justice.hsu-hh.de

The Predicament of the Third Actor:
 Other-regarding Preferences in Unstructured Bargaining
 Manuel Schwaninger a
 University of Vienna

 May 2020 b

Abstract
Other-regarding preferences are powerful drivers of human behavior, leading individuals to forgo their
own economic gains to share with the less fortunate. However, when bargaining about how to distribute
payoffs, it is unclear whether joint bargaining outcomes reflect individual preferences. In this study, I
theoretically examine how heterogeneous other-regarding preferences interact and aggregate, assuming
different functional forms of other-regarding preferences. Then, I test the different predictions against
each other in an unstructured bargaining experiment in which two subjects allocate payoffs between
themselves and an uninvolved third subject. The data reveal that fairness between the bargainers is more
important than fairness towards the third subject; bargainers only allocate payoff shares to third subjects
if the other bargainer is willing to allocate the same amount, even if their other-regarding preferences
differ strongly from each other when revealed individually. The results provide new insights into group
decision-making with internal conflict and offer important perspectives on why morals decline in
experimental markets with externalities, why communication does not help to overcome the bystander
effect, and why preferences regarding policies to support people in need depend on other states.

Keywords
Bargaining, Social preferences, Group decision-making, Internal conflict, Conditional altruism

JEL-Classification
C78, C92, D64, D91

a
 Manuel Schwaninger, University of Vienna, Department of Economic Sociology, Oskar-Morgenstern-Platz 1,
 1090 Vienna, Austria, manuel.schwaninger@univie.ac.at (corresponding author).
b
 I gratefully acknowledge funding by the German Forschungsgemeinschaft (DFG, KI 1419/2-1) and the
 Austrian Wissenschaftsfonds (FWF, I1888-G11). I thank Bernhard Kittel, Stefan Traub, Fabian Paetzel,
 Roman Hoffmann, Jan Sauermann, Marina Chugunova, and Mrinalini Cariappa for helpful comments and
 suggestions.

1. Introduction
How the costs and benefits of cooperation are distributed among actors is a key question for groups, whether
it is a state, a business cooperation or a union. Within these groups, it is often a coalition which forms the
necessary majority that decides how payoffs are distributed. Assuming that decision-makers are self-
interested, one would expect that actors outside of this coalition are left empty-handed, as allocating any
shares to third actors above their opportunity costs would be ‘coalitionally irrational’ (Aumann and
Maschler 1961). Yet, a vast amount of experimental research on other-regarding preferences conducted in
the last two decades indicates that individuals care not only about their own well-being but also about the
well-being of others (Cooper and Kagel 2016; Fehr and Schmidt 2006; Konow and Schwettmann 2016). If
the goal is to understand and predict empirical distribution decisions, these results suggest it is vital to
include other-regarding preferences into the analysis. In this study, I follow this notion and examine whether
and how bargaining outcomes reflect individual other-regarding preferences when a predefined majority of
two actors distribute payoffs between three actors, that is themselves and an uninvolved third actor.
 From a methodologically individualistic vantage point, it seems logical that individual other-regarding
preferences affect negotiated distribution outcomes. However, the relationship between individual other-
regarding preferences and collective decisions is more intricate than it appears at first. On the one hand,
observed decisions made by individuals alone are typically poor predictors of decisions made jointly
(Charness and Sutter 2012). Even though groups show considerable levels of other-regarding behavior
(Engel 2011)3, evidence suggests that groups are usually more self-interested than individuals (Charness
and Sutter 2012; Kugler et al. 2012). Yet, the hypothesis that self-interested individuals influence joint
decisions more strongly than prosocial individuals only yields ambivalent empirical results (Cason and Mui
1997; Franzen and Pointner 2014; Luhan et al. 2009). Overall, the literature is unclear on how other-
regarding preferences aggregate in collective decisions, which might even speak for a holistic perspective
on collective distribution decisions.
 On the other hand, the very nature of other-regarding preferences makes it unclear whether distribution
preferences of different actors influence the bargaining outcome independently. Considering that actors are
heterogeneous with respect to their other-regarding preferences implies that some bargaining actors are
willing to allocate more payoff shares to third actors than others. Consequently, if prosocial bargainers
follow their distribution preferences independent of the other bargainer, the agreements would lead to
distributions in which self-interested bargainers receive more payoff shares than prosocial bargainers. This,
however, can lead to a severe conflict between two fairness perspectives. Although some actors might

3
 For example, in the dictator game, frequently utilized to study other-regarding behavior without strategic reason,
 average team transfers lie between 10.8 and 25.6 percent of the endowment (Cason and Mui 1997; Franzen and
 Pointner 2014; Luhan et al. 2009).

