Experimental evidence suggests that the size of the foregone outside option does not affect the behavior of the opponent in a lost wallet and pie sharing games but that it matters in a mini-ultimatum game. In this paper we experimentally test a conjecture that it is the fairness property of the outside option which could be responsible for this effect. We compare the behavior of subjects in the lost wallet game when they face a fully unequal (“unfair”) outside option, i.e., the first mover gets 10 and the second mover gets nothing, and when they face an equal (“fair”) outside option, i.e., both get an equal amount of 5. Contrary to our conjecture we do not find a significant difference.Experimental economics; Outside option; Fairness

Maroš Servátka

Radovan Vadovic

English

Research Papers in Economics

1
DEPARTMENT OF ECONOMICS
COLLEGE OF BUSINESS AND ECONOMICS
UNIVERSITY OF CANTERBURY
CHRISTCHURCH, NEW ZEALAND
Does Fairness of the Outside Option Matter?
by Maroš Servátka and Radovan Vadovič
WORKING PAPER
No. 06/2008
Department of Economics
College of Business and Economics
University of Canterbury
Private Bag 4800, Christchurch
New Zealand2
WORKING PAPER No. 06/2008
Does Fairness of the Outside Option Matter?
by Maroš Servátka
1† and Radovan Vadovič
2
April 13, 2008
Abstract: Experimental evidence suggests that the size of the foregone outside option does not
affect the behavior of the opponent in a lost wallet and pie sharing games but that it matters in a
mini-ultimatum game. In this paper we experimentally test a conjecture that it is the fairness
property of the outside option which could be responsible for this effect. We compare the
behavior of subjects in the lost wallet game when they face a fully unequal (“unfair”) outside
option, i.e., the first mover gets 10 and the second mover gets nothing, and when they face an
equal (“fair”) outside option, i.e., both get an equal amount of 5. Contrary to our conjecture we
do not find a significant difference.
Keywords: Experimental economics; Outside option; Fairness
JEL Classification Codes: C72; C78; C91
Acknowledgements: We are grateful to Martin Dufwenberg for helpful discussions and to
SonderForschungsBereich 504 at the University of Mannheim for financial support.
1 Department of Economics, College of Business and Economics, University of Canterbury,
Private Bag 4800, Christchurch, New Zealand.
2 Department of Economics, Instituto Tecnológico Autónomo de México. E-mail:
rvadovic@itam.mx.
† Author for correspondence: Email: maros.servatka@canterbury.ac.nz.3
1.1 Introduction
The recent experimental studies of Dufwenberg and Gneezy (2000) and Brandts, Güth,
and Steihler (2006) have produced quite surprising and counterintuitive results that the size of
foregone outside option by the first mover does not affect the behavior of the second mover in a
lost wallet and pie sharing game, respectively. In fact, several prominent models predict exactly
the opposite type of behavior: For example, in the models of reciprocity (Falk and Fishbacher
(2006) and Dufwenberg and Kirschteiger (2004)) the first mover is kinder the higher the outside
option he foregoes as the potential cost of doing so is higher. This should be sufficient to induce
the second mover to be more reciprocal. Similarly, if the second mover is guilt-averse (Battigalli
and Dufwenberg (2007)), he should believe that the first mover expects to receive more the
higher the forgone outside option. This reasoning is also referred to as the psychological forward
induction.
The absence of a behavioral effect of the alternative that has not been chosen is a puzzle.
This is magnified by the fact that the same behavior is not observed uniformly across games. For
example, Charness and Rabin (2002) observe that the second mover’s behavior has been
influenced by the alternatives available to the first mover in a sequential game involving an
element of trust, very similar to the lost wallet and pie sharing games. Similarly, in a slightly
different experimental setting of a mini-ultimatum game Brandts and Solà (2001), Falk, Fehr,
and Fischbacher (2003), Cox and Deck (2005) find that the reference point significantly affects
the behavior of subjects, as explained by negative reciprocity. Brandts et al. (2006) conjecture
that it is because the outside option in their setting is very unfair as it gives everything to the first
mover. The same is true for the Dufwenberg and Gneezy (2000) study. In this paper we explore
this issue by studying whether subjects’ behavior responds to the equality (fairness) of the
outside option.
1.2 Relative Fairness of Outside Options
Based on Brandts et al. (2006) we conjecture that the relative fairness might play a role in
the decision-making process of the second mover and in particular when he is considering the4
outside option as a part of his decision. Consider the lost wallet game in which the first mover
decides to either choose IN, allowing the second mover to split the surplus between both players;
or to choose OUT, collecting the outside option. On an intuitive level, if the outside option is
very unfair towards the second mover, e.g., 10 for the first mover and 0 for the second mover,
then the second mover may disagree with such split and because of it disregard it entirely. On the
other hand, if the outside option is fair, the second mover consciences to it and is then willing to
spend more time considering its implications. According to our conjecture the fair outside
options are incorporated into second mover’s decision while unfair outside options are ignored.
To make this clearer suppose the outside option is   j i x x , , where i x and j x are both
nonnegative and denote what the first and the second mover gets on the outside. Consider now a
fairness weighting function   j i x x f , which corrects for the importance that the outside option
assumes in the mind of each player. That is, the outside options would be perceived as
      j j i j j j i i x x x f x x x f   , , , . The fairness weighting function satisfies the following
assumptions:
Assumption 1:   0 , 0  x f and   . 1 ,  x x f
Assumption 2: 0  i f for j i x x  , 0  i f for j i x x  and   . 0 0 ,  x f
Assumption 1 is motivated by our conjecture that fully unfair outside option is likely to
be ignored entirely by the player and fully fair outside option is likely to be most salient.
Assumption 2 says that the weight increases as the outside option becomes more equal and
decreases otherwise. Furthermore, the outside option which assigns everything to me can be
more pertinent to me as the one which assigns everything to the other player. This assumption is
consistent and could be justified by arguments akin to Fehr and Schmidt (1999) and Bolton and
Ockenfels (2000). A simple example of such fairness weighting function is
 