 2

consider it fair to reduce inequalities between the bargaining actors and the third actor, the same actors might
deem it unfair if only one bargaining partner pays for the costs.
 In this paper I argue that utility models that capture this conflict between overall and pairwise inequality
in its functional form (e.g., Fehr and Schmidt 1999) explain unstructured bargaining outcomes better than
utility models that are only concerned with average inequality (e.g., Bolton and Ockenfels 2000). I formally
derive closed-form solutions for the bargaining problem by applying the social preference functions to the
Nash bargaining solution (Nash 1950, 1953). The theoretical analysis offers new insights into the
distribution decisions of groups with internal conflict, which, to the best of my knowledge, have not been
discussed in the literature so far.
 The first result of the analysis implies that third actors only receive payoff shares if both bargaining
actors retain equal amounts of the payoff. Hence, similar to conditional cooperation (Fischbacher et al.
2001), where ‘cooperation’ in this case is sharing with the third actor, bargainers only conditionally share
the payoff. Yet, in contrast to conditional cooperation, the behavior is not conditioned on the actual
beneficiary but on the other bargainer, which means that the behavior is not directly reciprocal. Assuming
there are no direct economic interests of equality (Wilkinson and Pickett 2010), transferring payoff shares
to the third actor also does not benefit the bargainers economically.
 The second theoretical result suggests that a majority of the agreements settle on two focal points, the
even two-way split and the even three-way split. In other words, the third actor mostly receives none or one-
third of the payoff. This means that the bargaining outcomes are relatively polarized, which could explain
why a single distribution decision of a group must not correlate with the distribution preferences elicited of
each separate individual comprising the group.
 To test the predictions, I conduct a laboratory experiment in which subjects bargain consecutively with
different subjects over how to allocate payoffs between themselves and an uninvolved third subject. Then I
fit the different models to the observed bargaining behavior to assess which functional form explains the
preference aggregation mechanism best. To compare the subjects’ bargaining behavior with their individual
distribution choices, I additionally elicit subjects’ distributional preferences in individual choice tasks in
two treatments, either before or after the experiment.
 The empirical results show that other-regarding preferences derived from the bargaining behavior
correlate strongly with the revealed other-regarding preferences from the individual choice tasks. The results
suggest the joint decisions are not independent of individual other-regarding preferences, however, the
relationship is non-linear. Furthermore, observed bargaining outcomes fit the predictions derived by
pairwise inequality aversion significantly better than the alternative models or chance. In fact, payoffs
between the bargaining subjects are equal in more than 90 percent of the agreements. Moreover, as
predicted, the transfers are often polarized and, in a majority of cases, third subjects receive none or exactly
one-third of the payoff.

 3

The results contribute to several findings in the literature. Within the experimental literature, a main
result of studies on multilateral bargaining is that payoffs are typically more equally distributed than
theoretically predicted (Palfrey 2016). The presented study goes one step further to improve the
understanding of how other-regarding preferences interact and aggregate in unstructured bargaining
environments. The results also add perspective to markets with externalities (Falk and Szech 2013), in which
bargainers implicitly divide payoffs between themselves and an uninvolved third actor (Bartling et al. 2015;
Kirchler et al. 2016). Results in this field indicate that the fixed price premium, which has to be paid to
induce fewer externalities on the third actor, is mostly borne equally between the bargainers (Bartling et al.
2015). Furthermore, the evidence aligns with the results of Panchanathan et al. (2013) who find that, in a
dictator game with two dictators and one recipient, dictators mostly share the payoffs equally between each
other when they can communicate. Communication, which was supposed to resolve the bystander effect in
this experiment, might not have had the expected effect because it cannot cancel out the interpersonal payoff
comparisons between the dictators.
 From a broader perspective, the present study also adds to observations outside the laboratory. For
example, survey studies find that “citizens care deeply about the fairness of the responsibility-sharing
mechanism, rather than only the consequences of the asylum policy” (Bansak et al. 2017:1). In combination
with the presented results, the findings suggest that, even at a national level, fairness among the decision-
makers is an important factor that has to be considered when social policies are analyzed.
 The remainder of this paper is structured in the following way: First, I derive predictions of the different
utility models. In section 3, I describe the experimental design to compare the predictive quality of the
different models. In sections 4 and 5, I derive the hypotheses and present the results. Finally, I summarize
and discuss the findings.

2. Cooperative Bargaining Solution with Inequality Aversion
After more than three decades in disfavor, unstructured bargaining has recently regained increasing interest.
Advocates argue that results from unstructured bargaining have higher external validity than structured
bargaining (Camerer 2003; Tremewan and Vanberg 2016). Furthermore, the results allow for more
interesting analyses of the bargaining processes preceding the bargaining outcome (Camerer et al. 2019),
which are now possible due to developments in data science and econometrics (Karagözoğlu 2019). In this
particular study, using a free-form unstructured bargaining protocol has the additional advantage of making
bargainers strategically equivalent (Gächter and Riedl 2005; Galeotti et al. 2019), which means that other-
regarding preferences do not interact with the bargaining position. Hence, I start from an unstructured
bargaining setting and use a cooperative solution concept to analyze how other-regarding preferences
interact and aggregate.
 4

The basic question is how two individuals divide the payoff of cooperation or exchange among
themselves and a third individual if they bargain in an unrestricted and costless bargaining environment.
Building on Birkeland and Tungodden (2014), I make use of the Nash bargaining solution (Nash 1950) to
predict the division, allowing for heterogeneous other-regarding preferences. More concretely, suppose
there are = 3 individuals = , , . While individuals = , bargain over the distribution of a
bargaining value, , individual is excluded from bargaining. The two bargaining individuals can agree on
any triple = ( , , ) of payoff shares, ∈ [0, ], that belongs to the set of feasible bargaining
agreements = { ∶ + + ≤ }. The disagreement point is zero, = (0, 0, 0), which means that
individuals receive no payoff if they cannot agree on any offer and that disagreement entails the risk of
losing a potential increase of utility. I assume individuals and bargain over the payoff shares as if
they were solving the following optimization problem,

 ( ( ) − ( ) ) ∗ ( ( ) − ( ) ) subject to + + = , (1)

where ( ) is the utility of individual , which depends on the distribution of the payoff shares. If the utility
functions are convex, this bargaining solution is symmetric, independent of scale, independent of irrelevant
alternatives, and Pareto efficient (Nash 1950).4 Pareto efficiency implies that if the utility at the
disagreement point is zero, i.e. ( ) = 0, which applies to the utility functions I compare in the following,
an individual will not agree to any outcome resulting in a negative individual utility (Birkeland and
Tungodden 2014).
 In his original model, John Nash assumes all individuals aim to maximize their own monetary payoffs.
Assuming that utility increases linearly in an individual’s own payoffs, i.e. ( ) = , the distribution =
( /2, /2,0) maximizes the Nash product. In this case, the extension by individual introduces only
irrelevant alternatives and the third individual receives no payoff since the bargaining individuals are strictly
self-interested. In contrast, assuming individuals value not only their own payoffs, but also the relation of
their own payoffs to the payoffs of others, the third individual may receive some payoff shares. The outcome
then depends on the specific properties of the utility function of the two bargaining individuals and the
relative weights attached to own and other’s payoffs.
 Here, I examine three classes of outcome-based utility functions that incorporate the idea of other-
regarding preferences in different ways. As a reference, I derive predictions assuming preferences that are
described by the Cobb-Douglas form (henceforth CD), which is frequently used to model the trade-off
between own and others’ payoffs (Andreoni 1990; Andreoni and Miller 2002; Nax et al. 2015). The second
utility function integrates the properties proposed by Bolton and Ockenfels (2000) and conceptualizes
inequality aversion (henceforth BO). The third utility function was developed by Fehr and Schmidt (1999)

4
 For an extension to nonconvex problems, see Conley and Wilkie (1996).

 5

and conceptualizes pairwise inequality aversion (henceforth FS). After two decades of research on other-
regarding preferences, the literature is clear that the latter two models explain individual behavior accurately
in decision settings with the given properties where decision-makers face no equality-efficiency trade-off
(Konow and Schwettmann 2016) and have no further information about intentions, merit or need (Cooper
and Kagel 2016; Nicklisch and Paetzel 2020).

2.1. Cobb-Douglas Utility

To solve the optimization problem in (1), I consider each utility function separately, assuming that the utility
weight attached to other individuals’ payoffs varies across individuals in order to allow for heterogeneity of
other-regarding preferences. For a utility function of Cobb-Douglas form, I assume the utility to be
 ⁄( −1)
 ( ) = 
 1− 
 ∏ ≠ , 0 ≤ ≤ 1, (2)
where parameter 1 − weights own against others’ payoffs and rationalizes costly transfers to other
players. Using (2) in (1) and solving for gives:
 1
 ( , ) = 4 ( + ) . (3)

Hence, if > 0, then CD rationalizes positive transfers to the third individual. Depending on the weights
of the bargaining individuals, the payoff share of the excluded individual can lie within the range
 ( , ) ∈ [0; /2]. This means CD also rationalizes bargaining outcomes that allocate more payoff to
the third actor than to the bargaining individuals. If = = 2/3, then the bargainers would agree on the
even three-way split.

2.2. Inequality Aversion

BO assumes a utility function that decreases exponentially when the own payoffs deviate from the average
payoff,
 1 2
 ( ) = { − ( − ) ≠ 0,, 0 ≤ ,
 (4)
 0 = 0;
where parameter weights the inequality between own payoffs and mean payoffs. Using (4) in (1) and
solving for gives:

 1 1 1 + 2
 ( − ( + )) < ,
 ( , ) = { 3 2 3 . (5)
 0 ℎ ;

Similar to CD, BO predicts the third individual will obtain positive payoff shares if the disutility of
inequality of both players is sufficiently strong ( /( + ) > 3 /2). In contrast to CD, however, BO

 6

formalizes inequality aversion and the solution implies that it cannot be optimal that the third player’s payoff
share is higher than one third, i.e. ( , ) ∈ [0; /3].

2.3. Pairwise Inequality Aversion

FS assumes individuals compare their payoff pairwise to others’ payoffs and dislike disadvantageous
inequality more than advantageous inequality; that is,

 ( ) = − −1 ∑ ≠ max{ − , 0} − ∑ ≠ max { − , 0}, ≤ , 0 ≤ < 1; (6)
 −1

where parameters and express the disutility from being worse or better-off in payoffs. Using (6) in (1)
and solving for gives:
 3
 0 + ≤ + 1,
 3 −4( + )+4 4
 {(9 −6( + )+4) 
 3 4
 ( , ) = 
 4 
 + 1 < + < 3, (7)
 1 4
 3
 ≤ + ;
 3

Like BO, inequality aversion in FS also implies that ( , ) ∈ [0; 1/3]. One key difference between FS
and the other two bargaining solutions concerns the predicted payoff shares between the bargainers. CD and
BO rationalize different and independent payoff shares of the bargainers since the utility of own payoffs is
not affected by other payoffs or only affected by the mean, which is a constant. FS, on the other hand,
implies that any optimum requires even payoff shares between the bargaining individuals, i.e. = . The
reason is that the other-regarding preferences necessary to break this condition (1 + 0.5 < ) are never
realized due to the assumptions of the model ( ≤ and 0 ≤ < 1). Intuitively, the two bargainers will
always agree on even payoffs between themselves because the utility gained by reducing the payoff
difference to the third individual is always lower than the negative utility gained by increasing the payoff
difference to the bargaining partner simultaneously (and the lower utility from the lower payoff share). Thus,
in contrast to CD or BO, FS captures the idea that bargaining individuals are deeply concerned about a fair
allocation between themselves.
 Let me further discuss how the preferences modeled by FS aggregate through the Nash product. In
isolation, FS attains its inner maximum either when ( , 0, 0) or ( /3, /3, /3), depending on whether <
2/3 or > 2/3 (in the two-player case, ≶ 1/2). The worse-off weight only plays an indirect role as
it ensures that an individual does not prefer to get a lower payoff, but never becomes effective due to the
assumption ≤ . When two individuals bargain with each other over the distribution of some payoff, we
can differentiate three cases: both bargaining individuals are rather self-interested with < 2/3 and <
2/3, both individuals are rather prosocial with > 2/3 and > 2/3, or one individual prefers to
maximize own payoffs, < 2/3, while the other individual prefers equal payoffs, > 2/3.