2
2
1
4 1 , 









 
j i
j
j i x x
x
x x f . Notice that the outside option is most salient when i x and j x
are equal and completely neutral when player j gets nothing on the outside.5
Our notion of fairness weighting is consistent with the intriguing results reported in the
literature, Dufwenberg and Gneezy’s (2000) or Brandts et al. (2006). Take Dufwenberg and
Gneezy as an example. In their game they vary the outside option i x of the first mover to be 4,
7, 10, 13, and 16, while keeping the outside option of the second mover to be 0. If the first mover
does not take the outside option, the second mover gets to split a pie of 20; giving y to the first
mover and keeping 20 - y. Because in all of their treatments the outside option of the second
mover is fully unfair (zero), then according to our fairness weighting conjecture the perception of
it by the second mover should always be the same (0,0). Indeed, Dufwenberg and Gneezy do not
find any correlation between x and y and neither the y’s to be statistically significantly different
between treatments.
But not all evidence from the lost wallet game supports fairness weighting. Charness,
Haruvy, and Sonsino (2007) find a relationship between the size of the outside option available
to the first mover and the decision of the second mover in an experiment conducted over the
internet using a within subjects design and a strategy method. Due to their choice of the design it
remains unclear to what extent does the use of the strategy method play a role in determining the
results. We think that in this particular scenario (and especially within subjects) it can be prone
to producing a monotonic relationship between the variables of interest. Hence, we avoid using
the strategy method and design our experiment in a way that allows us to test whether NBS can
shed some light on subject’s behavior.
2. The Experiment
Our experiment consists of two treatments implemented in across-subject design. In both
treatments the subjects play the lost wallet game presented in Figure 1. The first mover chooses
IN or OUT. If he chooses OUT, the game ends. The first mover receives $10 ($5) and the second
mover receives $0 ($5). If the first mover chooses IN, the game continues. The second mover
then chooses how to split $30 between the two of them in $1 increments. That is, the second
mover chooses how much of $30 to give to the first mover, (y), and how much of it to keep,
  y  30 . The second mover’s choice determines the final payoffs. In the experiment we keep the6
total outside option pie constant at 10 in order to avoid a possible confounding effect that
subjects behave differently because there is a different amount of money on the table.
Figure 1. The Lost Wallet Game
The predicted behavior can vary between the two treatments for number of reasons that
were already mentioned and we do not want to favor any of them. However, let us use the notion
of psychological forward induction to illustrate the possible effect of fairness-weighting in our
experiment. Psychological forward induction applied to our game yields very simple predictions.
In the 10,0 treatment if the outside option was forgone by the first mover this should indicate to
the second mover that his opponent expects at least 10 in the chosen subgame. If the second
mover cares about the first mover’s expectations, e.g., if he is guilt-averse, then he should return
at least 10. Thus, without fairness-weighting, the psychological forward induction predicts that
the first mover is likely to receive more in the 10,0 treatment than in the 5,5 treatment. On the
other hand, with fairness-weighting, the outside option is perceived differently. In the treatment
10,0 the outside option is perceived as (0,0) and in treatment 5,5 it is perceived as (5,5) by the
second mover. Hence, if the perception of the second mover matters in the way described, then
OUT
IN
10 [5]
0 [5]
y
[ y ]
[ 30 – y ]
0 30
First mover
Second mover7
we have truly varied the outside option between our treatments. The psychological forward
induction then predicts that the first mover is likely to receive more in the 5,5 than in the 10,0