 7

The first two cases are straightforward. When two rather self-interested individuals bargain, they will
agree on the even two-way split. As long as both < 2/3, the specific better-off weights do not affect the
outcome because Nash’s bargaining solution ensures that the agreement is independent of scale. Whereas
when two rather prosocial individuals bargain, they will agree on the even three-way split since their
preferences are not conflicting.
 The most interesting case is the third, when one individual prefers maximum payoff and the other prefers
equal payoffs. In this case, the relative weights of the inequality aversion parameters determine the outcome,
which is shown graphically in Figure 1. It can be inferred that individuals with stronger preferences are
more assertive, enforcing their preferences. For example, let the better-off weight of an individual be =
9/20. Alone this individual prefers to maximize own payoffs. When bargains with an individual with
 = 14/20, who prefers equality, ‘s preferences are relatively stronger in comparison and individual 
enforces the even two-way split (in Figure 1, this point is indicated by a red cross). However, if individual
 has relatively stronger egalitarian preferences, say = 18/20, then the relative influence flips and the
dyad will agree on the even three-way split (red triangle).

 Figure 1. Predicted agreement depending on FS better-off weights.

 In other words, the more important profit (equality) is for an individual, the closer is the outcome to this
individual’s distribution preferences, since the individual is more reluctant to agree on a more (less) equal
distribution. Only when the preferences are relatively similarly weighted will the bargaining individuals
agree on a compromise by which they receive an even share and allocate a share between zero and one third
to the third actor. In a majority of cases, however, the Nash product transforms individual preferences into
the outcome preferred by the individual with stronger preferences.

 8

To compare how the three preference models shape the predictions, Figure 2 shows the predicted
transfers to the third actor assuming a uniform distribution of other-regarding weights within each class.5
The Figure illustrates that the predicted transfers follow distinctly different patterns depending on the
underlying assumption about the other-regarding preferences.

 Figure 2. Simulated outcomes: Payoff share of the third individual

Cobb-Douglas (CD): Inequality Aversion (BO): Pairwise Inequality Aversion (FS):
 ∈ (0,1), = 72; ∈ (0,2000), = 72; ∈ (0,1), = 72;

Predictions are rounded to 1/72.

3. Experimental Design
In this section, I describe the implemented experimental design. The working hypotheses for the design are
derived in the next section. The experiment, designed to emulate the theoretical environment, incentivizes
bilateral negotiations in which the participants must distribute payoffs between themselves and an
uninvolved third subject. In addition, I elicit distribution preferences in an individual choice setting. To
control for ordering effects, I vary the sequence of the bargaining game and the individual tasks between
subjects. In the I-B treatment, participants complete the individual decision tasks before they play the
bargaining game; in the B-I treatment, they complete the individual tasks after the main experiment.

4.1. Unstructured Bargaining

At the start of the bargaining game, two-thirds of the participants are randomly selected to bargain over the
distribution of payoffs and one-third of the participants are excluded from the payoff-relevant negotiations.
The role assignments remain constant throughout an entire session of the experiment. In each round, two
bargainers are matched together with one excluded participant and must bargain over the distribution of 72
points.

5
 The actual distribution of other-regarding preferences is unknown; assuming the distribution is uniform enables
 arguably the most insightful graphical comparison between the models.

 9

To make an offer, a subject has to allocate exactly 72 points between herself, the other bargainer and
the excluded subject who cannot participate in the negotiations.6 The format of the proposals is restricted to
numbers displayed on the computer screen. Further communication is prohibited during the experiment.
Subjects are able to send as many offers and counteroffers as they choose at any point during a round. The
most recent proposal of the other bargainer can be accepted at any time during the round by clicking on an
‘Accept’ button. In this sense, bargaining is costless, unrestricted and not subject to a specific protocol. If
the bargainers agree on a distribution of payoffs, the round ends and the payoffs are implemented for all
three subjects. The time limit to reach an agreement is two minutes. If no agreement is reached within the
time limit, all three subjects receive zero points. When an agreement is reached or the time ends, the subjects
are informed about their payoffs and a new round begins.
 Each session consists of 24 participants who engage in 20 rounds of negotiations. In the first five rounds,
the 16 bargainers are randomly rematched. In the last 15 rounds, the 16 subjects are matched such that each
bargainer bargains exactly once with all other bargainers. At the end of the session, three rounds are
randomly selected and paid out. In the meantime, the 8 excluded subjects also bargain with each other, but
their outcomes are not relevant for the payoff. The role of the bargainers and third subjects are known prior
to the bargaining game and are held constant to control for indirect reciprocity.

4.2. Individual distribution preferences

To compare the bargaining behavior with the decisions of the individual choice task, I elicit the individual
distribution preferences in two ways. All subjects complete an extended Equality-Equivalence test
(henceforth EET; Kerschbamer 2015) and a three-person random dictator game.
 The EET measures preferences for inequality aversion. It is an incentivized task assessing an
individual’s distributional preferences based on decisions between various distribution alternatives. In the
disadvantageous inequality block (DIB), subjects face five pairs of allocations and, for each pair, they must
choose whether they prefer an equal distribution between themselves and another subject (20, 20) or an
unequal distribution (20 + x, 30), where x ∈ {−5, −1, 0, 1, 5}. In the advantageous inequality block (AIB),
they must also choose whether they prefer an equal distribution (20, 20) or the unequal distribution (20 + x,
10), but the payoff share of the other subject is smaller. I can observe when a subject switches from left to
right and use this decision as a proxy for the inequality aversion weight. The EET originally includes five
items for DIB and AIB. I extend the latter with three additional items, where x ∈ {10, 20, 50}, to get a more
precise measure of the better-off weight. One decision is randomly chosen per subject and paid out to the
decision-maker and a paired recipient. Hence, each subject earns two payoffs, once as a decision-maker and

6
 I choose a relatively high number of points to broaden the action space of the subjects and allow for a meaningful
 variance of outcomes. Participants can use a calculator integrated in the bargaining interface.

 10

once as a recipient. It is ensured that a dictators’ recipient is not simultaneously the recipients’ dictator, so
decisions are not mutually payoff relevant.
 The dictator game elicits a subject’s most preferred distribution between herself and two other subjects.
Participants are randomly assigned to groups of three. Each participant must allocate exactly 72 points
between herself and two other subjects. At the end of the experiment, one of the three group members is
randomly selected as dictator and her decision is paid out. The group size and stakes are the same as in the
bargaining game. In comparison, the number of active decision-makers changes from one to two and the
number of passive group members changes from two to one. The three-person dictator game elicits the
distribution that a subject aims to enforce during the bargaining game.7
 All decisions in isolation are anonymous, and participants do not receive any information about their
payoff from the individual tasks until the end of the experiment. Since the participants are unaware of the
final outcomes of the individual tasks, the influence on the bargaining game should be relatively low in the
I-B treatment. To control for possible ordering or framing effects, I vary the order of the experiment and
elicit the individual preferences after the bargaining game in the B-I treatment.

4.3. Further Measurements

At the end of the experiment, the participants answer a short questionnaire. Since risk preferences are
frequently discussed in bargaining settings, I include a self-reported measure for risk preferences, which is
empirically more predictive of behavior than alternative incentivized measures (Dohmen et al. 2011;
Lönnqvist et al. 2015). To gain more information about factors that could influence the bargaining behavior,
I included questions about assertiveness, compassion, and trust (Danner et al. 2016; Soto and John 2017), a
self-reported assessment of the bargaining skills, and socio-economic background variables. See
Attachment 2 in the Supplementary Material for the full translated questionnaire.

4.4. Procedure

I conducted six sessions with 24 subjects each at the Vienna Center for Experimental Economics in March
2018, resulting in a sample of 144 participants evenly divided between the two treatments. All subjects were
university students, on average in their sixth semester, with a median age of 23. The experiment was fully
computerized using z-Tree (Fischbacher 2007) and the participants were recruited using ORSEE (Greiner
2015). All experimental sessions lasted fewer than two hours.

7
 For a dictator game utilizing the strategy method with two dictators and one recipient, I refer the reader to the study
 of Panchanathan et al. (2013). In this experiment, I included a separately incentivized battery with seven items that
 holds the sum of payoffs constant and distributes the payoff among three subjects. Designed similarly to the EET,
 these items aim to capture the willingness to share payoff with a third individual, given the payoff of a second
 individual and a constant sum of payoffs. In this paper, I focus on the decisions in the EET and dictator game. See
 the Table A1 in the Supplementary Material for all implemented items.

 11

The participants are all provided with written instructions. Instructions for the individual tasks and the
bargaining game are handed out after each other. Participants know that the experimental session consists
of several parts, but do not know the content of the future parts before the respective instructions are
provided. See Attachment 1 in the Supplementary Material for the instructions translated from German to
English.
 At the end of the experiment, the program converts the earned payoffs into Euros and the laboratory
assistants pay the participants separately and in private. In sum, the payoff of the participants consists of
three bargaining outcomes (3 randomly selected rounds) and three individual decisions (EET, additional
items, dictator game). The payoffs between the first and second part (B and I) were evenly weighted and
paid roughly the same on average. The participants earned, on average, 29.43 Euros, including a 5.71 Euro
show-up fee.

4. Hypotheses
My first research question targets the relationship between individual and bargaining behavior. From the
analysis in section 2, it follows that bargaining outcomes must not reflect the individual decisions
independently and linearly. Hence, a single joint bargaining decision might not necessarily correlate with
the individual distribution preferences. Nevertheless, in line with a traditional economic view, I assume
stable other-regarding preferences for the time horizon of the experiment. Hence, by observing two
individuals bargaining with several identical other individuals, I can compare the influence of the other-
regarding preferences between these two individuals by comparing the bargaining outcomes. Therefore, I
formulate my first hypothesis:

H1: The stronger the elicited other-regarding preferences in isolation, the higher the average transfer to
 the excluded subject in the bargaining game.