treatment.
2.1 Procedures
The sessions were conducted in October of 2006 in the SonderForschungsBereich 504
laboratory at the University of Mannheim in Germany. A total of 22 subject pairs participated in
the 10,0 treatment and 21 subject pairs in the 5,5 treatment. Most of the students had previously
participated in economics experiments, including trust games. On average, a session lasted about
35 minutes. Subjects earned on average 10.58 Euro plus in addition to a 4 Euro show up fee.
During the experiment all earnings were calculated in experimental dollars. At the end of the
experiment the subjects’ earnings were converted to Euro at the rate of 1 experimental dollar =
0.5 Euro. All sessions were computerized and run under single blind protocol using direct
response elicitation method
1
The participants were randomly and anonymously matched into pairs that consisted of the
first mover and the second mover. The assignment was done according to the following process.
Upon entering the laboratory subjects drew a ball from an urn. The number that was indicated on
the ball assigned their seat for the experiment. The computer workstations were matched into
fixed pairs to provide the maximum possible distance between first and second movers within
each pair. This was unknown to the subjects. Each subject was provided a hard copy of English
instructions that were identical across subjects. After the subjects finished reading the
instructions they were asked to fill out a control questionnaire to check for understanding. The
experimenters verified their answers and privately answered questions. Then the experimenters
publicly provided the correct answers to the questionnaire.
1 This was done in order to address our concerns with the strategy method in the given environment, although the
strategy method would yield a higher number of responses by the second movers. For comparison, Dufwenberg and
Gneezy (2000) use only 13 subject pairs in each of their treatments.8
2.2 Results
Figure 2 presents the summary of data for both treatments. Treatment 10,0 is displayed
on the left and treatment 5,5 on the right. Not surprisingly, twelve out of twenty two (55%) first
movers chose OUT when the outside option was 10 in comparison to seven out of twenty one
(33%) when it was 5. However, this difference is statistically not significant at the conventional
level (p = 0.223 Fisher exact test 2-sided).
Recall that the if the outside option is weighted by its fairness, the second mover, if called
upon play, is likely to implement a split with a higher y in the 5,5 than in the 10,0 treatment. In
our data we observe that the second movers chose on average y = 10.8 and y = 8.1 in 10,0 and
5,5 treatments, respectively. In order to assess the qualitative difference in the data, we test a
hypothesis that the choices of y are higher in the unequal 10,0 than in the equal 5,5 treatment.
However, the 1-sided two-sample Wilcoxon rank-sum test reports that this difference is not
significant (p = 0.144). Consequently, the hypothesis that choices of y are higher in the 5,5
treatment than in the 10,0 one, as predicted by the relative fairness of the outside options, is
rejected at p = 0.856. Hence, we conclude that the fairness of the outside option did not affect the
subjects’ behavior in our game.
Figure 2. Subjects’ Behavior9
3. Discussion
In this paper we tried to address the question whether the second mover ignores the
forgone outside option by the first mover as found in the previous literature because it gives
everything to the first mover. We chose to derive predictions based on a function which weights
the relative fairness of outside options. Our data reject the conjecture that it is the fairness
property which could be responsible for this effect. The result seems consistent with Cox et al.
(2007) who model reciprocity based on what is the maximal available payoff to the second
mover following the first mover’s action. From that perspective, the outside option is irrelevant,
as we have observed in our experiment.
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