 In order to further investigate how subjects’ other-regarding preferences aggregate and to measure the
explanatory power of the models, I proceed in two steps. First, I explain how I measure the model fit and
formulate my expectation based on the FS model. Second, I generate random bargaining outcomes and fit
the models to construct confidence intervals. These will allow me to qualify the goodness of fit when I fit
the models to the empirical data.
 To compare the models against each other, I estimate the individual other-regarding preferences that
explain the bargaining outcomes best to obtain the remaining sum of squared residuals (SSR). I do not
include the first five rounds in the empirical analysis to control for learning effects. Hence, in each session,
I observe sixteen individuals, = 1, … ,16, who bargain in fifteen rounds in new pairs , where ≠ ,
over the distribution of = 72 points. Thus, in each round, each pair can transfer a payoff , ∈ [0,72]

 12

to the excluded individual c. I estimate the parameters ̃ = , , , of CD, BO, and FS such that the Nash
bargaining solution minimizes the sum of squared residuals (SSR) between the actual and the predicted
 2
transfers, i.e. ∑120 ̃ , ̃ )) . The lower the remaining SSR, the better is the explanatory power
 1 ( , − ( 

of the functional form and the model in organizing the data.8 Hence, based on the expectation that the
bargainers evaluate the payoff distribution pairwise, I formulate the following working hypothesis:

H2: After estimating the best model fit, the sum of squared residuals derived from the FS model is lower
 than the sum of squared residuals derived from the BO and CD models.

 Next, I estimate parameters that minimize the SSR of randomly generated data. For one simulated
session, I generate 120 random transfer values (8 pairs times 15 rounds). Thereafter, I estimate the
parameters that fit these data best for each model, repeat this procedure 103 times, and calculate the 95-
 ̅̅̅̅). Table 1 provides the results. The lower bound in the
percent quantile of the mean squared residual ( 
column “Chance” states the threshold below which the bargaining behavior is not completely arbitrary. In
 ̅̅̅̅s of the empirical data lie below these thresholds, there is statistical evidence that
other words, if the 
bargaining behavior is at least partly systematic.
 Conducting similar simulations across models (Table 1, column “CD”, “BO”, “FS”) shows that all three
models are better in explaining each other’s simulated bargaining outcomes than random outcomes. The
partial overlap between the models, especially between CD and BO, makes it evident that there is a chance
of type one errors when I test H2. Therefore, in the empirical analysis, I will also draw on the two other
outcome criteria that separate the models distinctly: (I) How frequently do transfers above one third occur?
(II) How frequently are the payoff shares distributed equally between the bargaining partners?

 Table 1. Simulated Residuals.
 Estimated Model Generated Data
 Chance 1 CD 2 BO 2 FS 2
 CD 93.4 0.0 9.6 40.5
 [76.2, 111.0] [0.0, 0.0] [0.0, 24.2] [13.5, 56.4]
 BO 94.5 9.3 0.0 20.2
 [77.7, 112.8] [0.8, 22.5] [0.0, 0.6] [2.9, 40.6]
 FS 104.1 16.1 17.1 0.0
 [84.1, 126.5] [8.3, 26.5] [7.8, 29.3] [0.0, 0.5]
 Table shows the mean residual sum of squares (95%-quantiles in parenthesis).
 1 Transfers generated by chance are drawn from a uniform distribution within the theoretical predictions [0, 36].
 2 Other-regarding parameters for the CD, BO, and FS models are drawn from uniform distributions within the range [0, 1],

 [0, 2000] and [0, 1] to simulate the transfers.

8
 Given that I have to estimate one parameter for each individual in each model to predict the transfers, the models
 are all as parsimonious. To fit the non-linear functions, I use the R implementation of a particle swarm optimizer
 (Bendtsen 2012) and a simulated annealing process (Xiang et al. 2013).

 13

5. Results
Analyzing the data consists of three parts. In the first part, I give a descriptive overview of the observed
bargaining outcomes. In the second part, I compare the transfers from the bargaining game with the
individual decisions in the EET and the transfers in the dictator game. In the third part, I fit the three different
models and test which functional form explains the data most accurately.

5.1. Bargaining Outcomes

The bargaining data show that in 67.3 percent of the cases bargaining partners allocate a payoff share greater
than zero to the excluded individual. On average, they transfer 15.8 percent of the payoff. Figure 3 shows
the relative payoff share transferred to the third actor in the two treatments (I-B, B-I) over time. In the initial
rounds, the transfers decrease and converge to about 15 percent of the negotiable payoff. The average
transfers do not decrease significantly after round 5 in either treatment (Pearson corr., p = .59, p = .67). To
control for learning effects in the first 5 rounds, I concentrate on rounds 6 to 20 in the following analysis of
the data. Furthermore, there is no statistical difference between the average transfers in I-B and B-I
according to the Mann-Whitney test (in each round, p > .10).9 The statistical indifference between the two
treatments indicates no significant framing or ordering effects of the individual tasks on the bargaining
game.

 Figure 3. Payoff share of the third actor over time.

9
 All reported p-values refer to two-sided tests.

 14

As discussed in section 2, the predicted bargaining outcomes of the three models, CD, BO and FS, can
be distinguished on two levels: (I) the distribution of transfers to third actors and (II) the allocation of payoff
shares between the bargainers. Figure 4 is concerned with the first question and shows the distribution of
payoff shares transferred to the third individual. In line with the BO and FS models, transfers to third actors
virtually never exceed one-third of the payoff (0.01 percent). In a majority of cases, the bargaining subjects
transfer exactly zero (35.1 percent) or 24 (24.4 percent) points, which shows similarities with the patterns
predicted by FS. Another focal point seems to be one-sixth of the payoff (10.0 percent). Transferring 12
points may be attractive since it offers an even compromise between more self-interested and more other-
regarding subjects.

 Figure 4. Outcome distribution: Payoff share of the third individual.

 Concerning the second question, the results show that the payoff shares between the bargainers are
equal in 90.5 percent of the agreements. More precisely, in 17 out of the 720 negotiations (2.4 percent), the
subjects cannot agree on a distribution. In 456 of the 703 negotiations (64.9 percent), the third subject
receives more than zero points. In 429 out of these 456 negotiations (94.1 percent), the bargainers agree on
even payoffs between themselves.
 The data indicate that not only are the payoff shares of the bargainers equal in the outcomes, but they
are already equal when they propose the offers. From round 6 to 20, the subjects make 720 first offers. In
none of these offers does the proposer offer to pay more for the payoff share of the third subject than the
other bargainer. In response to received offers, the subjects make in sum 2288 counteroffers, of which 890
(38.9 percent) suggest an increase in the payoff share of the third subject. In only 31 (3.5 percent) of these
offers do the bargaining subjects propose to reduce their own payoff share more than the payoff share of the
other bargainer to pay for the higher transfer to the third actor. Out of these 31 offers, 21 ultimately equalize
the payoff shares between the bargainers, since the standing offer benefited the proposer of the counteroffer.

 15

When subjects suggest increasing the payoff share of the third actor, they primarily suggest reducing own
payoffs equally (57.1 percent) or they suggest that the other bargainer should pay more for the higher
transfer to the third actor (39.4 percent).

5.2. Relation between Bargaining Behavior and Individual Choice Tasks

The first hypothesis, H1, targets the relationship between individual and bargaining behavior. Generally,
subjects’ transfers to third actors vary considerably across the different rounds, in which they are matched
with different bargaining partners (mean individual range of transfers = 21.3 points). Yet, Figure 5 shows
the average transfers are relatively uniformly distributed in both treatments, which means some subjects
transfer more and some transfer less during the bargaining game. This implies that some participants are
more persistent with their preferences during bargaining than others despite the varying bargaining partners.

 Figure 5. Avg. transfers by individuals in the bargaining game.

 Avg. transfers betw. round 6 to 20 rounded to 1/72.

 To examine whether the average bargaining transfers are related to the individual other-regarding
preferences, I compare the behavior in the bargaining game with the behavior of the individual choice tasks.
The switching points of the two blocks of EET – DIB and AIB – provide information on the advantageous
and disadvantageous inequality aversion of the subjects. The median switching point for the bargaining
subjects lies at 3 out of 5 in DIB and 5 out of 8 in AIB. Subjects’ transfers in the three-player dictator game
give another measure of the distribution preferences. The dictators in the sample allocate on average 17.2
percent of the payoff share to each recipient.10 Most subjects allocate zero or two thirds (even three-way

10
 While the bargaining outcomes between the treatments are relatively similar, there is weak evidence that the mean
 transfer in the B-I treatment is higher than in the I-B treatment (Mann-Whitney test, p = .09), which means subjects
 transfer more if they play the dictator game after the bargaining game. The ordering effects may be explained by a
 willingness to equalize anticipated inequalities from the previous bargaining game.

 16

split) to the recipients. The correlation between the lower transfer in the dictator game and the switching
point in AIB is equal to 0.25 (p = .01).
 Regressions I – IV in Table 2 explain the average transfers in the bargaining game through the revealed
individual other-regarding preferences controlling for session fixed effects. Further controls include
observable traits, such as gender, age, field of study, experience in experiments, and self-reported
characteristics, such as risk preferences, bargaining skills, assessment on a political left-right scale,
extraversion, and agreeableness.
 The results suggest that subjects who transfer higher payoff shares in the dictator game also transfer
more during the bargaining game, which means that we can observe a behavioral consistency across the
individual choice and the bargaining game. Furthermore, in line with theoretical considerations,
advantageous inequality aversion (AIB) has a statistically significant relationship with the transfers in the
bargaining game, while disadvantageous inequality aversion (DIB) has no explanatory power. Hence, both
results support H1. The regression results remain robust if I control for further characteristics, of which none
is significant. The control variables remain statistically insignificant if I remove the incentivized other-
regarding measures from the regression (see Table 2.A in the Supplementary Material).

 Table 2. Relation between individual and bargaining behavior.
 Dependent variable: Avg. bargaining transfer
 I II III IV
 Dictator game 0.249*** 0.283***
 (0.058) (0.062)
 AIB 0.830*** 0.806***
 (0.269) (0.290)
 DIB 0.382 0.374
 (0.378) (0.441)
 Controls No Yes No Yes
 Observations 96 96 96 96
 2
 R 0.174 0.244 0.107 0.139
 F Statistic 18.705*** 2.588*** 5.291*** 1.155
 Fixed effects on session level. *** p < .01, ** p < .05, * p < .10.

 In sum, the data show that individual behavior and bargaining behavior are related, which suggests that
individual other-regarding preferences influence the bargaining results. In direct comparison, transfers to
excluded individuals are, on average, higher in the individual dictator game than in the bargaining game,
independent of whether the dictator game is played before or after the negotiations (paired Wilcoxon tests,
p < 0.01). Another notable observation is that a considerable number of individuals in the individual choice
tasks are not sensitive to disadvantageous inequality. Having to choose between two distributions, (36, 36,
0) and (18, 36, 18), where the first element in these triples indicates the own payoff, 39.6 percent select the

 17

latter distribution, even though this results in disadvantageous inequality. Disadvantageous inequality
aversion seems to be much more prevalent in the bargaining game.

5.3. Predicting the Bargaining Outcomes

To explain the bargaining outcomes, I optimize the other-regarding parameters with respect to the specific
functional forms. Figure 6 shows how the models perform in comparison. The explanatory power of a model
is better, when the squared residuals are lower. All three models, CD, BO and FS, perform significantly
 ̅̅̅̅ = 30.7, ̅̅̅̅
better when they are fitted to the empirical data than the randomly generated transfers ( 
 ̅̅̅̅ = 20.6), but the FS model also performs significantly better than CD and BO (both paired
= 31.8, 
Wilcoxon tests, p < 0.01). This result supports H2.

 Figure 6. Squared Residuals across Models

 ̅̅̅̅ of FS is significantly lower than the 
 Furthermore, the ̅̅̅̅ of an ordinary least squares model with
 ̅̅̅̅ = 28.6, paired Wilcoxon test, p < .01) or a tobit model with a lower limit at zero
individual fixed effects ( 
 ̅̅̅̅ = 28.1, paired Wilcoxon test, p < .01). To put these results into perspective, calculating the absolute
( 
residuals of FS and the best alternative (tobit model) reduces the mean residual from 3.8 points to 2.3 points,
which improves the average accuracy by 64 percent. The estimated better-off weights of the FS model also
correlate significantly with the behavior in the AIB (corr. = 0.31, p < 0.01) measured by the EET and the
transfers in the dictator game (corr. = 0.39, p < 0.01).

 18

6. Conclusion
Whenever a coalition has to allocate payoffs among a group of actors, socially concerned coalition members
may be willing to distribute payoffs to third actors. The question is, what deal can the bargainers make to
take third actors into account and who is willing to forgo payoffs to benefit the third actor. In this study, I
examine negotiated distribution outcomes in a controlled experimental environment to identify the influence
of other-regarding preferences on general bargaining patterns.
 I find that preferences aggregate systematically in groups with internal conflict. In more than 90 percent
of the bargaining outcomes, the payoff shares are equal between the bargaining subjects. The bargaining
subjects care about how much payoff is allocated to the third subject but they also care about how much the
other bargainer contributes to benefit the third subject. Since unilateral transfers would increase inequality
between the bargainers, transfers to third subjects are conditional on both bargaining subjects. In other
words, sharing with internal conflict involves two conflicting fairness aspects and a bargaining solution has
to respect both. If there is a conflict between the distributional preferences of the bargainers, the outcome
depends on the subject who has stronger preferences. The properties of the distribution outcome of the
bargaining agreements can be best explained by assuming pairwise inequality aversion (Fehr and Schmidt
1999) to solve the bargaining problem.
 Due to the abstract design of the experiment, the results offer new perspectives on several previously
observed results. First, the results can explain observations from survey studies. For example, the results fit
survey observations regarding policy preferences (Bansak et al. 2017) and increase their understanding
based on empirical evidence in an incentivized experiment. Second, the results offer a new perspective on
exchange behavior in externality producing experimental markets. On the one hand, conditional other-
regarding preferences might explain why the burden to decrease negative externalities on third subjects is
shared equally among market participants (Bartling et al. 2015). On the other hand, the results offer
additional insights on why fairness values decrease in markets, which has so far been primarily ascribed to
responsibility diffusion but eventually has to be attributed to intersubjective fairness concerns. Third, the
theoretical results might explain why “communication among dictators did not actually help recipients [and]
the bystander effect persisted” in a dictator game with two dictators and one recipient. Panchanathan, et al.
(2013:293), who examined whether the bystander effect can be overcome by communication, wonder “why
communication had so little effect on dictator behavior“. The answer may be that communication does not
help to overcome the problem of interpersonal payoff comparisons since individuals are also reluctant to
help third individuals if it creates inequalities between the dictators.
 At the same time, the scope of the results focuses on situations in which the perceived responsibility of
the decision-makers is ambiguous or diffused. In the structured three-person ultimatum game with a
proposer of an allocation, a responder and an excluded actor, as studied by Güth and Van Damme (1998),

 19

the responders with full information do not exhibit heterogenous behavior. Hence, the responders seem to
behave independently of the preceding allocation decision of the proposers, who make different decisions.
When Panchanathan et al. (2013) implement the strategy method in another treatment of the mentioned
study, they find that only 13 percent of all subjects condition their transfer on the transfer of the other
dictator. In contrast, 36 percent of all subjects compensate for other dictators’ self-interest. Similarly, when
Bartling et al. (2015) compare decisions in the market to the decisions of dictators, they also find that
subjects are more generous as dictators than as bargainers, even if the decision incentives are equivalent.
 Altogether, bilateral bargaining agreements can decrease and increase transfers to third actors,
depending on the bargaining actor with the strongest preferences in the dyad as transfers align. Whether one
or the other should be facilitated through institutional design is ultimately a normative question. However,
the question of how outcomes are influenced by institutional factors in these settings offers interesting future
research avenues. The disagreement point, an endogenously produced surplus and differently perceived
merits, or a shared social identity could change bargaining dynamics and their variation potentially leads to
stark outcome differences. Furthermore, one can examine whether the results presented here are robust to a
larger group size and whether median preferences can predict the outcome.

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